Abstract
A simple strategy for generating anisotropic meshes is introduced. The approach belongs to the class of metric-based mesh adaptation procedures where a field of metric tensors governs the adaptation. This development is motivated by the need of generating anisotropic meshes for complex geometries and complex flows. The procedure may be used advantageously for cases where global remeshing techniques become either unfeasible or unreliable. Each of the local operations used is checked in a variety of ways by taking into account both the volume and the surface mesh. This strategy is illustrated with surface mesh adaptation and with the generation of meshes suited for boundary layers analysis.
Two simple mesh operators are used to recursively modify the mesh: edge collapse and point insertion on edge. It is shown that using these operators jointly with a quality function allows to quickly produce an quality anisotropic mesh. Each adaptation entity, ie surface, volume or boundary layers, relies on a specific metric tensor field. The metric-based surface estimate is used to control the deviation to the surface and to adapt the surface mesh. The volume estimate aims at controlling the interpolation error of a specific field of the flow. The boundary layers metric-based estimate is deduced from a level-set distance function.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alauzet, F.: Size gradation control of anisotropic meshes. Finite Elements in Analysis and Design (2009) (Published online)
Alauzet, F., Frey, P.J., George, P.-L., Mohammadi, B.: 3D transient fixed point mesh adaptation for time-dependent problems: Application to CFD simulations. J. Comp. Phys. 222, 592–623 (2007)
Arsigny, V., Fillard, P., Pennec, X., Ayache, N.: Log-Euclidean metrics for fast and simple calculus on diffusion tensors. Magnetic Resonance in Medicine 56(2), 411–421 (2006)
Baker, T.: Three-dimensional mesh generation by triangulation of arbitrary point sets. AIAA Paper, 87-1124 (1987)
Baum, J.D., Löhner, R.: Numerical simulation of pilot/seat ejection from an F-16. AIAA Paper, 93-0783 (1993)
Baum, J.D., Luo, H., Löhner, R.: Numerical simulation of blast in the world trade center. AIAA Paper, 95-0085 (1995)
Berger, M.: A panoramic view of Riemannian geometry. Springer, Berlin (2003)
Borouchaki, H., Hecht, F., Frey, P.J.: Mesh gradation control. Int. J. Numer. Meth. Engrg. 43(6), 1143–1165 (1998)
Bottasso, C.L.: Anisotropic mesh adaption by metric-driven optimization. Int. J. Numer. Meth. Engng. 60, 597–639 (2004)
Castro-DĂaz, M.J., Hecht, F., Mohammadi, B., Pironneau, O.: Anisotropic unstructured mesh adaptation for flow simulations. Int. J. Numer. Meth. Fluids 25, 475–491 (1997)
Chen, L., Sun, P., Xu, J.: Optimal anisotropic simplicial meshes for minimizing interpolation errors in L p-norm. Math. Comp. 76(257), 179–204 (2007)
do Carmo, M.: Differential geometry of curves and surfaces. Prentice-Hall, Englewood Cliffs (1976)
Dobrzynski, C., Frey, P.J.: Anisotropic delaunay mesh adaptation for unsteady simulations. In: Proc. of 17th Int. Meshing Rountable, pp. 177–194. Springer, Heidelberg (2008)
Dompierre, J., Vallet, M.G., Fortin, M., Bourgault, Y., Habashi, W.G.: Anisotropic mesh adaptation: towards a solver and user independent cfd. AIAA Paper, 97-0861 (1997)
Frey, P.J., Borouchaki, H.: Surface meshing using a geometric error estimate. Int. J. Numer. Methods Engng. 58(2), 227–245 (2003)
Frey, P.J.: About surface remeshing. In: Proc. of 15th Meshing Rountable 15, pp. 123–136. Springer, Heidelberg (2000)
Frey, P.J., George, P.-L.: Mesh generation. Application to finite elements, 2nd edn. ISTE Ltd and John Wiley & Sons (2008)
George, P.L., Borouchaki, H.: Delaunay triangulation and meshing: application to finite elements. Hermès Science, Paris (1998)
