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Chapter 23. Grid Adaption

The solution-adaptive mesh refinement feature of FLUENT allows you torefine and/or coarsen your grid based on geometric and numerical solu-tion data. In addition, FLUENT provides tools for creating and viewingadaption fields customized to particular applications. The adaption pro-cess is described in detail in the following sections.

• Section 23.1: Using Adaption

• Section 23.2: The Adaption Process

• Section 23.3: Boundary Adaption

• Section 23.4: Gradient Adaption

• Section 23.5: Isovalue Adaption

• Section 23.6: Region Adaption

• Section 23.7: Volume Adaption

• Section 23.8: y+ and y∗ Adaption

• Section 23.9: Managing Adaption Registers

• Section 23.10: Adaption Controls

• Section 23.11: Improving the Grid by Smoothing and Swapping

23.1 Using Adaption

Two significant advantages of the unstructured mesh capability in FLU-ENT are:

• The reduced setup time compared to structured grids

c© Fluent Inc. November 28, 2001 23-1

Grid Adaption

• The ability to incorporate solution-adaptive refinement of the mesh

By using solution-adaptive refinement, you can add cells where they areneeded in the mesh, thus enabling the features of the flow field to bebetter resolved. When adaption is used properly, the resulting mesh isoptimal for the flow solution because the solution is used to determinewhere more cells are added. In other words, computational resources arenot wasted by the inclusion of unnecessary cells, as typically occurs in thestructured grid approach. Furthermore, the effect of mesh refinement onthe solution can be studied without completely regenerating the mesh.

23.1.1 Adaption Example

One example of how adaption can be used effectively is in the solutionof the compressible, turbulent flow through a 2D turbine cascade. Theinitial mesh, shown in Figure 23.1.1, is quite fine around the blade. Thesurface node distribution thus provides adequate definition of the bladegeometry, and enables the turbulent boundary layer to be properly re-solved without further adaption. On the other hand, the mesh on theinlet, outlet, and periodic boundaries is comparatively coarse. To ensurethat the flow in the blade passage is appropriately resolved, solution-adaptive refinement was used to create the mesh shown in Figure 23.1.2.

Although the procedure for solution adaption will vary according to theflow being solved, the adaption process used for the turbine cascade isdescribed here as an example. Note that while this example involvescompressible flow, the general procedure is applicable for incompressibleflows as well.

1. Display contours of pressure adaption function to determine a suit-able refinement threshold. (See Section 23.4.)

2. “Mark” the cells within the refinement threshold, creating a refine-ment register. (See Sections 23.2.1 and 23.4.)

3. Repeat the process described in steps 1 and 2, using gradients ofMach number as a refinement criterion.

23-2 c© Fluent Inc. November 28, 2001

23.1 Using Adaption

Grid

Figure 23.1.1: Turbine Cascade Mesh Before Adaption

Grid

Figure 23.1.2: Turbine Cascade Mesh After Adaption


Grid Adaption

4. To refine in the wake region, use isovalues of total pressure as acriterion. (See Section 23.5.) This causes cells within the boundarylayer and the wake to be marked, since these are both regions ofhigh total-pressure loss.

5. Use the Manage Adaption Registers panel to combine the three re-finement registers into a single register. (See Section 23.9.)

6. Limit the minimum cell volume for adaption to prevent the addi-tion of cells within the boundary layer, where the mesh was judgedto be fine enough already. (See Section 23.10.)

7. Refine the cells contained in the resulting adaption register. (SeeSection 23.9.)

8. Perform successive smoothing and swapping iterations using theSmooth/Swap Grid panel. (See Section 23.11.) This step is recom-mended if you are using conformal adaption.

As shown in Figure 23.1.2, the effect of refining on gradients is evidentin the finer mesh ahead of the leading edge of the blade and within theblade passage. The finer mesh in the wake region is due to the adaptionusing isovalues of total pressure.

23.1.2 Adaption Guidelines

The advantages of solution-adaptive refinement, when used properly as inthe turbine cascade example in Section 23.1.1, are significant. However,the capability must be used carefully to avoid certain pitfalls. Someguidelines for proper usage of solution-adaptive refinement are as follows:

• The surface mesh must be fine enough to adequately representthe important features of the geometry. For example, it would bebad practice to place too few nodes on the surface of a highly-curved airfoil, and then use solution refinement to add nodes onthe surface. Clearly, the surface will always contain the facetscontained in the initial mesh, regardless of the additional nodesintroduced by refinement.


23.1 Using Adaption

• The initial mesh should contain sufficient cells to capture the es-sential features of the flow field. Suppose, for example, that yourintention is to predict the shock forming around a bluff body insupersonic flow. In addition to having sufficient surface resolutionto represent the shape of the body, the initial mesh should alsocontain enough cells so that a reasonable first solution can be ob-tained. Subsequent gradient adaption can be used to sharpen theshock and establish a grid-independent solution.

• A reasonably well-converged solution should be obtained before youperform an adaption. If you adapt to an incorrect solution, cellswill be added in the wrong region of the flow. However, you mustuse careful judgment in deciding how well to converge the solutionbefore adapting, because there is a trade-off between adapting tooearly to an unconverged solution and wasting time by continuingto iterate when the solution is not changing significantly.

• In general, you should write a case and data file before starting theadaption process. Then, if you generate an undesirable mesh, youcan restart the process with the saved files.

• When performing gradient adaption, you must select suitable vari-ables. For some flows, the choice is clear. For instance, adaptingon gradients of pressure is a good criterion for refining in the regionof shock waves. In most incompressible flows, however, it makeslittle sense to refine on pressure gradients. A more suitable param-eter in an incompressible flow might be mean velocity gradients.If the flow feature of interest is a turbulent shear flow, it will beimportant to resolve the gradients of turbulent kinetic energy andturbulent energy dissipation, so these might be appropriate refine-ment variables. In reacting flows, temperature or concentration (ormole or mass fraction) of reacting species might be appropriate.

• Poor adaption practice can have adverse effects. One of the mostcommon mistakes is to over-refine a particular region of the solu-tion domain, causing very large gradients in cell volume. This canadversely affect the accuracy of the solution.


Grid Adaption

23.2 The Adaption Process

The adaption process has been separated into two distinct tasks. First,the individual cells are marked for refinement or coarsening based onthe adaption function, which is created from geometric and/or solutiondata. Next, the cell is refined or considered for coarsening based on theseadaption marks. The primary advantages of this modularized approachare the abilities to create sophisticated adaption functions and to exper-iment with various adaption functions without modifying the existingmesh.

It is highly recommended that you write a case and data file before!starting the adaption process. Then, if you generate an undesirablegrid, you can restart the process with the saved files.

Two different types of adaption are available in FLUENT: “conformal”and “hanging node” adaption. Hanging node adaption, the defaultmethod, is described in Section 23.2.2. Conformal adaption, which isavailable only for triangular and tetrahedral grids, is described in Sec-tion 23.2.3.

23.2.1 Adaption and Mask Registers

Invoking the Mark command creates an adaption register. It is calleda register because it is used in a manner similar to the way memoryregisters are used in calculators. For example, one adaption registerholds the result of an operation, another register holds the results ofa second operation, and these registers can be used to produce a thirdregister. An adaption register is basically a list of identifiers for eachcell in the domain. The identifiers designate whether a cell is neutral(not marked), marked for refinement, or marked for coarsening. Theadaption function is used to set the appropriate identifier. For example,to refine the cells based on pressure gradient, the solver computes thegradient adaption function for each cell. The cell value is compared tothe refining and coarsening threshold values and assigned the appropriateidentifier, specifically for this example:

• cell value < coarsen threshold: mark for coarsening



• coarsen threshold < cell value < refine threshold: don’t mark,neutral

• cell value > refine threshold: mark for refinement

The GUI and text interface commands generate adaption registers thatdesignate the cells marked for refinement or coarsening. These registerscan be converted to mask registers. Masks, unlike the adaption registers,maintain only two states: ACTIVE and INACTIVE. If the adaption reg-ister is converted to a mask, cells marked for refinement become ACTIVEcells, while those that are unmarked or marked for coarsening becomeINACTIVE. You can use a mask register to limit adaption to cells withina certain region. This process is illustrated below.

