UNSTRUCTURED GRID TECHNIQUES

An overview of the current state of the art in unstructured mesh techniques for computational fluid dynamics is given. The topics of mesh generation and adaptation, spatial discretization, and solution techniques for steady flows are covered. Remaining difficulties in these areas are highlighted, and directions for future work are outlined.

[1]  Alain Dervieux,et al.  Unstructured multigridding by volume agglomeration: Current status , 1992 .

[2]  Dimitri J. Mavriplis,et al.  Implicit Solvers for Unstructured Meshes , 1993 .

[3]  Ted D. Blacker,et al.  Paving: A new approach to automated quadrilateral mesh generation , 1991 .

[4]  Paresh Parikh,et al.  A package for unstructured grid generation and finite element flow solvers , 1989 .

[5]  Dimitri J. Mavriplis,et al.  AGGLOMERATION MULTIGRID FOR THE THREE-DIMENSIONAL EULER EQUATIONS , 1994 .

[6]  S. Osher Riemann Solvers, the Entropy Condition, and Difference , 1984 .

[7]  Dimitri J. Mavriplis,et al.  Adaptive mesh generation for viscous flows using delaunay triangulation , 1990 .

[8]  Rainald Loehner,et al.  Matching semi-structured and unstructured grids for Navier-Stokes calculations , 1993 .

[9]  A. Jameson ANALYSIS AND DESIGN OF NUMERICAL SCHEMES FOR GAS DYNAMICS, 1: ARTIFICIAL DIFFUSION, UPWIND BIASING, LIMITERS AND THEIR EFFECT ON ACCURACY AND MULTIGRID CONVERGENCE , 1995 .

[10]  James R. Stewart,et al.  A point implicit unstructured grid solver for the euler and Navier–Stokes equations , 1989 .

[11]  T. Hughes,et al.  The Galerkin/least-squares method for advective-diffusive equations , 1988 .

[12]  V. Venkatakrishnan,et al.  A UNIFIED MULTIGRID SOLVER FOR THE NAVIER-STOKES EQUATIONS ON MIXED ELEMENT MESHES , 1995 .

[13]  Rainald Loehner,et al.  Adaptive edge-based finite element schemes for the Euler and Navier-Stokes equations on unstructured grids , 1993 .

[14]  Timothy J. Barth,et al.  Application of direct solvers to unstructured meshes for the Euler and Navier-Stokes equations using upwind schemes , 1989 .

[15]  Dimitri J. Mavriplis,et al.  MULTIGRID TECHNIQUES FOR UNSTRUCTURED MESHES , 1995 .

[16]  Philip L. Roe,et al.  Discrete models for the numerical analysis of time-dependent multidimensional gas dynamics , 1986 .

[17]  T. Barth,et al.  A one-equation turbulence transport model for high Reynolds number wall-bounded flows , 1990 .

[18]  Tiow Seng Tan,et al.  An O(n2 log n) Time Algorithm for the Minmax Angle Triangulation , 1992, SIAM J. Sci. Comput..

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

[20]  T. Barth Aspects of Unstructured Grids and Finite-Volume Solvers for the Euler and Navier-Stokes Equations , 1994 .

[21]  V. Venkatakrishnan,et al.  Parallel implicit unstructured grid Euler solvers , 1994 .

[22]  V. Venkatakrishnan On the accuracy of limiters and convergence to steady state solutions , 1993 .

[23]  P. Roe,et al.  A frontal approach for node generation in Delaunay triangulations , 1992 .

[24]  L. Paul Chew,et al.  Constrained Delaunay triangulations , 1987, SCG '87.

[25]  T. Chan,et al.  Domain decomposition algorithms , 1994, Acta Numerica.

[26]  K. Riemslagh,et al.  A multigrid method for steady Euler equations on unstructured adaptive grids , 1993 .

[27]  Dimitri J. Mavriplis,et al.  A 3D AGGLOMERATION MULTIGRID SOLVER FOR THE REYNOLDS-AVERAGED NAVIER-STOKES EQUATIONS ON UNSTRUCTURED MESHES , 1995 .

