Viscous Flow Solvers for Aero/Hydrodynamic Analysis and Design

This paper reviews the principles underlying the development of numerical techniques for the solution of both steady and time dependent viscous flow problems. The combination of efficient high resolution schemes and parallel computing enables the effective use of viscous analyses in the preliminary stages of a design. Representative results, drawn by the authors work in several application areas, are presented.

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

[2]  Dimitri J. Mavriplis,et al.  ICASE Report No . 98-44 On Convergence Acceleration Techniques for Unstructured Meshes , 1998 .

[3]  V. Venkatakrishnan,et al.  IMPROVED MULTIGRID PERFORMANCE OF COMPRESSIBLE NAVIER-STOKES SOLVERS , 1998 .

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

[5]  A. Jameson,et al.  Aerodynamic shape optimization techniques based on control theory , 1998 .

[6]  A. Rizzi,et al.  Computation of flow around wings based on the Euler equations , 1984, Journal of Fluid Mechanics.

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

[8]  Wayne Smith,et al.  Multigrid solution of the Euler equations , 1987 .

[9]  Antony Jameson,et al.  A new implicit algorithm with multigrid for unsteady incompressible flow calculations , 1995 .

[10]  R. Henderson,et al.  Secondary instability in the wake of a circular cylinder , 1996 .

[11]  Antony Jameson,et al.  Transonic flow calculations for aircraft , 1985 .

[12]  Yiguang Ju,et al.  Lower-upper scheme for chemically reacting flow with finite rate chemistry , 1995 .

[13]  B. V. Leer,et al.  Towards the Ultimate Conservative Difference Scheme , 1997 .

[14]  AIAA-86-0103 Calculation of Inviscid Transonic Flow over a Complete Aircraft , 1986 .

[15]  David A. Caughey,et al.  Diagonal implicit multigrid algorithm for the Euler equations , 1987 .

[16]  Juan J. Alonso,et al.  Multigrid unsteady Navier-Stokes calculations with aeroelastic applications , 1995 .

[17]  Juan J. Alonso,et al.  Time-accurate simulation of helicopter rotor flows including aeroelastic effects , 1997 .

[18]  S. N. Tiwari,et al.  Numerical study of finite-rate supersonic combustion using parabolized equations , 1987 .

[19]  Antony Jameson,et al.  Fully conservative numerical solutions for unsteady irrotational transonic flow about airfoils , 1979 .

[20]  Steven R. Allmaras,et al.  Algebraic Smoothing Analysis of Multigrid Methods for the 2—D Compressible Navier-Stokes Equations , 1997 .

[21]  Juan J. Alonso,et al.  A Two-Dimensional Multigrid-Driven Navier-Stokes Solver for Multiprocessor Architectures , 2000 .

[22]  Luigi Martinelli,et al.  Calculations of viscous flows with a multigrid method , 1987 .

[23]  Adam P. Bruckner,et al.  Numerical simulation of hypervelocity projectiles in detonable gases , 1991 .

[24]  Juan J. Alonso,et al.  Automatic aerodynamic optimization on distributed memory architectures , 1996 .

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

[26]  Meng-Sing Liou,et al.  A Flux Splitting Scheme with High-Resolution and Robustness for Discontinuities(Proceedings of the 12th NAL Symposium on Aircraft Computational Aerodynamics) , 1994 .

[27]  A. Jameson,et al.  Optimum Aerodynamic Design Using the Navier–Stokes Equations , 1997 .

[28]  Seokkwan Yoon,et al.  Numerical study of chemically reacting flows using a lower-upper symmetric successive overrelaxation scheme , 1989 .

[29]  Arthur Rizzi,et al.  Computation of inviscid incompressible flow with rotation , 1985, Journal of Fluid Mechanics.

[30]  Antony Jameson,et al.  A new high resolution scheme for compressible viscous flows with shocks , 1995 .

[31]  Dimitri J. Mavriplis,et al.  On Convergence Acceleration Techniques for Unstructured Meshes , 1998 .

[32]  C. J. Schexnayder,et al.  Influence of Chemical Kinetics and Unmixedness on Burning in Supersonic Hydrogen Flames , 1980 .

[33]  S. Balachandar,et al.  Vortical structures in bluff body wakes , 1995 .

[34]  Antony Jameson,et al.  A FAST MULTIGRID METHOD FOR SOLVING THE NONLINEAR SHIP WAVE PROBLEM WITH A FREE SURFACE , 1994 .

[35]  S. P. Spekreijse,et al.  Multigrid solution of the steady Euler equations , 1988 .

[36]  S. Spekreijse,et al.  Multigrid Solution of the Steady Euler Equations. , 1989 .

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

[38]  H. Lehr,et al.  Experiments on Shock-Induced Combustion , 1972 .

[39]  Michael B. Giles,et al.  Preconditioning compressible flow calculations on stretched meshes , 1996 .

[40]  Antony Jameson,et al.  Fast multigrid method for solving incompressible hydrodynamic problems with free surfaces , 1993 .

[41]  Antony Jameson,et al.  Accelerating three-dimensional navier-stokes calculations , 1997 .

[42]  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 .

[43]  Philip L. Roe,et al.  Fluctuations and signals - a framework for numerical evolution problems. , 1800 .

[44]  C. W. Gear The numerical integration of ordinary differential equations , 1967 .

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

[46]  H. C. Yee,et al.  Semi-implicit and fully implicit shock-capturing methods for nonequilibrium flows , 1989 .

[47]  A. Jameson Solution of the Euler equations for two dimensional transonic flow by a multigrid method , 1983 .

[48]  Antony Jameson,et al.  Flux-limited schemes for the compressible Navier-Stokes equations , 1995 .

[49]  D. Brandt,et al.  Multi-level adaptive solutions to boundary-value problems math comptr , 1977 .

[50]  F. X. Caradonna,et al.  Experimental and Analytical Studies of a Model Helicopter Rotor in Hover , 1980 .

[51]  A. Jameson Computational algorithms for aerodynamic analysis and design , 1993 .

[52]  Charles H. K. Williamson,et al.  Measurements of base pressure in the wake of a cylinder at low Reynolds numbers , 1990 .

[53]  Antony Jameson,et al.  Multigrid algorithms for compressible flow calculations , 1986 .

[54]  Scott G. Sheffer,et al.  Parallel computation of supersonic reactive flows with detailed chemistry including viscous and species diffusion effects , 1997 .

[55]  B. V. Leer,et al.  Towards the ultimate conservative difference scheme. II. Monotonicity and conservation combined in a second-order scheme , 1974 .

[56]  M. Liou,et al.  A New Flux Splitting Scheme , 1993 .

[57]  C. Williamson The natural and forced formation of spot-like ‘vortex dislocations’ in the transition of a wake , 1992, Journal of Fluid Mechanics.

[58]  G. Dahlquist A special stability problem for linear multistep methods , 1963 .

[59]  R. P. Fedorenko The speed of convergence of one iterative process , 1964 .