Figure 23.2.1 shows a cloud of cells representing an adaption register(shaded cells are marked cells). Figure 23.2.2 illustrates the active cellsassociated with a mask register. If the mask is applied to (combinedwith) the adaption register, the new adaption register formed from thecombination has the marked cells shown in Figure 23.2.3. (Note thatthis example does not differentiate between refinement or coarseningmarks because the mask is applied to both types of marks.) For moreinformation on combining registers, see Section 23.9.

Figure 23.2.1: Adaption Register with Shaded Cells RepresentingMarked Cells


Grid Adaption

Figure 23.2.2: Mask Register with Shaded Cells Representing ActiveCells

Figure 23.2.3: New Adaption Register Created from Application of Mask



In summary, adaption registers can be created using geometric data,physical features of the flow field, and combinations of this information.Once created, adaption registers can be listed, displayed, deleted, com-bined, exchanged, inverted, and changed to mask registers.

23.2.2 Hanging Node Adaption

Grids produced by the hanging node adaption procedure are character-ized by nodes on edges and faces that are not vertices of all the cellssharing those edges or faces, as shown in Figure 23.2.4. Hanging nodegrid adaption provides the ability to operate on grids with a varietyof cell shapes, including hybrid grids. However, although the hangingnode scheme provides significant grid flexibility, it does require additionalmemory to maintain the grid hierarchy which is used by the renderingand grid adaption operations.

Hanging Node

Figure 23.2.4: Example of a Hanging Node

Hanging Node Refinement

The cells are refined by isotropically subdividing each cell marked forrefinement. Figures 23.2.5 and 23.2.6 illustrate the division of the sup-ported cell shapes described below:

• A triangle is split into 4 triangles.


Grid Adaption

• A quadrilateral is split into 4 quadrilaterals.

• A tetrahedron is split into eight tetrahedra. The subdivision con-sists of trimming each corner of the tetrahedron, and then subdivid-ing the enclosed octahedron by introducing the shortest diagonal.

• A hexahedron is split into 8 hexahedra.

• A wedge (prism) is split into 8 wedges.

• A pyramid is split into 6 pyramids and 4 tetrahedra.

To maintain accuracy, neighboring cells are not allowed to differ by morethan one level of refinement. This prevents the adaption from producingexcessive cell volume variations (reducing truncation error) and ensuresthat the positions of the “parent” (original) and “child” (refined) cellcentroids are similar (reducing errors in the flux evaluations).

Triangle Quadrilateral

Figure 23.2.5: Hanging Node Adaption of 2D Cell Types

Hanging Node Coarsening

The mesh is coarsened by reintroducing inactive parent cells, i.e., coa-lescing the child cells to reclaim the previously subdivided parent cell.An inactive parent cell is reactivated if all its children are marked forcoarsening. You will eventually reclaim the original grid with repeatedapplication of the hanging node coarsening. You cannot coarsen the gridany further than the original grid using the hanging node adaption pro-cess. Conformal coarsening, however, allows you to remove original gridpoints to reduce the density of the grid.



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Tetrahedron Hexahedron

Prism/Wedge Pyramid

Figure 23.2.6: Hanging Node Adaption of 3D Cell Types

23.2.3 Conformal Adaption

The conformal adaption process does not create hanging nodes. Instead,all the cells sharing an edge or face include all the nodes on those entities.The conformal refinement process adds nodes on edges and the conformalcoarsening removes nodes and retriangulates the resulting cavity.

Conformal Refinement

To refine the cell, boundary or internal faces (including periodic bound-ary faces) may be split. Figure 23.2.7 shows how the triangle labeledA would be split for refinement. The cells are refined by splitting thelongest edge of the triangle or tetrahedron. This technique has twoprimary advantages: the process is conservative and does not require in-terpolation to obtain the solution vector for the new cells, and repeatedrefinement of a skewed cell does not continue to increase grid skewness.

The present scheme finds the longest edge of any cell marked for refine-ment. The scheme then visits each of the cells that contain that edge and


Grid Adaption

Figure 23.2.7: Cells are Refined by Bisecting Longest Edge

searches for a longer edge. If any of the neighbor cells has a longer edge,the scheme spins around that new edge searching for yet a longer edge.Once it has arrived at the longest edge, it splits that edge. Althoughthis process maintains the quality of the triangulation with repeated ap-plication, it can cause many cells that were not marked for refinement tobe split. For example, Figure 23.2.8 shows the original cell marked forrefinement (marked with an X), and Figure 23.2.9 shows the final meshcreated by the refinement process.

Conformal Coarsening

The grid is coarsened by removing nodes that are shared by cells markedfor coarsening. If all the cells attached to the node are marked for coars-ening, the solver attempts to remove the node. The following local retri-angulation process is attempted for each of the nodes marked for removal:

1. A list of the cells attached to the marked node is generated. Re-moving these cells creates a cavity that must be retriangulated.

2. A list of the faces inside the cavity is generated.

3. A list of the faces on the cavity boundary is generated.

4. If the node to be removed is on a boundary, a new boundary trian-gulation is generated and those faces are added to the list of faceson the cavity.



Figure 23.2.8: Original Grid With One Cell Marked for Refinement

Figure 23.2.9: Final Grid After Refinement Process


Grid Adaption

5. From the list of faces on the cavity, a new Delaunay triangulationis created. (See the Theory chapter in the TGrid User’s Guide fora description of Delaunay triangulation.)

6. If the process is successful, the node, faces, and cells from theoriginal triangulation of the region are deleted.

7. All nodes associated with the cavity are removed from the list ofdoomed nodes to avoid consecutive coarsening in the same region.

8. The solution variables in the new cells are computed using a volume-weighted average.

Figure 23.2.10 illustrates the removal of node n1 and the resulting re-triangulation. In this example, the list of cells attached to the nodeincludes c1, c2, c3, c4, and c5; the list of faces inside the cavity includesf6, f7, f8, f9, and f10; and the list of faces on the cavity includesf1, f2, f3, f4, and f5. The new faces of the triangulation are f11 andf12, and the new cells are c6, c7, and c8.

Nodes introduced by refinement are called refinement nodes. Nodes thatexisted in the mesh before refinement are called original nodes. By de-fault, only refinement nodes can be removed in the coarsening process,but you can remove any node by resetting the node flags. For additionalinformation on node flags, see Section 23.10.

Presently, the grid-coarsening scheme is implemented only in the 2Dversion of FLUENT.



Figure 23.2.10: The Grid is Coarsened by Removing a Node and Retri-angulating the Region


Grid Adaption

23.2.4 Conformal vs. Hanging Node Adaption

For most problems, the hanging node adaption provides the most flexi-bility for grid adaption. However, the following points should aid you inselecting the appropriate type of adaption for your specific application.

• The conformal adaption method is only valid for tri and tet grids,while the hanging node adaption can be applied to all supportedcell shapes.

• The hanging node adaption is usually much more local in naturethan the conformal adaption. In conformal adaption, many cells inaddition to the marked cells may be refined due to the longest edgesplitting criteria. For highly graded grids, the initial conformalrefinement sweeps tend to exhibit substantial propagation of thecell refinement, sometimes refining the grid many cells away fromthe actual cell marked for refinement. (Subsequent refinements areusually much more local in nature.) The hanging node schemeonly propagates to maintain the refinement level difference, whichis much more confined.

