MULTIGRID TECHNIQUES FOR UNSTRUCTURED MESHES

An overview of current multigrid techniques for unstructured meshes is given. The basic principles of the multigrid approach are first outlined. Application of these principles to unstructured mesh problems is then described, illustrating various different approaches, and giving examples of practical applications. Advanced multigrid topics, such as the use of algebraic multigrid methods, and the combination of multigrid techniques with adaptive meshing strategies are dealt with in subsequent sections. These represent current areas of research, and the unresolved issues are discussed. The presentation is organized in an educational manner, for readers familiar with computational fluid dynamics, wishing to learn more about current unstructured mesh techniques.

[1]  W. K. Anderson,et al.  Multigrid acceleration of the flux split Euler equations , 1986 .

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

[3]  Graham Horton,et al.  A multi-level solution algorithm for steady-state Markov chains , 1994, SIGMETRICS.

[4]  W. K. Anderson,et al.  An implicit upwind algorithm for computing turbulent flows on unstructured grids , 1994 .

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

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

[7]  Graham Horton,et al.  A multi-level solution algorithm for steady-state Markov chains , 1994, SIGMETRICS.

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

[9]  D. J. Mavriplis,et al.  AGGLOMERATION MULTIGRID FOR VISCOUS TURBULENT FLOWS , 1994 .

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

[11]  Mark D. Sanetrik,et al.  Time-accurate Navier-Stokes calculations with multigrid acceleration , 1993 .

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

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

[14]  S. McCormick,et al.  The fast adaptive composite grid (FAC) method for elliptic equation , 1986 .

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

[16]  John Van Rosendale,et al.  Operator induced multigrid algorithms using semirefinement , 1989 .

[17]  A. Jameson.  Time dependent calculations using multigrid, with applications to unsteady flows past airfoils and wings , 1991 .

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

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

[20]  Per Weinerfelt,et al.  A coarse grid correction scheme for implicit multi block Euler calculations , 1995 .

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

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

[23]  Shlomo Ta'asan,et al.  Canonical forms of multidimensional steady inviscid flows , 1993 .

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

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

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

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

[28]  Y. Saad,et al.  GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems , 1986 .

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

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

[31]  Thomas J. R. Hughes,et al.  A data parallel finite element method for computational fluid dynamics on the Connection Machine system , 1992 .

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

[33]  A. Jameson.  Artificial diffusion, upwind biasing, limiters and their effect on accuracy and multigrid convergence in transonic and hypersonic flows , 1993 .

[34]  G. Raithby,et al.  A multigrid method based on the additive correction strategy , 1986 .

[35]  V. Venkatakrishnan,et al.  A 3D AGGLOMERATION MULTIGRID SOLVER FOR THE REYNOLDS-AVERAGED NAVIER-STOKES EQUATIONS ON UNSTRUCTURED MESHES , 1995 .

[36]  Stuart Connell,et al.  A 3D unstructured adaptive multigrid scheme for the Euler equations , 1993 .

[37]  Rolf Radespiel,et al.  Progress with multigrid schemes for hypersonic flow problems , 1995 .

[39]  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.

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

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

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

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

[44]  John Vassberg,et al.  A fast, implicit unstructured-mesh Euler method , 1992 .

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

[46]  Alain Dervieux,et al.  Unstructured volume‐agglomeration MG: Solution of the Poisson equation , 1994 .

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

[48]  Barry Koren,et al.  Damped, direction-dependent multigrid for hypersonic flow computations , 1989 .