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3D Navier3D Navier--Stokes Cutcell solver for Octree MeshesStokes Cutcell solver for Octree MeshesL. Bretonnet, Y. Li and C. HirschL. Bretonnet, Y. Li and C. Hirsch
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1Academy Colloquium on Immersed Boundary Methods. Amsterdam, 15-17 June 2009
OutlineOutline
1. Mesh generation process
2. Flow solver
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3. Validation test cases
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2Academy Colloquium on Immersed Boundary Methods. Amsterdam, 15-17 June 2009
Octree Mesh GenerationOctree Mesh Generation
The initial Octree mesh is generatedi H TMusing Hexpress .
The mesh covers the entire domain.The refinement is based either on a cell
size objective or on the surface curvature
TM
size objective or on the surface curvature.
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3Academy Colloquium on Immersed Boundary Methods. Amsterdam, 15-17 June 2009
Cutcell computationCutcell computation
• Detect cells intersecting the surface and store list ofintersecting triangles
• Using a seed point and a painting algorithm, detect cellsthat are entirely in the solid/fluid part of the domain.
C t i t ti f C t i ll ith f t i l• Compute intersection of Cartesian cell with surface triangles using polygon clipping algorithm. (Sutherland, Hogdman,1974)
• Compute “fluid” faces of the cutcell.
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.com • Build cutcell by grouping connected polygons.
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agglomerated with one of their neighbor.• Link neighbor cutcell faces
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Link neighbor cutcell faces.
Academy Colloquium on Immersed Boundary Methods. Amsterdam, 15-17 June 2009
Flow SolverFlow Solver
Spatial discretizationSolve compressible Navier-Stokes equationsCell-centered conservative finite-volume discretizationCell centered conservative finite volume discretizationInviscid fluxes discretized using JST or Roe schemeViscous fluxes purely centrally discretized
Time stepping and convergence accelerationExplicit 4-stage Runge-Kutta schemeLocal time-stepping
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pp gEfficient agglomeration multigrid, FMG (agglomeration)
Gradient computation
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pAt cell center using least-squareAt fluid face center as the average of neighboring cells gradientAt boundary face center using Green-Gauss.
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5Academy Colloquium on Immersed Boundary Methods. Amsterdam, 15-17 June 2009
Flow SolverFlow Solver
Cartesian solver optimizationCutcell faces are treated in an unstructured way using face-cell
connectivity, with optimization due to their x,y,z direction.connectivity, with optimization due to their x,y,z direction.Fluid cells are Cartesian. Finite difference formulas are used
whenever possible to accelerate the computation.Special treatment is needed for faces between cutcell and fluid p
cell to ensure conservation.
Pressure reconstruction
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The pressure at solid walls is reconstructed using the gradient in the cutcell center.
This is done to ensure correct pressure variation along the solid
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6Academy Colloquium on Immersed Boundary Methods. Amsterdam, 15-17 June 2009
Supersonic wedgeSupersonic wedge
15= oαInitial configuration :
318921
1000002
−
==
mkg
PaPM
ρ .1892.1= mkgρ
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2D wedge, Euler flow, Pressure field
Initial Cartesian mesh : 90x60
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7Academy Colloquium on Immersed Boundary Methods. Amsterdam, 15-17 June 2009
Supersonic wedgeSupersonic wedge
Pressure
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8Academy Colloquium on Immersed Boundary Methods. Amsterdam, 15-17 June 2009
Supersonic wedgeSupersonic wedge
Mach number
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9Academy Colloquium on Immersed Boundary Methods. Amsterdam, 15-17 June 2009
Subsonic cylinderSubsonic cylinderOUTLET
20=M
Initial configuration :
3. 1892.1
1000002.0
−=
==
mkg
PaPM
ρ
INLE
T
OU
TLET
OUTLET
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64 cells along the cylinder
Academy Colloquium on Immersed Boundary Methods. Amsterdam, 15-17 June 2009
Subsonic cylinderSubsonic cylinder
Pressure coefficient along the surface
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Coarse mesh Fine mesh
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Coarse mesh64 cells along the cylinder 128 cells along the cylinder
Academy Colloquium on Immersed Boundary Methods. Amsterdam, 15-17 June 2009
NACA 0012 profileNACA 0012 profile
M=0.8, Roe scheme, Venkatakrishnan limiters
o3=α
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Coarse mesh Fine mesh
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12Academy Colloquium on Immersed Boundary Methods. Amsterdam, 15-17 June 2009
NACA NACA 0012 0012 profileprofile
Mach number along the profile
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Coarse mesh Fine mesh
Academy Colloquium on Immersed Boundary Methods. Amsterdam, 15-17 June 2009
Laminar flat plateLaminar flat plate
OUTLET
Initial configuration :
INLE
T
1000002.0
==
PaPM
Initial configuration :
8400Re. 1892.1
1000003
≈=
=−mkg
PaP
ρ
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MIRROR SOLID
Boundary layer resolution :
X=0 X=0.7
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Coarse mesh (3 level of refinement) : 5 pointsAverage mesh (4 level of refinement) : 10 points
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Average mesh (4 level of refinement) : 10 pointsFine mesh (5 level of refinement) : 15 points
Academy Colloquium on Immersed Boundary Methods. Amsterdam, 15-17 June 2009
Laminar flat plateLaminar flat plate
Results for JST schemeResults for JST schemeFine mesh
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15Academy Colloquium on Immersed Boundary Methods. Amsterdam, 15-17 June 2009
Laminar flat plateLaminar flat plate
Results for Roe schemeResults for Roe schemeAverage mesh
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16Academy Colloquium on Immersed Boundary Methods. Amsterdam, 15-17 June 2009
Laminar flat plateLaminar flat plate
Skin frictionSkin friction
JST Roe
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17Academy Colloquium on Immersed Boundary Methods. Amsterdam, 15-17 June 2009
Laminar inclined plateLaminar inclined plate
OUTLET
LET
INL
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6 levels of refinement15829 cells
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Re = 728015 points inside the boundary layer
Academy Colloquium on Immersed Boundary Methods. Amsterdam, 15-17 June 2009
Laminar inclined plateLaminar inclined plate
Results for JST schemeResults for JST scheme
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19Academy Colloquium on Immersed Boundary Methods. Amsterdam, 15-17 June 2009
Laminar inclined plateLaminar inclined plate
Results for Roe schemeResults for Roe scheme
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20Academy Colloquium on Immersed Boundary Methods. Amsterdam, 15-17 June 2009
Conclusion and perspectivesConclusion and perspectives
Conclusion A 3D Octree Cutcell mesh generator has been buildA 3D Octree Cutcell mesh generator has been buildA dedicated optimized solver has been implementedThe solver is validated for 2D Euler cases and the laminar flat plate
FutureNavier-Stokes validation on 2D cases
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Navier-Stokes validation on 2D casesValidation on 3D cases.Turbulence modelingImplicit residual smoothing
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PreconditioningLES
Example of 3D mesh : Pressure field for DLR F4
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Example of 3D mesh : Pressure field for DLR F4
Academy Colloquium on Immersed Boundary Methods. Amsterdam, 15-17 June 2009