• The connectivity of the original grid is retained in the hanging nodeadaption scheme, but the conformal adaption method will modifythe connectivity with refinement and coarsening. This could haveaccuracy implications for grids used in unsteady problems withperiodic behavior (e.g., vortex shedding behind a cylinder) if youperform successive refinements and coarsenings. However, onlyconformal coarsening allows you to coarsen the initial grid, andthis is only available in 2D.

• The hanging node adaption has a memory penalty associated withmaintaining the grid hierarchy and temporarily storing the edges in3D. The conformal adaption has no memory overhead other thanthe additional nodes, faces and cells added to increase the griddensity.


23.3 Boundary Adaption


If more cells are required on a boundary, they can be added using bound-ary adaption. The boundary adaption function allows you to mark orrefine cells in the proximity of the selected boundary zones. The abilityto refine the grid near one or more boundary zones is provided becauseimportant fluid interactions often occur in these regions, such as thedevelopment of strong velocity gradients in the boundary layer near awall.

23.3.1 Boundary Adaption Example

An example of a grid that can be improved with boundary adaption isshown in Figure 23.3.1. This mesh has only two cells on the verticalface of a step. Boundary adaption on the zone corresponding to theface of the step can be used to increase the number of cells, as shown inFigure 23.3.2. Note that this procedure cannot increase the resolutionof a curved surface. Therefore, if more cells are required on a curvedsurface where the shape of the surface is important, it is preferable tocreate the mesh with sufficient surface nodes before reading it into thesolver.

23.3.2 Steps for Performing Boundary Adaption

Three different methods are available for boundary adaption:

• adaption based on a cell’s distance from the boundary, measuredin number of cells

• adaption based on the normal distance of a cell from the boundary

• adaption based on a target boundary volume and growth factor

You can make use of any of these methods in the Boundary Adaptionpanel (Figure 23.3.3).

Adapt −→Boundary...

The steps for using each method are described below.


Grid Adaption

Grid

Figure 23.3.1: Mesh Before Adaption

Grid

Figure 23.3.2: Mesh After Boundary Adaption



Figure 23.3.3: The Boundary Adaption Panel

Boundary Adaption Based on Number of Cells

The general procedure for performing adaption based on a cell’s distancefrom the boundary in terms of the number of cells is listed below:

1. In the Boundary Adaption panel, select Cell Distance under Options,choose the boundary zones near which you want to refine cells inthe Boundary Zones list, and click Apply.

2. Open the Contours panel by clicking on the Contour... button.

3. In the Contours panel, enable Filled contours, disable Node Values,choose Adaption... and Boundary Cell Distance in the Contours Ofdrop-down list, select the appropriate surfaces (3D only), and clickDisplay to see the location of cells with each value of boundary celldistance. By displaying different ranges of values (as described inSection 25.1.2), you can determine the cell distance of the cells youwish to adapt.

4. In the Boundary Adaption panel, set the Number of Cells to the de-sired value. If you retain the default value of 1, only those cells that


Grid Adaption

have edges (2D) or faces (3D) on the specified boundary zone(s)(i.e., those cells with a boundary cell distance of 1) will be markedor adapted. If you increase the value to 2, cells with a boundarycell distance of 2 will also be marked/adapted, and so on.

5. (optional) If you want to set any adaption options (described inSection 23.10), click on the Controls... button to open the GridAdaption Controls panel.

6. Click Mark to mark the cells for refinement by placing them in anadaption register (which can be manipulated as described in Sec-tion 23.9), or click Adapt to perform the refinement immediately.

Boundary Adaption Based on Normal Distance

The general procedure for performing refinement based on a cell’s normaldistance from the boundary is listed below:

1. In the Boundary Adaption panel, select Normal Distance under Op-tions, choose the boundary zones near which you want to refinecells in the Boundary Zones list, and click Apply.


3. In the Contours panel, enable Filled contours, disable Node Values,choose Adaption... and Boundary Normal Distance in the ContoursOf drop-down list, select the appropriate surfaces (3D only), andclick Display to see the location of cells with each value of normaldistance. By displaying different ranges of values (as described inSection 25.1.2), you can determine the normal distance of the cellsyou wish to adapt.

4. In the Boundary Adaption panel, set the Distance Threshold to thedesired value. Cells with a normal distance to the selected bound-ary zone(s) less than or equal to this value will be marked oradapted.





Boundary Adaption Based on Target Boundary Volume

This boundary adaption allows you to refine cells based on a targetboundary cell volume and an exponential growth function. This allowsyou to produce grids with cells that have the target volume near theselected boundaries and exponentially larger (or smaller) cells as you getfurther from the boundaries. The cells are marked for refinement basedon the following equation:

Vn > Vboundaryeαd (23.3-1)

where Vn is the volume of the cell, Vboundary is the specified boundaryvolume (Boundary Volume), α is the exponential growth factor (GrowthFactor), and d is the normal distance of the cell centroid from the selectedboundaries. Vboundarye

αd is the target volume for a cell.

The general procedure for this type of boundary refinement is listedbelow:

1. In the Boundary Adaption panel, select Volume Distance under Op-tions, set the Boundary Volume and Growth Factor to the desiredvalues, choose the boundary zones in the Boundary Zones list whereyou want the Boundary Volume to be applied, and click Apply.


3. In the Contours panel, enable Filled contours, disable Node Values,choose Adaption... and Boundary Volume Distance in the ContoursOf drop-down list, select the appropriate surfaces (3D only), andclick Display to see contours of the target volume. You can modifythe values of any of the inputs (Boundary Volume, Growth Factor,and/or Boundary Zones), click on Apply in the Boundary Adaptionpanel, and then redisplay the contour plot to visualize the modifiedtarget volume distribution.


Grid Adaption



23.4 Gradient Adaption

The gradient adaption function allows you to mark cells or adapt thegrid based on the gradient (undivided Laplacian) of the selected fieldvariables.

23.4.1 Gradient Adaption Approach

The primary goal of solution-adaptive grid refinement is to efficientlyreduce the numerical error in the digital solution. Unfortunately, directerror estimation for point-insertion adaption schemes is difficult becauseof the complexity of accurately estimating and modeling the error inthe adapted grids. Assuming the greatest error occurs in high-gradientregions, the readily available physical features of the evolving flow fieldmay be used to drive the grid adaption process. The equidistributionadaption technique used by FLUENT multiplies the undivided Laplacianof the selected solution variable by a characteristic length scale [256]. Thelength scale is the square (2D) or cube (3D) root of the cell volume. Theintroduction of this length scale permits resolution of both strong andweak disturbances, increasing the potential for more accurate solutions.You can, however, reduce or eliminate the volume weighting by changingthe gradient Volume Weight in the Grid Adaption Controls panel (seeSection 23.10 for details). For example, the gradient function in twodimensions has the following form:

|ei| = (Acell)r2 |∇2f | (23.4-1)

where ei is the error indicator, Acell is the cell area, r is the gradientvolume weight, and ∇2f is the undivided Laplacian of the desired field



variable, f . The default value of the gradient volume weight is unity,which corresponds to full volume weighting; a value of zero will eliminatethe volume weighting, and values between 0 and 1 will use proportionalweighting of the volume.

Any of the field variables available for contouring can be used in thegradient adaption function. Interestingly, these scalar functions includeboth geometric and physical features of the numerical solution. There-fore, in addition to traditional adaption to physical features, such as thevelocity, you may choose to adapt to the cell volume field to reduce rapidvariations in cell volume.

23.4.2 Gradient Adaption Example

A good example of the use of gradient adaption is the solution of thesupersonic flow over a circular cylinder. The initial mesh, shown inFigure 23.4.1, is very coarse, even though it contains sufficient cells toadequately describe the shape of the cylinder. The mesh ahead of thecylinder is too coarse to resolve the shock wave that forms in front ofthe cylinder. In this instance, because there will be a jump in pressureacross the shock, it is clear that pressure is a suitable variable to usein gradient adaption. Several adaptions are necessary, however, beforethe shock can be properly resolved. The mesh after several adaptions isshown in Figure 23.4.2.