[28]  D. Mavriplis Multigrid solution of the two-dimensional Euler equations on unstructured triangular meshes , 1987 .

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

[30]  Neal T. Frink,et al.  Upwind Scheme for Solving the Euler Equations on Unstructured Tetrahedral Meshes , 1992 .

[31]  Mark E. Braaten,et al.  Three-Dimensional Unstructured Adaptive Multigrid Scheme for the Navier-Stokes Equations , 1996 .

[32]  J. T. Oden,et al.  Geometry based Delaunay tetrahedralization and mesh movement strategies for multi-body CFD , 1992 .

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

[34]  Marie-Pierre Leclercq,et al.  Résolution des équations d'Euler par des méthodes multigrilles : conditions aux limites en régime hypersonique , 1990 .

[35]  T. Hughes,et al.  MULTI-DIMENSIONAL UPWIND SCHEME WITH NO CROSSWIND DIFFUSION. , 1979 .

[36]  D. Mavriplis Three dimensional unstructured multigrid for the Euler equations , 1991 .

[37]  Robert E. Tarjan,et al.  Unstructured multigrid strategies on massively parallel computers: a case for integrated design , 1994, 1994 Proceedings of the Twenty-Seventh Hawaii International Conference on System Sciences.

[38]  P. George,et al.  Automatic mesh generator with specified boundary , 1991 .

[39]  O. Widlund Domain Decomposition Algorithms , 1993 .

[40]  William Gropp,et al.  Newton-Krylov-Schwarz Methods in CFD , 1994 .

[41]  Rainald Loehner,et al.  A new ALE adaptive unstructured methodology for the simulation of moving bodies , 1994 .

[42]  David E. Keyes,et al.  Application of Newton-Krylov methodology to a three-dimensional unstructured Euler code , 1995 .

[43]  W. K. Anderson,et al.  A grid generation and flow solution method for the Euler equations on unstructured grids , 1994 .

[44]  Jaime Peraire,et al.  An implicit finite element method for high speed flows , 1991 .

[45]  Nigel P. Weatherill,et al.  Calculation of steady compressible flowfields with the finite element method , 1993 .

[46]  B. Joe Three-dimensional triangulations from local transformations , 1989 .

[47]  Charles L. Lawson,et al.  Transforming triangulations , 1972, Discret. Math..

[48]  W. Mulder A new multigrid approach to convection problems , 1989 .

[49]  K. Morgan,et al.  An adaptive implicit/explicit finite element scheme for compressible viscous high speed flow , 1989 .

[50]  Thomas J. R. Hughes,et al.  A new finite element formulation for computational fluid dynamics: IV. A discontinuity-capturing operator for multidimensional advective-diffusive systems , 1986 .

[51]  N. Ron-Ho,et al.  A Multiple-Grid Scheme for Solving the Euler Equations , 1982 .

[52]  L. Fezoui,et al.  A class of implicit upwind schemes for Euler simulations with unstructured meshes , 1989 .

[53]  Yannis Kallinderis,et al.  Hybrid Prismatic/Tetrahedral Grid Generation for Viscous Flows Around Complex Geometries , 1996 .

[54]  Kazuhiro Nakahashi,et al.  FDM-FEM zonal method for viscous flow computations over multiple-bodies , 1987 .

[55]  Timothy Baker,et al.  Unstructured meshes and surface fidelity for complex shapes , 1991 .

[56]  C. Lawson Software for C1 Surface Interpolation , 1977 .

[57]  V. Venkatakrishnan Convergence to steady state solutions of the Euler equations on unstructured grids with limiters , 1995 .

[58]  Jean-Antoine Désidéri,et al.  Compressible flow solvers using unstructured grids , 1992 .

[59]  V. Venkatakrishnan,et al.  A PERSPECTIVE ON UNSTRUCTURED GRID FLOW SOLVERS , 1995 .

[60]  Dimitri J. Mavriplis,et al.  Accurate Multigrid Solution of the Euler Equations on Unstructured and Adaptive Meshes , 1988 .

