A gas‐kinetic scheme for the modified Baer–Nunziato model of compressible two‐phase flow

Abstract

SUMMARY Numerical methods for the Baer–Nunziato model of compressible two‐phase flow have attracted much attention in recent years. In this paper, a two‐phase Bhatnagar–Gross–Krook (BGK) model is constructed in which the non‐conservative terms in the Baer–Nunziato model are considered as the external forces and the collisions both with particles of their phases and other phases are taken into consideration. On the basis of this BGK model, the so‐called modified Baer–Nunziato model is derived and a gas‐kinetic scheme for this modified model is presented. The distribution functions are constructed at the cell interface based on the integral solutions of the BGK equations for both phases. Then, numerical fluxes can be obtained by taking moments of the distribution functions, and non‐conservative terms are explicitly introduced into the construction of numerical fluxes. In this method, not only the iterative processes in the exact Riemann solvers are eliminated but also the collisions with the particles of other phases are taken into account. Copyright © 2012 John Wiley & Sons, Ltd.