A typical application of gradient adaption for an incompressible flowmight be a mixing layer, which—like the example above—involves adiscontinuity.

23.4.3 Steps for Performing Gradient Adaption

You will perform gradient adaption in the Gradient Adaption panel (Fig-ure 23.4.3).

Adapt −→Gradient...

The general procedure for performing gradient adaption is listed below:

1. In the Gradient Adaption panel, select the desired solution variablein the Gradients Of drop-down list and click on Compute.


Grid Adaption

Grid

Figure 23.4.1: Bluff-Body Mesh Before Adaption

Grid

Figure 23.4.2: Bluff-Body Mesh After Gradient Adaption



Figure 23.4.3: The Gradient Adaption Panel


3. In the Contours panel, enable Filled contours, disable Node Values,choose Adaption... and Existing Value in the Contours Of drop-downlist, select the appropriate surfaces (3D only), and click Display tosee the location of cells with each gradient value. By displayingdifferent ranges of values (as described in Section 25.1.2), you candetermine the range of gradients for which you want to adapt cells.

4. In the Gradient Adaption panel, set the Refine Threshold. Cells withgradient values above this value will be marked or refined.

5. If you want to coarsen the grid, set the Coarsen Threshold to a non-zero value. Cells with gradient values below the specified value willbe marked or coarsened.

Note that if you are using hanging node adaption (the default),you will not be able to create a grid that is coarser than the orig-inal grid. For this, you must use conformal adaption. Note alsothat conformal coarsening is only available for 2D or axisymmetricgeometries. See Section 23.10 for details.


Grid Adaption


7. Click Mark to mark the cells for adaption (refinement/coarsening)by placing them in an adaption register (which can be manipulatedas described in Section 23.9), or click Adapt to perform the adaptionimmediately.

(If you wish to disable refinement or coarsening, or marking for refine-ment or coarsening, you can turn off the Refine or Coarsen option beforemarking or adapting.)

23.5 Isovalue Adaption

Some flows may contain flow features that are easy to identify basedon values of a certain quantity. For instance, wakes represent a totalpressure deficit, and jets are identifiable by a region of relatively high-velocity fluid. Since it is known that these regions also contain largegradients of important flow quantities (such as k and ε in turbulentflows) it may be more convenient to perform an isovalue adaption on therelevant flow quantity than to refine on gradients of the individual flowvariables.

The isovalue adaption function allows you to mark or refine cells insideor outside a specified range of a selected field variable function. Thegrid can be refined or marked for refinement based on geometric and/orsolution vector data. Specifically, any quantity in the display list offield variables can be used for the isovalue adaption. Some examples ofhow you might use the isovalue marking/adaption feature include thefollowing:

• Create masks using coordinate values or the quadric function.

• Refine cells that have a velocity magnitude within a specified range.

• Mark and display cells with a pressure or continuity residual out-side of a desired range to determine where the numerical solutionis changing rapidly.



The approach used in isovalue adaption function is to compute the spec-ified value for each cell (velocity, quadric function, centroid x coordinate,etc.), and then visit each cell, marking for refinement the cells that havevalues inside (or outside) the specified ranges.

23.5.1 Isovalue Adaption Example

An example of a problem in which isovalue adaption is useful is shownin Figure 23.5.1. The mesh for an impinging jet is displayed togetherwith contours of x velocity. An isovalue adaption based on x velocityallows refinement of the mesh only in the jet, with the result shown inFigure 23.5.2.

Caution must be used when adapting to isovalues to prevent large gradi-!ents in cell volume. As explained in Section 23.1, this can affect accuracyand impede convergence. One approach to rectifying large gradients incell volume is to adapt to cell-volume change, as demonstrated in Sec-tion 23.7.2.

23.5.2 Steps for Performing Isovalue Adaption

You will perform isovalue adaption in the Iso-Value Adaption panel (Fig-ure 23.5.3).

Adapt −→Iso-Value...

The general procedure for performing isovalue adaption is listed below:

1. In the Iso-Value Adaption panel, select the desired solution variablein the Iso-Values Of drop-down list and click on Compute to updatethe Min and Max fields.

2. Choose the Inside or Outside option and set the Iso-Min and Iso-Maxvalues.

• If you choose Inside, cells with isovalues between Iso-Min andIso-Max will be marked or refined.

• If you choose Outside, cells with isovalues less than Iso-Min orgreater than Iso-Max will be marked or refined.


Grid Adaption

Contours of X-Velocity (m/s)

1.00e+00

9.00e-01

8.00e-01

7.00e-01

6.00e-01

5.00e-01

4.00e-01

3.00e-01

2.00e-01

1.00e-01

Figure 23.5.1: Impinging Jet Mesh Before Adaption Shown TogetherWith Contours of x Velocity

Grid

Figure 23.5.2: Impinging Jet Mesh After Isovalue Adaption



Figure 23.5.3: The Iso-Value Adaption Panel




Grid Adaption

23.6 Region Adaption

Many mesh generators create meshes with cell volumes that grow veryrapidly with distance from boundaries. While this avoids a dense grid asa matter of course, it might also create problems if the mesh is not fineenough to resolve the flow. But if it is known a priori that a finer meshis required in a certain region of the solution domain, the mesh can berefined using region adaption.

The region adaption function marks or refines cells inside or outside aregion defined by text or mouse input. Presently, the grid can be refinedor marked inside or outside a hexahedron (quadrilateral in 2D), a sphere(circle in 2D), or a cylinder. The region-based marking/adaption featureis particularly useful for refining regions that intuitively require goodresolution: e.g., the wake region of a blunt-body flow field. In addition,you can use the region marking to create mask adaption registers thatcan be used to limit the extent of the refinement and coarsening.

23.6.1 Defining a Region

The basic approach to the region adaption function is to first definea hexahedral (quadrilateral), spherical (circular), or cylindrical region.You will define the hexahedron (quadrilateral) by entering the coordi-nates of two points defining the diagonal. The sphere (circle) is definedby entering the coordinates of the center of the sphere and its radius. Todefine a cylinder, you will specify the coordinates of the points definingthe cylinder axis, and the radius. In 3D this will define a cylinder. In 2D,you will have an arbitrarily oriented rectangle with length equal to thecylinder axis length and width equal to the radius. A rectangle definedusing the cylinder option differs from one defined with the quadrilateraloption in that the former can be arbitrarily oriented in the domain whilethe latter must be aligned with the coordinate axes.

You can either type the exact coordinates into the appropriate real en-try fields or select locations with the mouse on displays of the grid orsolution field. After the region is defined, each cell that has a centroidinside/outside the specified region is marked for refinement.



23.6.2 Region Adaption Example

Figure 23.6.1 shows a mesh that was created for solving the flow arounda flap airfoil. The mesh is very fine near the surface of the airfoil sothat the viscous-affected region may be resolved. However, the meshgrows very rapidly away from the airfoil, with the result that the flowseparation known to occur on the suction surface of the flap will not beproperly predicted. To circumvent this problem, the grid was adaptedwithin circular regions (selected by mouse probe) surrounding the flap.The result is shown in Figure 23.6.2. Note that when the region adaptionwas performed, the minimum cell volume for adaption was limited (asdescribed in Section 23.10) to prevent the very small cells near the surfacefrom being refined further.

Grid

Figure 23.6.1: Flap-Airfoil Mesh Before Adaption


Grid Adaption

Grid

Figure 23.6.2: Flap-Airfoil Mesh After Region Adaption

23.6.3 Steps for Performing Region Adaption

You will perform region adaption in the Region Adaption panel (Fig-ure 23.6.3).

Adapt −→Region...

The general procedure for performing isovalue adaption is listed below:

1. In the Region Adaption panel, choose the Inside or Outside option.

• If you choose Inside, cells with centroids within the specifiedregion will be marked or refined.