[61]  I. Babuska,et al.  ON THE ANGLE CONDITION IN THE FINITE ELEMENT METHOD , 1976 .

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

[63]  Timothy J. Baker,et al.  Three dimensional mesh generation by triangulation of arbitrary point sets , 1987 .

[64]  V. Venkatakrishnan,et al.  IMPLICIT SCHEMES AND PARALLEL COMPUTING IN UNSTRUCTURED GRID CFD , 1995 .

[65]  Russ D. Rausch,et al.  Spatial Adaptation of Unstructured Meshes for Unsteady Aerodynamic Flow Computations , 1992 .

[66]  J. Peraire,et al.  A 3D finite element multigrid solver for the Euler equations , 1992 .

[67]  David C. Slack,et al.  Time integration algorithms for the two-dimensional Euler equations on unstructured meshes , 1994 .

[68]  Dorothee Martin,et al.  An implicit, linelet-based solver for incompressible flows , 1992 .

[69]  Y. Kallinderis,et al.  New multigrid approach for three-dimensional unstructured, adaptive grids , 1994 .

[70]  J. W. Ruge,et al.  4. Algebraic Multigrid , 1987 .

[71]  Marshal L. Merriam,et al.  An efficient advancing front algorithm for Delaunay triangulation , 1991 .

[72]  S. Sutharshana,et al.  Automatic three-dimensional mesh generation by the modified-octree technique: Yerry M A and Shepard, M SInt. J. Numer. Methods Eng. Vol 20 (1984) pp 1965–1990 , 1985 .

[73]  Dimitri J. Mavriplis,et al.  Coarsening Strategies for Unstructured Multigrid Techniques with Application to Anisotropic Problems , 1995, SIAM J. Sci. Comput..

[74]  S. Pirzadeh Unstructured Viscous Grid Generation by Advancing-Layers Method , 1994 .

[75]  Mark S. Shephard,et al.  Automatic three‐dimensional mesh generation by the finite octree technique , 1984 .

[76]  Dimitri J. Mavriplis,et al.  A THREE DIMENSIONAL MULTIGRID REYNOLDS-AVERAGED NAVIER-STOKES SOLVER FOR UNSTRUCTURED MESHES , 1994 .

[77]  Timothy J. Baker,et al.  Mesh adaptation strategies for problems in fluid dynamics , 1997 .

[78]  B. Palmerio An attraction-repulsion mesh adaption model for flow solution on unstructured grids , 1994 .

[79]  N. Weatherill,et al.  Unstructured grid generation using iterative point insertion and local reconnection , 1995 .

[80]  Michael J. Aftosmis,et al.  On the Accuracy, Stability, and Monotonicity of Various Reconstruction Algorithms for Unstructured Meshes , 1994 .

[81]  Dimitri J. Mavriplis,et al.  UNSTRUCTURED MESH GENERATION AND ADAPTIVITY , 1995 .

[82]  S. Rebay Efficient Unstructured Mesh Generation by Means of Delaunay Triangulation and Bowyer-Watson Algorithm , 1993 .

[83]  W. K. Anderson,et al.  Implicit/Multigrid Algorithms for Incompressible Turbulent Flows on Unstructured Grids , 1995 .

[84]  Dimitri J. Mavriplis,et al.  Three-dimensional multigrid Reynolds-averaged Navier-Stokes solver for unstructured meshes , 1995 .

[85]  John T. Batina,et al.  Implicit upwind solution algorithms for three-dimensional unstructured meshes , 1993 .

[86]  N T Frink,et al.  Recent Progress Toward a Three-Dimensional Unstructured Navier-Stokes Flow Solver , 1994 .

[87]  J. Peraire,et al.  Finite Element Flux-Corrected Transport (FEM-FCT) for the Euler and Navier-Stokes equations , 1987 .

[88]  Timothy J. Barth,et al.  The design and application of upwind schemes on unstructured meshes , 1989 .

