FINITE ELEMENT METHODS FOR NAVIER-STOKES EQUATIONS
FINITE ELEMENT METHODS FOR NAVIER-STOKES EQUATIONS
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DOI：
10.1146/annurev.fl.24.010192.001123
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发表时间：
1992
影响因子：
27.7
通讯作者：
R. Glowinski;O. Pironneau
中科院分区：
文献类型：
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作者：
R. Glowinski;O. Pironneau
本文的主要目的是解决可压缩和不可压缩粘性流动的Navier-Stokes方程的有限元解。作者认为，大多数通用和可靠的不可压缩粘性流模拟器都是基于有限差分方法的;这些模拟器可以处理复杂的几何形状和边界条件、自由表面和湍流效应，非常适合工业应用。另一方面，关于可压缩粘性流动模拟，特别是在高雷诺数和马赫数时，情况就不那么令人满意了，为了达到不可压缩流动模拟所达到的程度，还必须取得很大的进展。在这篇文章中，其范围已自愿限制，我们集中在这些主题结合我们自己的工作和他人的工作，我们熟悉的。本文分为两个部分：在第一部分（第一节至第五节），我们讨论了不可压缩粘性流动的解决方案的基础上运营商分裂的各种成分。通过分裂，在每个时间步得到两个子问题族：一个是对流扩散型的，另一个与定常Stokes方程有关
The main goal of this article is to address the finite element solution of the Navier-Stokes equations modeling compressible and incompressible viscous flow. It is the opinion of the authors that most general and reliable incompressible viscous flow simulators arc based on finite clement method ologies; these simulators, which can handle complicated geometries and boundary conditions, free surfaces, and turbulence effects, are well suited to industrial applications. On the other hand, the situation is much less satisfying concerning compressible viscous flow simulation, particularly at high Reynolds and Mach numbers and much progress must still be made in order to reach the degree of achievement obtained by the incompressible flow simulations. In this article, whose scope has been voluntarily limited, we concentrate on those topics combining our own work and the work of others with which we are familiar. The paper has been divided into two parts: In the first part (Sections I to 5) we discuss the various ingredients of a solution methodology for incompressible viscous flow based on operator splitting. Via splitting one obtains, at each time step, two families of subproblems: one of advection-diffusion type and one related to the steady Stokes