求解非定常不可压Navier-Stokes方程的一种高精度并行算法  

A High-order Parallel Numerical Method for Solving Unsteady Incompressible Navier-Stokes Equations

作　　者：倪诗浩[1] 田振夫[1] 

机构地区：[1]复旦大学航空航天系,上海200433

出　　处：《复旦学报（自然科学版）》2016年第3期315-320,共6页Journal of Fudan University：Natural Science

基　　金：国家自然科学基金(91330112;11372075)

摘　　要：采用一阶投影法,建立了一种基于MPI求解非定常不可压N-S方程的高精度并行算法.该算法在空间上可达到4阶精度,其中,对流项中的1阶导数和粘性项中的2阶导数分别采用WENO格式和4阶对称型宽格式进行离散,而Poisson方程则采用4阶精度的紧致格式进行迭代求解.通过对2维Taylor涡列和双周期双剪切边界层流动问题及3维回转体绕流问题的数值计算,验证了算法的可靠性及其并行效率.On the basis of the projection method, a high-order parallel algorithm for solving the unsteady incompressible Navier-Stokes（N-S） equations using MPI standard is presented. This algorithm can reach fourthorder accuracy in space. WENO（Weighted Essentially Non-Oscillatory） scheme is used to discretize the first derivative of the non-linear convective terms and the fourth-order symmetrical scheme is used in the discretization of the second derivatives of viscous terms respectively. Pressure Poisson equation is approximated using a fourthorder compact difference scheme. For assessing the effectiveness and parallel efficiency of the algorithm, a two- dimensional Taylor vortex column problem, a doubly-periodic double shear layer problem and a three-dimensional flow around a solid of revolution are numerically solved.

关 键 词：并行算法 标准消息传递界面 WENO格式 投影法 高精度 

分 类 号：O35[理学—流体力学]