• If you choose Outside, cells with centroids outside the specifiedregion will be marked or refined.

2. Specify the shape of the region. In 2D, you may choose a Quadrilateral,Circle, or Cylinder. In 3D, you may choose a Hexahedron, Sphere,or Cylinder.



Figure 23.6.3: The Region Adaption Panel


Grid Adaption

3. Define the region by entering values into the panel or by using themouse.

In the panel the inputs are as follows:

• To define a hexahedron or quadrilateral, you will input thecoordinates of two points defining the box’s diagonal: (Xmini-mum,Yminimum,Zminimum) and (Xmaximum,Ymaximum, Zmax-imum) for a hexahedron, or (Xminimum,Yminimum) and (Xmax-imum,Ymaximum) for a quadrilateral.

• To define a sphere or circle, you will input the coordinatesof its center—(Xcenter,Ycenter,Zcenter) for a sphere or (Xcen-ter,Ycenter) for a circle—and its Radius.

• To define a cylinder, you will input the minimum and max-imum coordinates defining the cylinder axis—(X-Axis Min,Y-Axis Min,Z-Axis Min) and (X-Axis Max,Y-Axis Max,Z-Axis Max)for 3D or (X-Axis Min,Y-Axis Min) and (X-Axis Max,Y-AxisMax) for 2D—as well as the Radius of the cylinder. (In 2D,this will be the width of the resulting rectangle.)

To define the region using the mouse, click on the Select Points WithMouse button. Using the mouse probe (the right mouse button,by default), you may select the input coordinates from a display ofthe grid or solution field. See Section 25.3 for details about mousebutton functions.) After you select the points, the values will beloaded automatically into the appropriate fields in the panel. Ifyou want, you can edit these values before marking or adapting.

• To define a hexahedron or quadrilateral, you can select thetwo points of the diagonal in any order.

• To define a sphere or circle, first select the location of thecentroid and then select a point that lies on the sphere/circle(i.e., a point that is one radius away from the centroid).

• To define a cylinder, first select the two points that define thecylinder axis and then select a point that is one radius awayfrom the axis.

4. (optional) If you want to set any adaption options (described inSection 23.10), click on the Controls... button to open the Grid


23.7 Volume Adaption

Adaption Controls panel.



As mentioned in Section 23.1, it is best for both accuracy and conver-gence to have a mesh in which the changes in cell volume are gradual.If the mesh creation or adaption process has resulted in a mesh thatdoes not have this property, the grid can be improved by using volumeadaption with the option of refining based on either the cell volume orthe change in volume between the cell and its neighbors.

23.7.1 Approach

Marking or refining the grid based on volume magnitude is most oftenused to remove large cells or to globally refine the mesh. The procedure isto mark for refinement any cell with a volume greater than the specifiedthreshold value.

Marking or refining the grid based on the change in cell volume is usedto improve the smoothness of the grid. The procedure is to mark forrefinement any cell that has a volume change greater than the specifiedthreshold value. The volume change is computed by looping over thefaces and comparing the ratio of the cell neighbors to the face. Forexample, in Figure 23.7.1 the ratio of V1/V2 and the ratio of V2/V1 iscompared to the threshold value. If V2/V1, for example, is greater thanthe threshold, then C2 is marked for refinement.

23.7.2 Volume Adaption Example

The mesh in Figure 23.7.2 was created for the purpose of computing aturbulent jet. Local refinement was used in TGrid to create a mesh thatis fine in the region of the jet, but coarse elsewhere. This created a verysharp change in cell volume at the edge of the jet.


Grid Adaption

Figure 23.7.1: The Volume Change is Computed as the Ratio of theVolumes of the Cells Neighboring a Face

To improve the mesh, it was refined using volume adaption with thecriterion that the maximum cell volume change should be less than 50%.The minimum cell volume for adaption was also limited. The resultingmesh, after smoothing and swapping, is shown in Figure 23.7.3. It canbe seen that the interface between the refined region within the jet andthe surrounding mesh is no longer as sharp.

23.7.3 Steps for Performing Volume Adaption

You will perform volume adaption in the Volume Adaption panel (Fig-ure 23.7.4).

Adapt −→Volume...

The general procedure for performing volume adaption is listed below:

1. In the Volume Adaption panel, specify whether you want to adaptbased on volume magnitude or volume change by selecting theMagnitude or Change option.

2. Click on Compute to update the Min and Max fields. These fieldswill show the range of cell volumes or cell volume changes (definedin Section 23.7.1), depending on your selection in step 1.

3. Set the Max Volume or Max Volume Change value. If you havechosen to adapt based on volume Magnitude, cells that have vol-umes greater than Max Volume will be marked or refined. If you



Grid

Figure 23.7.2: Jet Mesh Before Adaption

Grid

Figure 23.7.3: Jet Mesh After Volume Adaption Based on Change inCell Volume


Grid Adaption

Figure 23.7.4: The Volume Adaption Panel

are adapting based on volume Change, cells with volume changesgreater than Max Volume Change will be marked or refined.



23.8 y+ and y∗ Adaption

FLUENT provides three different options for near-wall modeling of tur-bulence (standard wall functions, non-equilibrium wall functions, andthe enhanced wall treatment). As described in Section 10.9, there arecertain mesh requirements for each of these near-wall modeling options.

Since it is often difficult to gauge the near-wall resolution requirementswhen creating the mesh, y+ and y∗ adaption have been provided to en-able you to appropriately refine or coarsen the mesh along the wall duringthe solution process. If you are using the enhanced wall treatment, you



will adapt to y+; if you are using wall functions, you can adapt to eithery+ or y∗.

23.8.1 Approach

The approach is to compute y+ or y∗ for boundary cells on the specifiedviscous wall zones, define the minimum and maximum allowable y+ or y∗,and mark and/or adapt the appropriate cells. Cells with y+ or y∗ valuesbelow the minimum allowable threshold will be marked for coarseningand cells with y+ or y∗ values above the maximum allowable thresholdwill be marked for refinement (unless coarsening or refinement has beendisabled).

23.8.2 y+ Adaption Example

Figure 23.8.1 shows the mesh for a duct flow, with the top boundarybeing the wall and the bottom boundary being a symmetry plane. Afteran initial solution, it was determined that y+ values of the cells on thewall boundary were too large, and y+ adaption was used to refine them.The resulting mesh is shown in Figure 23.8.2. This figure shows that theheight of the cells along the wall boundary has been reduced during therefinement process. However, the cell-size distribution on the wall afterrefinement is much less uniform than in the original mesh, which is anadverse effect of y+ adaption.

See Section 10.9 for guidelines on recommended values of y+ or y∗ fordifferent near-wall treatments.

23.8.3 Steps for Performing y+ or y∗ Adaption

You will perform y+ or y∗ adaption in the Y+/Y* Adaption panel (Fig-ure 23.8.3).

Adapt −→Y+/Y*...

The general procedure for performing y+ or y∗ adaption is listed below:

1. In the Y+/Y* Adaption panel, select Y+ or Y* as the adaptionType. (Select Y+ if you are using the enhanced wall treatment; if


Grid Adaption

Grid

Figure 23.8.1: Duct-Flow Mesh Before Adaption

Grid

Figure 23.8.2: Duct-Flow Mesh After y+ Adaption



Figure 23.8.3: The Y+/Y* Adaption Panel

you are using wall functions, you can select either type.)

2. Choose the wall zones for which you want boundary cells to bemarked or adapted in the Wall Zones list, and click on Compute toupdate the Min and Max fields. (Note that the values displayedare the minimum and maximum values for all wall zones, not justthose selected.)

3. Set the Min Allowed and Max Allowed. Cells with y+ or y∗ valuesbelow Min Allowed will be coarsened or marked for coarsening, andcells with y+ or y∗ values above Max Allowed will be refined ormarked for refinement.

