Robust partial remeshing strategy for position management and body motion in CFD simulationsSimone Gremmoa , Vladimir Gaelb , Jean-François Remaclec , Charles Hirschb , Grégory Coussementa

MotivationIn recent years, the evolution of Computational Fluid Dynamics (CFD) techniques has increased the number of applications where the numerical analysis can be applied [1]; thanks to the growth of the available computing power, it is now possible to simulate unsteady flows around complex geometries, to optimize aerodynamic performances and to investigate fluid-structure interactions. The time spent for the actual simulation is often equivalent or even smaller than the time required in the pre-processing phase, when the computational domain is defined and the computational grid is created. This last step is crucial for the accuracy of the results, imposing many constraints on the size and “quality” of the mesh cells that are used for domain discretization.The present work presents a robust and flexible partial remeshing strategy suitable when the generation of the computational grid becomes a recursive process:● insertion of the same geometry at different location in the computational domain (e.g. wind turbines in a wind farm), ● optimization studies where geometry is modify locally (e.g. atmospheric dispersion for different wind directions in urban area)● moving bodies inside the computational domain (e.g. booster separation from space-launch vehicle)

Strategy Implementation1)Mark vertices in the overlap region

Octree leaves are filled with the background-mesh verticesOctree boxes intersecting with and inside the moving mesh “envelope” are markedBackground-mesh vertices inside the boxes selected at previous step are marked

2)Mark cells that share the vertices marked at step 13)Remove cells from background mesh4)Create the “stitching mesh” in the gap between “envelope” and “interface” surfaces

GMSH is used to build the stitching mesh5)Optimize the stitching mesh6)Merge the three meshes: background mesh, moving mesh and stitching mesh

ResultsWe focus our attention on a moving-body test case. A sphere with diameter D is moved in the computational domain with an imposed trajectory (75 time steps). The background mesh is chosen to be a cylinder of radius = 7D and height=28D; the moving mesh around the sphere is a parallelepiped with square base 3Dx3D and height 5.5D. Two configurations are analyzed:1)a coarse mesh suitable for simulating a laminar flow around a sphere (Re=40)2)a refined mesh suitable for simulating a turbulent flow around a sphere (Re=5 · 10 6 )

Stitching mesh – GMSHThe stitching mesh conformally connects the interface and the envelope surfaces. This region mostly contains tetrahedra, but some pyramids need to be added as a transitional layer between hexahedra and the tetrahedra. At first some ‘‘flat’’ pyramids are added and then inflated inside the domain.

1)Split all the quad-faces in 4 trianglesCalculate barycenter of the quad-faceTriangulate the quad

2)Mesh the region between the surfacesUse the newly triangulated surfaceDelaunay method is used

3)Inflate the ‘‘flat’’ pyramids4)Optimize the stitching mesh

Conclusions and ongoing developmentsFully automatic and flexible strategy that aims at reducing the time required for mesh generation when this involves repetitive operations.● The high-quality mesh elements around the the solid walls is conserved as long as possible● Mesh-generation computational cost is weakly related to the complexity of the geometry inside the moving meshes● This approach can handle hybrid meshes and is not limited to a specific cell topology● The quality and the number of elements in the resulting mesh are stable throughout the simulation● Limited region requiring an interpolation

● Smooth transition in cell sizes is required for the stitching mesh● Stitching mesh quality needs to be improved (valid cells, but some slivers may be present)

● Optimization of the gap size between the ‘‘interface’’ and the ‘‘envelope’’● Improve the pyramid insertion strategy

● Coupling with the solver needs to be finalized (ALE formulation, interpolation strategy)

Future improvements: add stitching-mesh deformation (number of remeshing is reduced)

Strategy overviewThe two goals are to minimize the region where the mesh needs to be reconstructed and to preserve a good mesh quality around the bodies

Partial remeshing strategy1)Generation of the background mesh2)Generation of the mesh around each moving object3)Detection for the overlap region between meshes4)Delete cells from background mesh in the overlap regions5)Insertion of the moving meshes into the background mesh with holes6)Generation of a conformal “stitching mesh” connection between the two meshes.

ToolsCFD tools by Numeca:● HEXPRESS/Hybrid (hexa-dominant volume-to-surface mesh generator)● FINE/Open (compressible/incompressible finite-volume solver)● GMSH (full-tetra surface-to-volume mesh generator)

Build octree Mark octree boxes

Mark vertices Mark cells to be removed

Laminar Test Case Turbulent Test CaseHigh Reynolds BL

Background mesh: 573,578 cells Moving mesh: 161,924 cells Background mesh: 1,594,591 cells Moving mesh: 12,698,310 cells

Resulting Mesh t = 1 Resulting Mesh t = 75 Resulting Mesh t = 1 Resulting Mesh t = 75

Stitching mesh does not depend on complexity of the geometry inside the moving mesh

No invalid cells are created throughout the process.Mesh quality remain constant for all time steps.

Small difference in cell-sizes: thin stitching mesh Bigger difference in cell-sizes: stitching mesh thicker

a: University of Mons, Belgium – b: Numeca Int., Belgium – c: Université catholique de Louvain, Belgium Corresponding author: email: simone.gremmo@umons.ac.be - Tel.: +32-65-374-509