七方程可压缩多相流模型的HLLC格式及应用

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

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.

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 multicompo- nent 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 ld 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.