Navier—Stokes方程有限元并行计算方法最新进展

摘要

Navier-Stokes equations are the basic equations in fluid mechanics, for which the development of parallel numerical methods is one of the hot research topics in computational mathematics and computational fluid dynamics. This paper gives an overview of existing parallel finite element methods for the Navier-Stokes equations. The classifications, the basic ideas, the advantages and disadvantages of different methods are discussed. Finally, the perspectives and challenges in developing parallel finite element methods for the Navier-Stokes equations are given.%Navier—Stokes方程是流体力学的基本方程，其并行数值求解方法是当前计算数学和计算流体力学领域的最前沿课题之一。综述了Navier-Stokes方程有限元并行计算方法的研究现状。将已有的方法进行分类，分别介绍了其基本思想，评述了各种有限元并行计算方法的优缺点，讨论了有限元并行计算方法所面临的问题，并对其发展趋势进行了展望。