Modified Gamma-Based Model for Solving Low Mach Number Compressible Two Phase Flows

Abstract

This paper presents some modifications of the gamma-based model developed by K.M. Shyue (J. Comput. Phys., 1998, 142, 208-242). In deriving process of the original model, pressure equilibrium and an isentropic condition are not involved explicitly. Therefore, to adopt these physical conditions, we improved evolution equations for problem-dependent material quantities (e.g. ratio of specific heat). As a result, a non-conservative term associated with the pressure relaxation was added to the equations. The modifications have no effect on an oscillation-free property of the original model. Furthermore, because division by a volume fraction is not included in the present model, an inherent property of mixture-type models is maintained. To capture contact discontinuity sharply, we utilized an approximate Riemann solver HLLC with a third-order MUSCL interpolation. Finally, we carried out one-dimensional numerical tests in order to evaluate the influence on accuracy. Numerical results show that the modified model has good capability for simulating low Mach number flow problems.

Keywords

• two-phase flow
• mixture model
• low mach number
• interface capturing
• non-conservative term