Parallel anisotropic mesh adaptation with boundary layers for automated viscous flow simulations

This paper presents a set of parallel procedures for anisotropic mesh adaptation accounting for mixed element types used in boundary layer meshes, i.e., the current procedures operate in parallel on distributed boundary layer meshes. The procedures accept anisotropic mesh metric field as an input for the desired mesh size field and apply local mesh modifications to adapt the mesh to match/satisfy the specified mesh size field. The procedures fully account for the parametric geometry of curved domains and maintain the semi-structured nature of the boundary layer elements. The effectiveness of the procedures is demonstrated on three viscous flow examples that include the ONERA M6 wing, a heat transfer manifold, and a scramjet engine.

[1]  Robert M. O'Bara,et al.  Toward simulation-based design , 2004 .

[2]  J. Oden,et al.  A Posteriori Error Estimation in Finite Element Analysis: Oden/A Posteriori , 2000 .

[3]  J. Peraire,et al.  UNSTRUCTURED TETRAHEDRAL MESH GENERATION FOR THREE-DIMENSIONAL VISCOUS FLOWS , 1996 .

[4]  Bruce T. Murray,et al.  Approximation of Cahn–Hilliard diffuse interface models using parallel adaptive mesh refinement and coarsening with C1 elements , 2008 .

[5]  Onkar Sahni,et al.  Scalable implicit finite element solver for massively parallel processing with demonstration to 160K cores , 2009, Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis.

[6]  Viktoria Schmitt,et al.  Pressure distributions on the ONERA M6 wing at transonic Mach numbers , 1979 .

[7]  Onkar Sahni,et al.  Cardiovascular flow simulation at extreme scale , 2010 .

[8]  Mark S. Shephard,et al.  3D anisotropic mesh adaptation by mesh modification , 2005 .

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

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

[11]  S. Connell,et al.  Semistructured mesh generation for three-dimensional Navier-Stokes calculations , 1995 .

[12]  Rüdiger Verfürth,et al.  A posteriori error estimation and adaptive mesh-refinement techniques , 1994 .

[13]  Christina Freytag,et al.  Using Mpi Portable Parallel Programming With The Message Passing Interface , 2016 .

[14]  Rainald Löhner,et al.  Generation of non‐isotropic unstructured grids via directional enrichment , 2000 .

[15]  Rolf Rannacher,et al.  An optimal control approach to a posteriori error estimation in finite element methods , 2001, Acta Numerica.

[16]  Rainald Löhner,et al.  Adaptive h‐refinement on 3D unstructured grids for transient problems , 1992 .

[17]  Frédéric Alauzet,et al.  Parallel anisotropic 3D mesh adaptation by mesh modification , 2006, Engineering with Computers.

[18]  David L. Marcum,et al.  Generation of unstructured grids for viscous flow applications , 1995 .

[19]  Charles A. Taylor,et al.  Efficient anisotropic adaptive discretization of the cardiovascular system , 2006 .

[20]  Paul-Louis George,et al.  An efficient algorithm for 3D adaptive meshing , 2001 .

[21]  M. Giles,et al.  Adjoint methods for PDEs: a posteriori error analysis and postprocessing by duality , 2002, Acta Numerica.

[22]  Onkar Sahni,et al.  Neighborhood communication paradigm to increase scalability in large-scale dynamic scientific applications , 2012, Parallel Comput..

[23]  Alan M. Shih,et al.  Efficient Hybrid Surface/Volume Mesh Generation Using Suppressed Marching-Direction Method , 2013 .

[24]  Carlo L. Bottasso,et al.  A Procedure for Tetrahedral Boundary Layer Mesh Generation , 2002, Engineering with Computers.

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

[26]  Graham Coates,et al.  Rapid re-meshing and re-solution of three-dimensional boundary element problems for interactive stress analysis , 2012 .

[27]  Oh Joon Kwon,et al.  A parallel unstructured dynamic mesh adaptation algorithm for 3‐D unsteady flows , 2005 .

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

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

[30]  Frédéric Hecht,et al.  Anisotropic unstructured mesh adaption for flow simulations , 1997 .

