Ten Years in the Making: AUSM-Family

We begin by describing the motivations that gave birth to the original AUSM scheme and then focus on the ingredients that has spurred its growth and acceptance by the world of computational fluid dynamics. As it has played out more in the field, weaknesses have also surfaced. Hence, nutrients and supplements are prescribed to help it grow and stay strong and robust. In this paper, we will describe the saga of efforts owing to researchers who have contributed to building up the AUSM-family for the CFD community. It is hoped that a healthy scheme will contribute to the accurate and robust solution of problems encountered in a wide range of disciplines. We analyze numerical mass fluxes with an emphasis on their capability for accurately capturing shock and contact discontinuities. We will present a new scheme for the pressure flux, along with results for a host of test problems.

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

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

[3]  Meng-Sing Liou,et al.  Low-diffusion flux-splitting methods for real fluid flows at all speeds , 1999 .

[4]  Kyu Hong Kim,et al.  An improvement of AUSM schemes by introducing the pressure-based weight functions , 1998 .

[5]  Meng-Sing Liou,et al.  An Accurate and Robust Flux Splitting Scheme for Shock and Contact Discontinuities , 1997, SIAM J. Sci. Comput..

[6]  Denis Darracq,et al.  Computation of Unsteady Turbulent Airfoil Flows with an Aeroelastic AUSM+ Implicit Solver , 1998 .

[7]  M. Liou.  A Sequel to AUSM , 1996 .

[8]  M. S. Liou,et al.  Progress Towards and Improved CFD Method : AUSM+ , 1995 .

[9]  Jan Vierendeels,et al.  An extension of the preconditioned advection upstream splitting method for 3D two-phase flow calculations in circulating fluidized beds , 2002 .

[10]  Thomas W. Roberts,et al.  The behavior of flux difference splitting schemes near slowly moving shock waves , 1990 .

[11]  J. Quirk.  A Contribution to the Great Riemann Solver Debate , 1994 .

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

[13]  Meng-Sing Liou,et al.  Mass Flux Schemes and Connection to Shock Instability , 2000 .

[14]  H. Paillere,et al.  Approximate riemann solvers and flux vector splitting schemes for two-phase flow , 1999 .

[15]  R. Radespiel.  Efficient computation of compressible flows , 1998 .

[16]  R. Schwane,et al.  An Implicit Flux-vector Splitting Scheme for the Computation of Viscous Hypersonic Flows , 1989 .

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

[18]  Philip L. Roe,et al.  A comparison of numerical flux formulas for the Euler and Navier-Stokes equations , 1987 .

[19]  Meng-Sing Liou,et al.  Numerical speed of sound and its application to schemes for all speeds , 1999 .

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

[21]  Matthias Meinke,et al.  Simulation of internal and free turbulent flows , 1999 .

[22]  Jean-Marc Moschetta,et al.  The sonic point glitch problem: A numerical solution , 1998 .

[23]  Pierre Sagaut,et al.  An algorithm for unsteady viscous flows at all speeds , 2000 .

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

[25]  Rolf Radespiel,et al.  Accurate flux vector splitting for shocks and shear layers , 1995 .

[26]  I. Bohachevsky,et al.  Finite difference method for numerical computation of discontinuous solutions of the equations of fluid dynamics , 1959 .

[27]  J. Edwards.  A low-diffusion flux-splitting scheme for Navier-Stokes calculations , 1997 .