Preconditioning Algorithms for the Computation of Multi-Phase Mixture Flows

Preconditioned time-marching algorithms are developed for a class of isothermal compressible multi-phase mixture flows, relevant to the modeling of sheetand super-cavitating flows in hydrodynamic applications. Using the volume fraction and mass fraction forms of the multi-phase governing equations, three closely related but distinct preconditioning forms are derived. The resulting algorithm is incorporated within an existing multi-phase code and several representative solutions are obtained to demonstrate the capabilities of the method. Comparisons with measurement data suggest that the compressible formulation provides an improved description of the cavitation dynamics compared with previous incompressible computations.

[1]  C. Merkle,et al.  Computational modeling of the dynamics of sheet cavitation , 1998 .

[2]  H. Rouse,et al.  Cavitation and pressure distribution: head forms at zero angle of yaw , 1948 .

[3]  Robert B. Eddington,et al.  Investigation of supersonic phenomena in a two- phase liquid-gas tunnel , 1970 .

[4]  S. Venkateswaran,et al.  Analysis of preconditioning methods for the euler and navier-stokes equations , 1999 .

[5]  S. Venkateswaran,et al.  Efficiency and accuracy issues in contemporary CFD algorithms , 2000 .

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

[7]  V. K. Kedrinskii,et al.  Shock waves in a liquid containing gas bubbles , 1980 .

[8]  P. Wesseling.  Non-convex hyperbolic systems , 1999 .

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

[10]  Robert F. Kunz,et al.  A preconditioned navier-stokes method for two-phase flows with application to Cavitation prediction , 1999 .

[11]  D. R. Stinebring,et al.  Validation of High Reynolds Number, Unsteady Multi-Phase CFD Modeling for Naval Applications , 2001 .

[12]  G. E. Reisman,et al.  Observations of shock waves in cloud cavitation , 1998, Journal of Fluid Mechanics.

[13]  Vineet Ahuja,et al.  A hybrid unstructured mesh solver for multi-fluid mixtures , 1999 .

[14]  J. Witte,et al.  Mixing shocks in two-phase flow , 1969, Journal of Fluid Mechanics.

[15]  Albert May,et al.  Water Entry and the Cavity-Running Behavior of Missiles , 1975 .

[16]  L. K. Taylor,et al.  Unsteady three-dimensional incompressible Navier-Stokes computations for a prolate spheroid undergoing time-dependent maneuvers , 1995 .

[17]  D. R. Stinebring,et al.  An Investigation of Cavity Cycling for Ventilated and Natural Cavities. , 1983 .

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

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

[20]  L. van Wijngaarden,et al.  One-Dimensional Flow of Liquids Containing Small Gas Bubbles , 1972 .