anisotropic mesh adaptation by mesh modification

This paper describes an effective anisotropic mesh adaptation procedure for general 3D geometries using mesh modification operations. The procedure consists of four interacted high level components: refinement, coarsening, projecting boundary vertices and shape correction. All components are governed by an anisotropic mesh metric field that represents the desired element size and shape distribution. The paper presents the application for the procedure in anisotropic adaptive 3D simulations. 2005 Elsevier B.V. All rights reserved.

[1]  A. Liu,et al.  On the shape of tetrahedra from bisection , 1994 .

[2]  Mark S. Shephard,et al.  Parallel refinement and coarsening of tetrahedral meshes , 1999 .

[3]  Paul-Louis George,et al.  Optimization of Tetrahedral Meshes , 1995 .

[4]  Mark S. Shephard,et al.  a General Topology-Based Mesh Data Structure , 1997 .

[5]  Adrian Bowyer,et al.  Computing Dirichlet Tessellations , 1981, Comput. J..

[6]  J. Bey,et al.  Tetrahedral grid refinement , 1995, Computing.

[7]  Raúl A. Feijóo,et al.  Adaptive finite element computational fluid dynamics using an anisotropic error estimator , 2000 .

[8]  M. Fortin,et al.  Anisotropic mesh adaptation: towards user‐independent, mesh‐independent and solver‐independent CFD. Part II. Structured grids , 2002 .

[9]  Mark S. Shephard,et al.  On Anisotropic Mesh Generation and Quality Control in Complex Flow Problems , 2001, IMR.

[10]  Joseph M. Maubach,et al.  Local bisection refinement for $n$-simplicial grids generated by reflection , 2017 .

[11]  F. Bornemann,et al.  Adaptive multivlevel methods in three space dimensions , 1993 .

[12]  T. Hughes,et al.  Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations , 1990 .

[13]  P. George,et al.  Delaunay mesh generation governed by metric specifications. Part I algorithms , 1997 .

[14]  Peter Hansbo,et al.  On advancing front mesh generation in three dimensions , 1995 .

[15]  Michael L. Accorsi,et al.  Parachute fluid-structure interactions: 3-D computation , 2000 .

[16]  C.R.E. de Oliveira,et al.  Tetrahedral mesh optimisation and adaptivity for steady-state and transient finite element calculations , 2001 .

[17]  Martin Berzins,et al.  A 3D UNSTRUCTURED MESH ADAPTATION ALGORITHM FOR TIME-DEPENDENT SHOCK-DOMINATED PROBLEMS , 1997 .

[18]  B. Joe,et al.  Relationship between tetrahedron shape measures , 1994 .

[19]  Kenneth E. Jansen,et al.  A stabilized finite element method for the incompressible Navier–Stokes equations using a hierarchical basis , 2001 .

[20]  Douglas N. Arnold,et al.  Locally Adapted Tetrahedral Meshes Using Bisection , 2000, SIAM Journal on Scientific Computing.

[21]  Mark T. Jones,et al.  Adaptive refinement of unstructured finite-element meshes , 1997 .

[22]  William H. Beyer,et al.  CRC standard mathematical tables , 1976 .

[23]  J. Peiro,et al.  Adaptive remeshing for three-dimensional compressible flow computations , 1992 .

[24]  Eberhard Bänsch,et al.  Local mesh refinement in 2 and 3 dimensions , 1991, IMPACT Comput. Sci. Eng..

[25]  Gustavo C. Buscaglia,et al.  Anisotropic mesh optimization and its application in adaptivity , 1997 .

[26]  J. Remacle,et al.  Anisotropic adaptive simulation of transient flows using discontinuous Galerkin methods , 2005 .

[27]  Mark S. Shephard,et al.  Accounting for curved domains in mesh adaptation , 2003 .