George, P.L., Hecht, F., Saltel, E.: Fully automatic mesh generator for 3d domains of any shape. Impact of Comuting in Science and Engineering 2, 187–218 (1990)
Hecht, F., Mohammadi, B.: Mesh adaptation by metric control for multi-scale phenomena and turbulence. AIAA Paper, 97-0859 (1997)
Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.: Optimization by simulated annealing. Science 220(4598), 671–680 (1983)
Li, X., Remacle, J.-F.: Anisotropic mesh gradation control. In: Proc. of 13th Meshing Rountable, Williamsburg, VA, USA (2004)
Löhner, R.: Regridding surface triangulations. J. Comp. Phys. 126, 1–10 (1996)
Löhner, R.: Renumbering strategies for unstructured-grid solvers operating on shared-memory, cache-based parallel machines. Comput. Meth. Appl. Mech. Engrg. 163, 95–109 (1998)
Löhner, R.: Generation of unstructured grids suitable for RANS calculations. AIAA Paper, 99-0662 (1999)
Löhner, R.: Applied CFD techniques. Wiley, New-York (2001)
Löhner, R.: Generation of viscous grids with ridges and corners. AIAA Paper, 07-3832 (2007)
Löhner, R., Parikh, P.: Three-dimensionnal grid generation by the advancing-front method. Int. J. Numer. Meth. Fluids 8(8), 1135–1149 (1988)
Loseille, A.: Adaptation de maillage 3D anisotrope multi-échelles et ciblé à une fonctionnelle. Application à la prédiction haute-fidélité du bang sonique. PhD thesis, Université Pierre et Marie Curie, Paris VI, Paris, France (2008)
Loseille, A., Alauzet, F.: Continuous mesh model and well-posed continuous interpolation error estimation. RR-6846, INRIA (2009)
Loseille, A., Alauzet, F., Dervieux, A., Frey, P.J.: Achievement of second order mesh convergence for discontinuous flows with adapted unstructured mesh adaptation. AIAA Paper, 07-4186 (2007)
Marcum, D.L.: Adaptive unstructured grid generation for viscous flow applications. AIAA Journal 34(8), 2440–2443 (1996)
Marcum, D.L.: Efficient generation of high-quality unstructured surface and volume grids. Engrg. Comput. 17, 211–233 (2001)
Mavriplis, D.J.: An advancing front delaunay triangulation algorithm designed for robustness. J. Comp. Phys. 117, 90–101 (1995)
Pain, C.C., Umpleby, A.P., de Oliveira, C.R.E., Goddard, A.J.H.: Tetrahedral mesh optimisation and adaptivity for steady-state and transient finite element calculations. Comput. Meth. Appl. Mech. Engrg. 190, 3771–3796 (2001)
Park, M.A.: Adjoint-based, three-dimensional error prediction and grid adaptation. AIAA Paper 42(9), 1854–1862 (2006)
Peraire, J., Vahdati, M., Morgan, K., Zienkiewicz, O.C.: Adaptive remeshing for compressible flow computations. J. Comp. Phys. 72, 449–466 (1987)
Ramamurti, R., Löhner, R.: Simulation of flow past complex geometries using a parallel implicit incompressible flow solver. AIAA Paper, CP-933 (1993)
Schall, E., Leservoisier, D., Dervieux, A., Koobus, B.: Mesh adaptation as a tool for certified computational aerodynamics. Int. J. Numer. Meth. Fluids 45, 179–196 (2004)
Sethian, S.: Level-set methods and fast marching methods. Cambridge University Press, Cambridge (1999)
Tam, A., Ait-Ali-Yahia, D., Robichaud, M.P., Moore, M., Kozel, V., Habashi, W.G.: Anisotropic mesh adaptation for 3D flows on structured and unstructured grids. Comput. Meth. Appl. Mech. Engrg. 189, 1205–1230 (2000)
Vallet, M.-G., Manole, C.-M., Dompierre, J., Dufour, S., Guibault, F.: Numerical comparison of some hessian recovery techniques. Int. J. Numer. Meth. Engrg. 72, 987–1007 (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Loseille, A., Löhner, R. (2009). On 3D Anisotropic Local Remeshing for Surface, Volume and Boundary Layers. In: Clark, B.W. (eds) Proceedings of the 18th International Meshing Roundtable. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04319-2_35
Download citation
DOI: https://doi.org/10.1007/978-3-642-04319-2_35
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04318-5
Online ISBN: 978-3-642-04319-2
eBook Packages: EngineeringEngineering (R0)