Note that if you are using hanging node adaption (the default),you will not be able to create a grid that is coarser than the orig-inal grid. For this, you must use conformal adaption. Note alsothat conformal coarsening is only available for 2D or axisymmetricgeometries. See Section 23.10 for details.

4. (optional) If you want to set any adaption options (described in


Grid Adaption

Section 23.10), click on the Controls... button to open the GridAdaption Controls panel.

5. Click Mark to mark the cells for adaption (refinement/coarsening)by placing them in an adaption register (which can be manipulatedas described in Section 23.9), or click Adapt to perform the adaptionimmediately.

(If you wish to disable refinement or coarsening, or marking for refine-ment or coarsening, you can turn off the Refine or Coarsen option beforemarking or adapting.)

23.9 Managing Adaption Registers

You can manipulate, delete, and display adaption registers that you havecreated by marking cells for adaption. Since these registers will be usedto adapt the grid, the ability to manipulate them provides you withadditional control over the adaption process.

Management of adaption registers is performed in the Manage AdaptionRegisters panel (Figure 23.9.1).

Adapt −→Manage...

(You can also open this panel by clicking on the Manage... button in anyof the adaption panels.)

For additional information about registers, see Section 23.2.1.

Overview

The creation of hybrid adaption functions is generally motivated by thedesire to confine the adaption to a specific region (using masks) and/orcreate a more accurate error indicator. FLUENT provides a few basictools to aid in creating hybrid adaption functions. First, you can cre-ate the initial adaption registers using geometric and/or solution vectorinformation. After creating the adaption registers, you can manipulatethese registers and their associated refinement and coarsening marks.The registers are manipulated by changing the type and/or combining



Figure 23.9.1: The Manage Adaption Registers Panel


Grid Adaption

them to create the desired hybrid function. The marks are manipu-lated by using Exchange, Invert, Limit, and Fill operations. Finally, youcan delete, display, and most importantly, adapt to the hybrid adaptionfunctions.

For example, you can capture the shock wave generated on a wedge ina supersonic flow field by adapting the grid to the gradients of pressure.The pressure gradient near the surface of the wedge, however, is rela-tively small. You might therefore use the velocity field to resolve theequally important boundary layer near the surface of the wedge. If youadapt to pressure, regions near the surface might be coarsened. If yousubsequently adapted to velocity, these same regions might be refined,but the net result would be no gain in resolution. But if you combinethe velocity and pressure gradient adaption functions, the new adaptionfunction would allow increased resolution in both regions. The relativeweight of the two functions in the hybrid function is determined by thevalues of the refinement and coarsening thresholds you specify for eachof the flow field variables. If, in addition, you decided to refine the shockand boundary layer only near the leading edge of the wedge, you couldcreate a circle at the leading edge of the wedge using the region adaptionfunction, change this new register to a mask, and combine it with thehybrid gradient function.

23.9.1 Manipulating Adaption Registers

There are three basic tools available for modifying and manipulatingadaption registers: changing type, combining, and deleting.

Changing Register Types

Presently, there are two types of registers: adaption registers and maskregisters. The present adaption functions accessed through the GUI andtext interface generate adaption registers—i.e., registers that designatethe cells marked for refinement or coarsening. These registers can beconverted to mask registers, however, by changing their type. Mask reg-isters, unlike the adaption registers, only maintain two states: ACTIVEand INACTIVE. If the adaption register is converted to a mask, thecells marked for refinement are ACTIVE, and all other cells are INAC-



TIVE; i.e., the cells marked for coarsening are ignored. Commonly, theadaption registers converted to masks are those that are generated byadaption functions that mark cells exclusively for refinement, such as re-gion or isovalue adaption functions. The other major difference betweenadaption and mask registers is the manner in which they are combined.

To change the type of one or more registers from adaption to mask, orvice versa, follow these steps:

1. Choose the register(s) in the Registers list.

2. Click on the Change Type button under Register Actions.

The new type of the register (or of the most recently selected or des-elected register, if multiple registers are selected) will be shown as theType under Register Info. You can select each register individually to seewhat its current type is.

Combining Registers

After the individual adaption registers have been created and appropri-ately modified, these registers are combined to create hybrid adaptionfunctions. Any number of registers can be combined in the followingmanner:

• All adaption registers are combined into a new adaption register.

• All mask registers are combined into a new mask register.

• The new adaption and mask registers are combined.

Any number of adaption registers can be combined in the following man-ner:

• If the cell is marked for refinement in any of the registers, markthe cell for refinement in the new register (bitwise OR).

• If the cell is marked for coarsening in all of the registers, mark thecell for coarsening in the new register (bitwise AND).


Grid Adaption

The mask registers are combined in a manner similar to the refinementmarks: if any cell is marked ACTIVE, the cell in the new register ismarked ACTIVE (bitwise OR).

Finally, in the combination of an adaption and mask register, only cellsthat are marked in the mask register can have an adaption mark in thecombined register (bitwise AND).

For example, creating an adaption function based on pressure gradientmay generate cells marked for refinement and coarsening throughout theentire solution domain. If this register is then combined with a maskregister created from cells marked inside a sphere, only the cells insidethe sphere will be marked for refinement or coarsening in the new register.

The effect of masks depends on the order in which they are applied. Forexample, consider two adjacent, circular masks. Applying one mask tothe adaption register and then applying the other mask to the result ofthe first combination would give a much different result than applyingthe combination of the two masks to the initial adaption register. (Thesecond combination results in a greater possible number of marked cells.)

To combine two or more registers, follow these steps:

1. Choose the registers in the Registers list.

2. Click on the Combine button under Register Actions.

The selected registers will remain intact, and the register(s) resultingfrom the combination will be added to the Registers list. In some in-stances, three new registers may be created: a combination of the adap-tion registers, a combination of the mask registers, and then a combina-tion of the two combined registers.

For more information about combining registers, see Section 23.2.1.

Deleting Registers

Any number of adaption registers can be deleted. The primary reasonfor deleting registers is to discard unwanted adaption registers, reducingpossible confusion and the potential for generating undesired results by



selecting these castaways. In addition, only 32 adaption registers canexist at one time. You may therefore need to discard unwanted registersto make room for new ones.

To permanently remove one or more registers, follow these steps:


2. Click on the Delete button under Register Actions.

23.9.2 Modifying Adaption Marks

The adaption marks are the identifiers that designate whether a cellshould be refined, coarsened, or neutral. Presently, four basic tools areprovided for modifying the adaption marks: Exchange, Invert, Limit, andFill operations.

The Exchange operation changes all cells marked for refinement into cellsmarked for coarsening, and all cells originally marked for coarseninginto cells marked for refinement. Commonly, this operator is applied toadaption registers that have only refinement marks. For example, theexchange operation can be used to coarsen a rectangular region. First,you create an adaption register that marks a rectangular region of cellsfor refinement. Next, you use the Exchange operation to modify the cellmarks, creating a rectangular region with cells marked for coarsening.

The Invert operation can only be used with mask registers. It toggles themask markings: all cells marked ACTIVE are switched to INACTIVE,and all cells marked INACTIVE are switched to ACTIVE. For example,if you generate a mask that defines a circular region, you can quicklymodify the mask to define the region outside of the circle using theInvert operation.

The Limit operation applies the present adaption volume limit to theselected adaption register. (For information on adaption limits, see Sec-tion 23.10.) Commonly, you would use this operation to determine theeffect of the present limits on the adaption process. You can use thevolume limit to create a more uniform mesh by setting the limit to refine


Grid Adaption

only large cells. After all the cells have reached a uniform size, you cancontinue the refinement process to the desired resolution.

Finally, the Fill operation marks for coarsening all cells in the adaptionregister that are not marked for refinement. You may want to use the Filloperation if you are combining multiple registers to make a new register.When you combine registers, a cell will be marked for coarsening only if itis marked for coarsening in all of the registers. If you create an adaptionregister with an operation that only marks cells for refinement, but youdo not want to prohibit coarsening, you should use the Fill operationbefore combining the register with any other registers.

