On the computation of multi-material flows using ALE formulation

Computation of compressible multi-fluid flows with a general equation of state using interface tracking and moving grid approach is discussed in this paper. The AUSM+, HLLC, and Godunov methods are presented and implemented in the context of arbitrary Lagrangian-Eulerian formulation for solving the unsteady compressible Euler equations. The developed methods are fully conservative, and used to compute a variety of multi-component flow problems, where the equations of state can be drastically different and stiff. Numerical results indicate that both ALE HLLC and Godunov schemes demonstrate their simplicity and robustness for solving such multi-phase flow problems, and yet ALE AUSM+ scheme exhibits strong oscillations around material interfaces even using a first order monotone scheme and therefore is not suitable for this class of problems.

[1]  S. Osher,et al.  Computing interface motion in compressible gas dynamics , 1992 .

[2]  R. Abgrall.  How to Prevent Pressure Oscillations in Multicomponent Flow Calculations , 1996 .

[3]  Rainald Loehner,et al.  A hybrid interface capturing method for compressible multi-fluid flows on unstructured grids , 1996 .

[4]  Andrew B. Wardlaw,et al.  Spherical solutions of an underwater explosion bubble , 1998 .

[5]  Hervé Guillard,et al.  Godunov type method on non-structured meshes for three-dimensional moving boundary problems , 1994 .

[6]  C. Mader.  Numerical modeling of detonations , 1979 .

[7]  G. D. van Albada,et al.  A comparative study of computational methods in cosmic gas dynamics , 1982 .

[8]  J. Falcovitz,et al.  A Singularities Tracking Conservation Laws Scheme for Compressible Duct Flows , 1994 .

[9]  Smadar Karni,et al.  Multicomponent Flow Calculations by a Consistent Primitive Algorithm , 1994 .

[10]  Randall J. LeVeque,et al.  Two-Dimensional Front Tracking Based on High Resolution Wave Propagation Methods , 1996 .

[11]  P. Roe.  Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes , 1997 .

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

[13]  B. Leer,et al.  Flux-vector splitting for the Euler equations , 1997 .

[14]  Jean-Yves Trépanier,et al.  Discrete form of the GCL for moving meshes and its implementation in CFD schemes , 1993 .

[15]  C. W. Hirt,et al.  Volume of fluid (VOF) method for the dynamics of free boundaries , 1981 .

[16]  Xiaolin Li,et al.  Robust Computational Algorithms for Dynamic Interface Tracking in Three Dimensions , 1999, SIAM J. Sci. Comput..

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

[18]  Michael A. Leschziner,et al.  Average-State Jacobians and Implicit Methods for Compressible Viscous and Turbulent Flows , 1997 .

[19]  Charbel Farhat,et al.  Geometric conservation laws for flow problems with moving boundaries and deformable meshes, and their impact on aeroelastic computations , 1996 .

[20]  Keh-Ming Shyue,et al.  An Efficient Shock-Capturing Algorithm for Compressible Multicomponent Problems , 1998 .

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

[22]  Yang-Yao Niu,et al.  SIMPLE CONSERVATIVE FLUX SPLITTING FOR MULTI-COMPONENT FLOW CALCULATIONS , 2000 .

[23]  G. J. Ball,et al.  A Free-Lagrange method for unsteady compressible flow: simulation of a confined cylindrical blast wave , 1996 .

[24]  Rainald Löhner,et al.  An accurate, fast, matrix-free implicit method for computing unsteady flows on unstructured grids , 2001 .

[25]  R. Smith,et al.  AUSM(ALE) , 1999 .

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