Implicit/Multigrid Algorithms for Incompressible Turbulent Flows on Unstructured Grids

An implicit code for computing inviscid and viscous incompressible flows on unstructured grids is described. The foundation of the code is a backward Euler time discretization for which the linear system is approximately solved at each time step with either a point implicit method or a preconditioned generalized minimal residual (GMRES) technique. For the GMRES calculations, several techniques are investigated for forming the matrix?vector product. Convergence acceleration is achieved through a multigrid scheme that uses nonnested coarse grids that are generated using a technique described in the present paper. Convergence characteristics are investigated and results are compared with an exact solution for the inviscid flow over a four-element airfoil. Viscous results, which are compared with experimental data, include the turbulent flow over a NACA 4412 airfoil, a three-element airfoil for which Mach number effects are investigated, and three-dimensional flow over a wing with a partial-span flap.

[1]  Kent Robertson Van Horn,et al.  Design and application , 1967 .

[2]  E. Cuthill,et al.  Reducing the bandwidth of sparse symmetric matrices , 1969, ACM '69.

[3]  Alan J. Wadcock,et al.  Flying-Hot-wire Study of Flow Past an NACA 4412 Airfoil at Maximum Lift , 1979 .

[4]  Achi Brandt,et al.  Multilevel Adaptive Computations in Fluid Dynamics , 1980 .

[5]  Alan George,et al.  Computer Solution of Large Sparse Positive Definite , 1981 .

[6]  J. Pasciak,et al.  Computer solution of large sparse positive definite systems , 1982 .

[7]  I. M. Hall,et al.  Test cases for the plane potential flow past multi-element aerofoils , 1985, The Aeronautical Journal (1968).

[8]  M. D. Salas,et al.  Far-field boundary conditions for transonic lifting solutions to the Euler equations , 1986 .

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

[10]  C. Hsu,et al.  An implicit flux-difference splitting scheme for three-dimensional, incompressible Navier-Stokes solutions to leading edge vortex flows , 1986 .

[11]  W. K. Anderson,et al.  Navier-Stokes Computations of Vortical Flows Over Low-Aspect-Ratio Wings , 1987 .

[12]  E. Turkel,et al.  Preconditioned methods for solving the incompressible low speed compressible equations , 1987 .

[13]  S. Rogers,et al.  An upwind differencing scheme for the time-accurate incompressible Navier-Stokes equations , 1988 .

[14]  Y. Saad,et al.  Krylov Subspace Methods on Supercomputers , 1989 .

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

[16]  Sukumar Chakravarthy,et al.  Unified formulation for incompressible flows , 1989 .

[17]  Yousef Saad,et al.  Hybrid Krylov Methods for Nonlinear Systems of Equations , 1990, SIAM J. Sci. Comput..

[18]  Stuart E. Rogers,et al.  Upwind differencing scheme for the time-accurate incompressible Navier-Stokes equations , 1990 .

[19]  L. K. Taylor,et al.  Unsteady three-dimensional incompressible algorithm based on artificial compressibility , 1991 .

[20]  G. Volpe.  On the use and the accuracy of compressible flow codes at low Mach numbers , 1991 .

[21]  Philip L. Roe,et al.  Characteristic time-stepping or local preconditioning of the Euler equations , 1991 .

[22]  Larry Wall,et al.  Programming Perl , 1991 .

[23]  Thomas J. R. Hughes,et al.  A globally convergent matrix-free algorithm for implicit time-marching schemes arising in finite element analysis in fluids , 1991 .

[24]  D. Whitfield.  Unsteady three-dimensional incompressible Euler and Navier-Stokes solver for stationary and dynamic grids , 1991 .

[25]  A. Godfrey.  Topics on spatially high-order accurate methods and pre-conditioning for the Navier-Stokes equations with finite-rate chemistry , 1992 .

[26]  P. Spalart.  A One-Equation Turbulence Model for Aerodynamic Flows , 1992 .

[27]  F. Menter.  Improved two-equation k-omega turbulence models for aerodynamic flows , 1992 .

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

[29]  F. Menter.  ZONAL TWO EQUATION k-w TURBULENCE MODELS FOR AERODYNAMIC FLOWS , 1993 .

[30]  C. L. Merkle,et al.  The application of preconditioning in viscous flows , 1993 .

[31]  D. Bonhaus.  An upwind multigrid method for solving viscous flows on unstructured triangular meshes. M.S. Thesis , 1993 .

[32]  W. Hackbusch.  Iterative Solution of Large Sparse Systems of Equations , 1993 .

[33]  Eli Turkel,et al.  Review of preconditioning methods for fluid dynamics , 1993 .

[34]  Unstructured Meshes,et al.  An Upwind Multigrid Method for Solving Viscous Flows on , 1993 .

[35]  Kazuhiro Kusunose,et al.  Grid generation and Navier-Stokes analysis of multi-element airfoils , 1994 .

[36]  Jonathan Weiss,et al.  Preconditioning Applied to Variable and Constant Density Time-Accurate Flows on Unstructured Meshes , 1994 .

[37]  Dana A. Knoll,et al.  Comparison of standard and matrix-free implementations of several Newton-Krylov solvers , 1994 .

[38]  Stuart E. Rogers,et al.  Progress in high-lift aerodynamic calculations , 1993 .

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

[40]  Richard H. Pletcher,et al.  An implicit numerical scheme for the simulation of internal viscous flow on unstructured grids , 1994 .

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

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

[43]  L K Taylor,et al.  TIME ACCURATE INCOMPRESSIBLE NAVIER-STOKES SIMULATION OF THE FLAPPING FOIL EXPERIMENT , 1994 .

[44]  Timothy Barth,et al.  Steiner triangulation for isotropic and stretched elements , 1995 .

[45]  Stuart E. Rogers,et al.  Navier-Stokes Analysis of the Flow About a Flap Edge , 1995 .

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

[47]  W. K. Anderson,et al.  Navier-Stokes Computations and Experimental Comparisons for Multielement Airfoil Configurations , 1993 .

[48]  John C. Lin,et al.  Optimization of an Advanced Design Three-Element Airfoil at High Reynolds Numbers , 1995 .

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

[50]  A. Chorin.  A Numerical Method for Solving Incompressible Viscous Flow Problems , 1997 .

[51]  Russell M. Cummings,et al.  Navier-Stokes Analysis of the Flow About a Flap Edge , 1995 .

[52]  DimitriJ.,et al.  TURBULENT FLOW CALCULATIONS USING UNSTRUCTURED AND ADAPTIVE MESHES , 2022 .