七方程可压缩多相流模型的HLLC格式及应用

针对Saurel和Abgrall提出的两速度两压力的七方程可压缩多相流模型,改进了其数值解法并应用于模拟可压缩多介质流动问题.在Saurel等的算子分裂法基础上,根据Abgrall的多相流系统应满足速度和压力的均匀性不随时间改变的思想,推导了与HLLC格式一致的非守恒项离散格式以及体积分数发展方程的迎风格式.进一步,通过改变分裂步顺序,构造了稳健的结合算子分裂的三阶TVD龙格-库塔方法.最后通过几个一维和二维高密度比高压力比气液两相流算例,显示了该方法在计算精度和稳健性上的改进效果. 

AN HLLC SCHEME FOR THE SEVEN-EQUATION MULTIPHASE MODEL AND ITS APPLICATION TO COMPRESSIBLE MULTICOMPONENT FLOW

In this paper,the numerical method for the two-pressure and two-velocity seven-equation model presented by Saurel and Abgrall is improved and applied to numerical simulation of compressible multicomponent flows.Based on the operator splitting method given by Saurel et al.and the idea proposed by Abgrall that "for a two phase system,uniformity in velocity and pressure at t=0 will be kept on the same variable during its temporal evolution",discretization for the non-conservative terms and upwind scheme for the volume fraction evolution equation are derived in terms of the underlying HLLC approximate Riemann solver used for the conservation equations.Moreover,the third-order TVD Runge-Kutta method is implemented in conjunction with the operator splitting to obtain a robust procedure by reordering the sequence of operators.Numerical tests with several 1d and 2d compressible gas-liquid multicomponent flow problems with high density and high pressure ratios demonstrate that the present method is more accurate and robust than previous methods.