【摘要】 基于完全重叠型区域分解技巧,提出三种求解非定常Navier-Stokes方程的有限元并行算法.其基本思想是首先对空间施行完全重叠区域分解,然后各个处理器使用向后Euler格式独立并行求解关于时间t的常微分方程;对于非线性的对流项,分别采用半隐格式和全隐格式进行处理.算法中每个处理器所负责的子问题是一个全局问题,它定义在整个求解区域上,但绝大部分自由度来自其所负责的子区域,从而使得算法实现简单,通信需求少.数值算例验证了算法的有效性及其良好的并行性能.更多还原

【Abstract】 Based on fully overlapping domain decomposition,three parallel finite element algorithms for time-dependent Navier-Stokes equations are proposed.Basic idea of algorithms is to discretize spatial space with fully overlapping domain decomposition technique,and then to solve ordinary differential equations with respect to time independently in backward Euler scheme on overlapped subdomains.The nonlinear convective term is dealt with semi-and fully-implicit schemes,respectively.In these algorithms,each subproblem is a global problem with vast majority of degrees of freedom associated with a particular subdomain that is responsible for,which allows algorithms to be implemented easily with low communication costs.Numerical test illustrates efficiency and good parallel performance of the algorithms.更多还原