[89]  Tony F. Chan,et al.  Domain decomposition and multigrid algorithms for elliptic problems on unstructured meshes , 1994 .

[90]  Jacques Periaux,et al.  Numerical simulation of 3-D hypersonic Euler flows around space vehicles using adapted finite elements , 1987 .

[91]  A Jameson,et al.  CALCULATION OF IN VISCID TRANSONIC FLOW OVER A COMPLETE AIRCRAFT , 1986 .

[92]  D. Michalek,et al.  Grid-independent upwind scheme for multidimensional flow , 1993 .

[93]  V. Venkatakrishnan,et al.  IMPLICIT METHOD FOR THE COMPUTATION OF UNSTEADY FLOWS ON UNSTRUCTURED GRIDS , 1995 .

[94]  Bram van Leer,et al.  Design of Optimally Smoothing Multi-Stage Schemes for the Euler Equations , 1989 .

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

[96]  Dimitri J. Mavriplis,et al.  Algebraic turbulence modeling for unstructured and adaptive meshes , 1990 .

[97]  T. Hughes,et al.  A multi-element group preconditioned GMRES algorithm for nonsymmetric systems arising in finite element analysis , 1989 .

[98]  O. C. Zienkiewicz,et al.  Adaptive remeshing for compressible flow computations , 1987 .

[99]  A. Jameson,et al.  Numerical solution of the Euler equations by finite volume methods using Runge Kutta time stepping schemes , 1981 .

[100]  O. Zienkiewicz,et al.  A new approach to the development of automatic quadrilateral mesh generation , 1991 .

[101]  S. Lo A NEW MESH GENERATION SCHEME FOR ARBITRARY PLANAR DOMAINS , 1985 .

[102]  Michael B. Giles,et al.  Preconditioning on stretched meshes , 1995 .

[103]  Shahyar Pirzadeh,et al.  Viscous unstructured three-dimensional grids by the advancing-layers method , 1994 .

[104]  Jay P. Boris,et al.  Flux-corrected transport. I. SHASTA, a fluid transport algorithm that works , 1973 .

[105]  Dimitri J. Mavriplis,et al.  Agglomeration multigrid for two-dimensional viscous flows , 1995 .

[106]  T. Barth,et al.  An unstructured mesh Newton solver for compressible fluid flow and its parallel implementation , 1995 .

[107]  Thomas J. R. Hughes,et al.  Recent progress in the development and understanding of SUPG methods with special reference to the compressible Euler and Navier-Stokes equations†‡ , 1987 .

[108]  Bruno Stoufflet,et al.  TVD Schemes to Compute Compressible Viscous Flows on Unstructured Meshes , 1989 .

[109]  Rainald Löhner,et al.  Adaptive H-refinement on 3-D unstructured grids for transient problems , 1989 .

[110]  A. Dervieux,et al.  Looking for O(N) Navier-Stokes solutions on non-structured meshes , 1993 .

[111]  J. M. Tembulkar,et al.  On generating quadrilateral elements from a triangular mesh , 1992 .

[112]  D. F. Watson Computing the n-Dimensional Delaunay Tesselation with Application to Voronoi Polytopes , 1981, Comput. J..

[113]  Dimitri J. Mavriplis,et al.  Unstructured and adaptive mesh generation for high Reynolds number viscous flows , 1991 .

[114]  David Sidilkover,et al.  A GENUINELY MULTIDIMENSIONAL UPWIND SCHEME AND EFFICIENT MULTIGRID SOLVER FOR THE COMPRESSIBLE EULER EQUATIONS , 1994 .

[115]  C. Hirsch,et al.  Characteristic decomposition methods for the multidimensional euler equations , 1986 .

[116]  M. Raw,et al.  Robustness of coupled Algebraic Multigrid for the Navier-Stokes equations , 1996 .

[117]  P. Roe Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes , 1997 .

[118]  Michael Ian Shamos,et al.  Computational geometry: an introduction , 1985 .

[119]  Joe F. Thompson,et al.  Aspects of numerical grid generation - Current science and art , 1993 .