The steps for modifying adaption marks are as follows:


2. Click on the Exchange, Invert, Limit, or Fill button under MarkActions.

23.9.3 Displaying Registers

Viewing the cell markings is often helpful in the process of creatinghybrid adaption functions. You can plot a marker at the cell centroidand/or a wireframe of the cell to view the state of the cell. By default,the cells marked for refinement are colored in red, and the cells markedfor coarsening are marked in cyan. In addition, cells marked ACTIVE ina mask register are also colored red. These are the cells that are markedfor adaption, but the final number of cells added or subtracted from thegrid will depend on the adaption limits and the grid characteristics.

To display a register, follow these steps:

1. Choose the register in the Registers list.

2. If desired, set any of the display options described below by clickingon the Options... button.

3. Click on the Display button.



Adaption Display Options

Various aspects of the adaption register display can be modified, suchas the wireframe visibility and shading, marker visibility, color, size, andsymbol, and whether surface or zone grids are drawn with the display.

The adaption register display capability allows you to view the cells thatare flagged for adaption. Depending on the dimension of the problemand the number of flagged cells, you may wish to customize the adaptiondisplay options. For instance, a common method for viewing flagged cellsin 2D is to draw the grid and filled wireframes, but this is impractical in3D. In three dimensions, you may want to plot the centroid markers ofthe cells with the grid of selected boundary zones.

You can display the flagged cells in an adaption or mask register, usingmarkers and/or wireframes. The marker is a symbol placed at the cen-troid of the cell. There is a refine marker and a coarsen marker. Youcan change the symbol, color, and size of these markers. A wireframeis composed of the edges of the triangle or tetrahedron. Its color is thesame as the respective marker color, and it can be filled, if desired.

Finally, portions of the grid can be drawn with the marker symbols orwireframes to aid in evaluating the location of marked cells.

All of these options are set in the Adaption Display Options panel (Fig-ure 23.9.2).

Adapt −→Display Options...

(You can also open this panel by clicking on the Options... button in theManage Adaption Registers panel.)

• To enable or disable the display of wireframes for cells marked forrefinement/coarsening, turn the Wireframe option on or off underRefine and/or Coarsen. To draw filled wireframes (i.e., using a solidcolor, instead of the outline) turn on the Filled option.

• To enable or disable the display of markers for cells marked for re-finement/coarsening, turn the Marker option on or off under Refineand/or Coarsen. If you use markers, you can specify their size inthe Size field, and their symbol in the Symbol drop-down list.


Grid Adaption

Figure 23.9.2: The Adaption Display Options Panel

• To change the color of the refine or coarsen markers/wireframes, se-lect a new color in the Color drop-down list under Refine or Coarsen.By default, refine markers/wireframes are red and coarsen mark-ers/wireframes are cyan.

• To include portions of the grid in the register display, enable theDraw Grid option. The Grid Display panel will appear automatically,and you can set the grid display parameters there. When you clickon Display in the Manage Adaption Registers panel, the grid display,as defined in the Grid Display panel, will be included in the registerdisplay.

23.9.4 Adapting to Registers

The primary objective is to adapt the grid to efficiently increase the ac-curacy of the solution. These register tools provide you with the abilityto create hybrid adaption functions customized to your flow-field appli-cation. Finally, the customized adaption function is used to direct therefinement and coarsening of the grid.


23.10 Grid Adaption Controls

To perform the adaption, follow these steps:

1. Choose the register in the Registers list.

2. Click on the Adapt button.


FLUENT allows you to change the adaption type from hanging node toconformal, or place restrictions on the cell zones, the size of cells thatcan be adapted, and the total number of cells that can be producedfrom the adaption process. You can also modify the intensity of thevolume weighting in the gradient function, restrict the adaption processto refinement and/or coarsening, and control which nodes are eligible forpossible elimination from the grid during conformal coarsening.

All parameters controlling these aspects of adaption are set in the GridAdaption Controls panel (Figure 23.10.1).

Adapt −→Controls...

Figure 23.10.1: The Grid Adaption Controls Panel

(You can also open this panel by clicking on the Controls... button inany of the adaption panels.)


Grid Adaption

Recall that it is highly recommended that you write a case and data file!before starting the adaption process. Then, if you generate an undesir-able grid, you can restart the process with the saved files.

Controlling the Type of Adaption

You can choose to use hanging node or conformal adaption. You can alsorestrict the adaption process to the addition of grid resolution throughrefinement and/or the removal of grid density through coarsening.

• To use hanging node adaption (the default), select Hanging in theType frame, and to use conformal adaption, select Conformal. Thehanging node and conformal adaption procedures are described indetail in Section 23.2.

• To enable/disable refinement, turn the Refine option on or off.

• To enable/disable coarsening, turn the Coarsen option on or off.

Limiting Adaption By Zone

You can limit the adaption process to specified cell zones. The cellscomposing the fluid and solid regions of the analysis generally have verydifferent resolution requirements and error indicators. By limiting theadaption to a specific cell zone, you can use different adaption functionsto create the optimal grid.

To limit the adaption to a particular cell zone (or to particular cell zones),select the cell zones in which you want to perform adaption in the Zoneslist. By default, adaption will be performed in all cell zones.

Limiting Adaption By Cell Volume or Volume Weight

The minimum cell volume limit restricts the refinement process to cellswith volumes greater than the limit. You can use this to initiate therefinement process on larger cells, gradually reducing the limit to createa uniform cell size distribution. Set this limit in the Min Cell Volumefield.



In addition, the gradient volume weight can be modified. A value of zeroeliminates volume weighting, a value of unity uses the entire volume, andvalues between 0 and 1 scale the volume weighting. Set this value in theVolume Weight field. For more information, see Section 23.4.1.

Limiting the Total Number of Cells

The maximum number of cells is a restriction that prevents FLUENTfrom creating more cells than you consider appropriate for the presentanalysis. In addition, it saves you the time you might have spent waitingfor the grid adaption process to complete the creation of these cells, whichcould be substantial if you saturate your computer memory resources.This premature termination of the refinement process can, however, pro-duce undesirable grid quality depending on the order in which the cellswere visited. The order of visitation is based on the cell arrangement inmemory, which in general can be quite random.

You can set the total number of cells allowed in the grid in the Max #of Cells field. The default value of zero places no limits on the numberof cells.

Controlling Node Removal During Conformal Coarsening

You can control the removal of nodes during coarsening by modifyingthe node removal flags. The node removal flags control which nodesare eligible for possible elimination from the grid. (The node removalflags apply to conformal adaption only. For hanging node adaption, onlyrefinement nodes can be removed during coarsening, and they are alwaysremoved.)

Nodes introduced by refinement are called refinement nodes, and nodesthat existed in the mesh before refinement are called original nodes.FLUENT maintains a section in the case file with the node flags. If thissection doesn’t exist (i.e., when you first read a grid), it identifies allnodes as original nodes. In addition, it also distinguishes between nodeson boundary, internal, and periodic zones for both original nodes andnodes created by adaptive refinement.

To guarantee that the original shape of the domain boundaries is main-


Grid Adaption

tained, usually only nodes introduced by refinement are removed. Forexample, consider the grid of a rectangular domain. If one of the nodeson the edges of the rectangle is removed the shape is not modified, butif one of the corner nodes of the rectangle is eliminated, the shape ischanged from a quadrilateral to a pentagon.

You can, however, modify this default behavior by changing the noderemoval flags. The most common modification is to allow the removalof original internal nodes. Removing internal nodes does not destroythe shape of the boundary. In fact, it can be very helpful if the initialgrid has substantial resolution in a region with minor or no changes inphysical features.

