基于Van Leer+AUSM混合格式超声速流场的并行数值算法研究

Research on Parallel Numerical Simulation of N-S Equations Based on Van Leer+AUSM Scheme

基于CLUSTER集群并行体系结构与消息传递库MPI并行环境,开展了超声速流场的并行数值算法研究。计算网格采用多块对接粘性结构网格,控制方程为积分形式的Navier-Stokes(N-S)方程,空间离散采用基于Van Leer+AUSM混合格式的有限体积法,粘性项采用中心格式离散并利用格林定理计算粘性通量中的导数项,时间推进采用五步R-K法,应用一方程S-A模型计算湍流的粘性。并行计算采用分区并行的思想,设计了满足负载平衡要求的区域分解和通讯方法,编程上采用单控制流多数据流(SPMD)模型以及Master/Slave并行模式。最后,通过对某弹丸和某制导火箭弹超声速流动的数值模拟,验证了并行算法的准确性、高效性和处理复杂几何外形的能力。

This paper is to study parallel algorithm of numerical simulation of N-S Equations based on Van Leer＋AUSM Scheme on PC-CLUSTERS that is distributed memory architecture using the MPI standard library.Finite volume method is used in spatial discrimination,Van Leer＋AUSM flux splitting scheme is developed to calculate the convection flux,the viscous flux is calculated by central finite volume scheme.The multistage five Runge-Kutta time-stepping scheme is applied to temporal discretisation.Spalart-Allmaras one-equation turbulence model is implemented to evaluate the turbulent viscosity.In the parallel algorithm design,Physics-region-partition is proposed.A new communication method between partitions is presented,which meets load balance among nodes.Finally numerical experiments are made for supersonic flow.In some extent,the numerical results confirm the feasibility and validate its accuracy and ability of parallel algorithm mentioned above to deal with complex flow.