[31]  Carl Ollivier-Gooch,et al.  Tetrahedral mesh improvement using swapping and smoothing , 1997 .

[32]  Yannis Kallinderis,et al.  A dynamic adaptation scheme for general 3-D hybrid meshes , 2005 .

[33]  David R. Owen,et al.  Performance comparisons of tree‐based and cell‐based contact detection algorithms , 2007 .

[34]  Godfried T. Toussaint,et al.  Tetrahedralization of Simple and Non-Simple Polyhedra , 1993, CCCG.

[35]  Timothy J. Tautges,et al.  Toward interoperable mesh, geometry and field components for PDE simulation development , 2007, Engineering with Computers.

[36]  Yannis Kallinderis,et al.  Hybrid grid generation for turbomachinery and aerospace applications , 2000 .

[37]  Kazuhiro Nakahashi,et al.  Unstructured Mesh Generation For Viscous Flow Computations , 2002, IMR.

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

[39]  Mark S. Shephard,et al.  Boundary layer mesh generation for viscous flow simulations , 2000 .

[40]  Jean-François Remacle,et al.  Anisotropic Mesh Gradation Control , 2004, IMR.

[41]  François Guibault,et al.  Proposal of Benchmarks for 3D Unstructured Tetrahedral Mesh Optimization , 2007 .

[42]  Y. Kallinderis,et al.  Adaptive refinement-coarsening scheme for three-dimensional unstructured meshes , 1993 .

[43]  Xiaolin Li,et al.  Enabling scalable parallel implementations of structured adaptive mesh refinement applications , 2007, The Journal of Supercomputing.

[44]  Mark S. Shephard,et al.  Mesh modification procedures for general 3d non-manifold domains , 2003 .

[45]  Xiangrong Li,et al.  Anisotropic adaptive finite element method for modelling blood flow , 2005, Computer methods in biomechanics and biomedical engineering.

[46]  Adrien Loseille,et al.  Robust Boundary Layer Mesh Generation , 2012, IMR.

[47]  J. Oden,et al.  A Posteriori Error Estimation in Finite Element Analysis , 2000 .

[48]  Yannis Kallinderis,et al.  Parallel adaptation of general three-dimensional hybrid meshes , 2010, J. Comput. Phys..

[49]  Pascal Frey,et al.  Anisotropic mesh adaptation for CFD computations , 2005 .

[50]  François Guibault,et al.  Benchmarks for 3D Unstructured Tetrahedral Mesh Optimization , 1998, IMR.

[51]  Mark S. Shephard,et al.  Efficient distributed mesh data structure for parallel automated adaptive analysis , 2006, Engineering with Computers.

[52]  Shahyar Pirzadeh,et al.  Unstructured Viscous Grid Generation by Advancing-Layers Method , 1993 .

[53]  Xin He,et al.  Applications of dynamic hybrid grid method for three-dimensional moving/deforming boundary problems , 2012 .

[54]  Frédéric Alauzet,et al.  On the use of anisotropic a posteriori error estimators for the adaptative solution of 3D inviscid compressible flows , 2009 .

[55]  Barry Joe,et al.  Construction of Three-Dimensional Improved-Quality Triangulations Using Local Transformations , 1995, SIAM J. Sci. Comput..

[56]  Onkar Sahni,et al.  Boundary Layer Adaptivity for Transonic Turbulent Flows , 2013 .

[57]  Onkar Sahni,et al.  Adaptive boundary layer meshing for viscous flow simulations , 2008, Engineering with Computers.

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

[59]  Tommy Minyard,et al.  Adaptive hybrid grid methods , 2000 .

[60]  Carlo L. Bottasso,et al.  Anisotropic mesh adaption by metric‐driven optimization , 2004 .

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

[62]  Oubay Hassan,et al.  Unstructured mesh methods for the solution of the unsteady compressible flow equations with moving boundary components , 2007, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[63]  Leonid Oliker,et al.  Parallel tetrahedral mesh adaptation with dynamic load balancing , 2013, Parallel Comput..