As mentioned before, removing original boundary or periodic nodes can!alter shape, and in some instances may even destroy topology, producinga worthless grid. Therefore, exercise extreme discretion when removingoriginal boundary and periodic nodes. As always, it is recommendedthat you write a case and data file before starting the adaption process.Then, if you generate an undesirable grid, you can restart the processwith the saved files.

By default, only the removal of refinement nodes is allowed, as indicatedby the enabled status of Boundary - Refined, Internal - Refined, and Pe-riodic - Refined and the disabled status of Boundary - Original, Internal -Original, and Periodic - Original in the Grid Adaption Controls panel. Ifyou want to disable the removal of these types of nodes, you can do so byturning off the associated check button. Similarly, if you want to enabletheir removal, turn on the associated check button.

23.11 Improving the Grid by Smoothing and Swapping

Smoothing and face swapping are tools that complement grid adaption,usually increasing the quality of the final numerical mesh. Smoothingrepositions the nodes and face swapping modifies the cell connectivity toachieve these improvements in quality.

Face swapping is applicable only to grids with triangular or tetrahedral!cells.



Smoothing and swapping are performed using the Smooth/Swap Gridpanel (Figure 23.11.1).

Adapt −→Smooth/Swap...

Figure 23.11.1: The Smooth/Swap Grid Panel

23.11.1 Smoothing

Two smoothing methods are available in FLUENT: Laplace smoothingand skewness-based smoothing. The first can be applied to all types ofgrids, but the second is available only for triangular/tetrahedral meshes.

For triangular and tetrahedral grids, it is recommended that you always!use the skewness-based smoothing method; reserve the Laplacian methodonly for quadrilateral and hexahedral grids.

Laplacian Smoothing

When you use the Laplace method, a Laplacian smoothing operator isapplied to the unstructured grid to reposition nodes. The new nodeposition is the average of the positions of its node neighbors. The re-laxation factor (a number between 0.0 and 1.0) multiplies the computed


Grid Adaption

node position increment. A value of zero results in no movement of thenode and a value of unity results in movement equivalent to the entirecomputed increment. Figure 23.11.2 illustrates the new node positionfor a typical configuration of quadrilateral cells.

Figure 23.11.2: Result of Smoothing Operator on Node Position (dashedline is original grid and solid line is final grid)

This repositioning strategy tends to improve the skewness of the mesh,but usually relaxes the clustering of node points. In extreme circum-stances, the present operator may create grid lines that cross over theboundary, creating negative cell volumes. This is most likely to occurnear sharp or coarsely resolved convex corners, especially if you per-form multiple smoothing operations with a large relaxation factor. Fig-ure 23.11.3 illustrates an initial tetrahedral grid before one unrelaxedsmoothing iteration creates grid lines that cross over each other (Fig-ure 23.11.4).



Figure 23.11.3: Initial Grid Before Smoothing Operation

Figure 23.11.4: Grid Smoothing Can Cause Grid-Line Crossing


Grid Adaption

The default smoothing parameters are designed to improve grid qualitywith minimal adverse effects, but you should always take the precautionof saving a case file before you smooth your mesh. If you apply a con-servative relaxation factor and start with a good quality initial grid, thefrequency of failure due to smoothing is extremely low in two dimensions.However, corruption of the grid topology occurs much more frequentlyin three dimensions, particularly with tetrahedral grids. The skewness-based smoothing is recommended for triangular and tetrahedral grids.

The smoothing operator can also be applied repeatedly, but as the num-ber of smoothing sweeps increase, the node points have a tendency topull away from boundaries and the grid tends to lose any clusteringcharacteristics.

Steps for Laplacian Smoothing

To perform Laplacian smoothing, you will follow these steps:

1. In the Smooth/Swap Grid panel (Figure 23.11.1), select laplace inthe Method drop-down list under Smooth.

2. Set the factor by which to multiply the computed position incre-ment for the node in the Relaxation Factor field. The lower thefactor, the more reduction in node movement.

3. Specify the number of successive smoothing sweeps to be performedon the grid in the Number of Iterations field. The default value is4.

4. Click the Smooth button.

Skewness-Based Smoothing

When you use skewness-based smoothing, FLUENT applies a smoothingoperator to the grid, repositioning interior nodes to lower the maximumskewness of the grid. FLUENT will try to move interior nodes to improvethe skewness of cells with skewness greater than the specified “minimumskewness.” This process can be very time-consuming, so you should onlyperform smoothing on cells with high skewness. Improved results can



be obtained by smoothing the nodes several times. There are internalchecks that will prevent a node from being moved if moving it causesthe maximum skewness to increase, but it is common for the skewnessof some cells to increase when a cell with a higher skewness is beingimproved. Thus, you may see the average skewness increase while themaximum skewness is decreasing.

You should carefully consider whether the improvements to the mesh due!to a decrease in the maximum skewness are worth the potential increasein the average skewness. Performing smoothing only on cells with veryhigh skewness (e.g., 0.8 or 0.9) may lessen the adverse effects on theaverage skewness.

Skewness-based smoothing is available only for triangular and tetrahe-!dral grids.

Steps for Skewness-Based Smoothing

To perform skewness-based smoothing, you will follow these steps:

1. In the Smooth/Swap Grid panel (Figure 23.11.1), select skewness inthe Method drop-down list under Smooth.

2. Set the minimum cell skewness value for which node smoothingwill be attempted in the Minimum Skewness field. FLUENT willtry to move interior nodes to improve the skewness of cells withskewness greater than this value. By default, Minimum Skewnessis set to 0.4 for 2D and 0.8 for 3D.

3. Specify the number of successive smoothing sweeps to be performedon the grid in the Number of Iterations field. The default value is4.

4. Click the Smooth button.

Skewness-based smoothing should be alternated with face swapping (seeSection 23.11.3).


Grid Adaption

23.11.2 Face Swapping

Face swapping can be used to improve the quality of a triangular ortetrahedral grid.

Triangular Grids

The approach for triangular grids is to use the Delaunay circle test todecide if a face shared by two triangular cells should be swapped. A pairof cells sharing a face satisfies the circle test if the circumcircle of one celldoes not contain the unshared node of the second cell. Figure 23.11.5illustrates cell neighbors that do and do not satisfy the circle test. Incases where the circle test is not satisfied, the diagonal or face is swapped,as illustrated in Figure 23.11.6.

Figure 23.11.5: Examples of Cell Configurations That Satisfy and DoNot Satisfy the Circle Test



Figure 23.11.6: The Face is Swapped to Satisfy the Delaunay Circle Test

Repeated application of the face-swapping technique will produce a con-strained Delaunay mesh. If a grid is a Delaunay grid, it is a unique tri-angulation that maximizes the minimum angles in the mesh. Thus, thetriangulation tends towards equilateral cells, providing the most equi-lateral grid for the given node distribution. (See the Theory chapterin the TGrid User’s Guide for more information about Delaunay meshgeneration.)

Tetrahedral Grids

For tetrahedral grids, face swapping consists of searching for config-urations of three cells sharing an edge and converting them into twocells sharing a face to decrease skewness and the cell count. (See Fig-ure 23.11.7.)

Figure 23.11.7: 3D Face Swapping


Grid Adaption

Steps for Face Swapping

To perform face swapping, simply click on the Swap button until thereported Number Swapped is 0. The Number Visited indicates the totalnumber of faces that were visited and tested for possible face swapping.

23.11.3 Combining Skewness-Based Smoothing and FaceSwapping

As mentioned in Section 23.11.1, skewness-based smoothing should usu-ally be alternated with face swapping. Guidelines for this procedure arepresented here.

1. Perform 4 smoothing iterations using a Minimum Skewness of 0.8for 3D, or 0.4 for 2D.

2. Swap until the Number Swapped decreases to 0.

3. For 3D grids, decrease the Minimum Skewness to 0.6 and repeatthe smoothing/swapping procedure.


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