On the extension of the AUSM+ scheme to compressible two-fluid models

Abstract This paper describes the extension of the AUSM+ scheme to the four-equation isentropic and six-equation compressible two-fluid models for gas/liquid flow, using as equations of state the perfect gas law for the gas and either Tait’s law or the stiffened gas law for the liquid. Numerical results on well-known two-fluid air/water flow benchmark problems, from nearly incompressible flows to fully compressible flows, are presented and discussed.

[1]  E. Toro Godunov Methods: Theory and Applications , 2001 .

[2]  L. Huang Pseudo-unsteady difference schemes for discontinuous solutions of steady-state, one-dimensional fluid dynamics problems , 1981 .

[3]  Richard Saurel,et al.  A Riemann Problem Based Method for the Resolution of Compressible Multimaterial Flows , 1997 .

[4]  Stojan Petelin,et al.  Modelling of Two-Phase Flow with Second-Order Accurate Scheme , 1997 .

[5]  S. Osher,et al.  A Non-oscillatory Eulerian Approach to Interfaces in Multimaterial Flows (the Ghost Fluid Method) , 1999 .

[6]  J. Edwards,et al.  Ausm schemes and extensions for low mach and multiphase flows , 1999 .

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

[8]  A Comparison of Roe, VFFC and AUSM+ Schemes for Two-Phase Water/Steam Flows , 2001 .

[9]  I. Toumi A weak formulation of roe's approximate riemann solver , 1992 .

[10]  Frédéric Coquel,et al.  A Numerical Method Using Upwind Schemes for the Resolution of Two-Phase Flows , 1997 .

[11]  J. Romate,et al.  An approximate Riemann solver for a two-phase flow model with numerically given slip relation , 1998 .

[12]  Meng-Sing Liou,et al.  Recent progress and applications of AUSM , 1998 .

[13]  D. Darracq,et al.  Time-accurate fluid-structure coupling for turbulent flows , 1998 .

[14]  S. Osher,et al.  Upwind difference schemes for hyperbolic systems of conservation laws , 1982 .

[15]  Charles-Henri Bruneau Sixteenth International Conference on Numerical Methods in Fluid Dynamics , 1998 .

[16]  H. Bruce Stewart,et al.  Two-phase flow: Models and methods , 1984 .

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

[18]  R. Abgrall,et al.  A Multiphase Godunov Method for Compressible Multifluid and Multiphase Flows , 1999 .

[19]  A. A. Amsden,et al.  Numerical calculation of multiphase fluid flow , 1975 .

[20]  Eleuterio F. Toro,et al.  On Riemann solvers for compressible liquids , 1998 .

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

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

[23]  Lionel Sainsaulieu,et al.  Finite volume approximation of two phase-fluid flows based on an approximate Roe-type Riemann solver , 1995 .

[24]  I. Toumi,et al.  An upwind numerical method for two-fluid two-phase flow models , 1996 .

[25]  Hansong Tang,et al.  A Second-Order Accurate Capturing Scheme for 1D Inviscid Flows of Gas and Water with Vacuum Zones , 1996 .

[26]  Meng-Sing Liou,et al.  Low-Diffusion Flux-Splitting Methods for Real Fluid Flows with Phase Transitions , 2000 .

[27]  H. Städtke,et al.  Numerical simulation of multi-dimensional two-phase flow based on flux vector splitting , 1997 .

[28]  S. Clerc,et al.  Numerical Simulation of the Homogeneous Equilibrium Model for Two-Phase Flows , 2000 .

[29]  J. Edwards,et al.  Low-Diffusion Flux-Splitting Methods for Flows at All Speeds , 1997 .

[30]  Keh-Ming Shyue,et al.  Regular Article: A Fluid-Mixture Type Algorithm for Compressible Multicomponent Flow with van der Waals Equation of State , 1999 .

[31]  V. H. Ransom,et al.  Regularization of Two-Phase Flow Models , 1997 .

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

[33]  D. Bestion,et al.  The physical closure laws in the CATHARE code , 1990 .

[34]  Rainald Löhner,et al.  A fast, matrix-free implicit method for compressible flows on unstructured grids , 1998 .

[35]  Keh-Ming Shyue,et al.  A fluid-mixture type algorithm for compressible multicomponent flow with Mie-Grüneisen equation of state , 2001 .