A comparison of time-discretization/linearization approaches for the incompressible Navier–Stokes equations

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• 作者：Volker John ; Gunar Matthies and Joachim Rang
• 关键词：Incompressible Navier– ; Stokes equations ; Rosenbrock methods ; Implicit θ ; -schemes ; Fixed point iteration
• 刊名：Computer Methods in Applied Mechanics and Engineering
• 出版年：2006
• 出版时间：15 September 2006
• 年：2006
• 卷：195
• 期：44-47
• 页码：5995-6010
• 全文大小：364 K

文摘

This paper presents a numerical study of two ways for discretizing and linearizing the time-dependent incompressible Navier–Stokes equations. One approach consists in first applying a semi-discretization in time by a fully implicit θ-scheme. Then, in each discrete time, the equations are linearized by a fixed point iteration. The number of iterations to reach a given stopping criterion is a priori unknown in this approach. In the second approach, Rosenbrock schemes with s stages are used as temporal discretization. The non-linearity of the Navier–Stokes equations is treated internally in the Rosenbrock methods. In each discrete time, exactly s linear systems of equations have to be solved. The numerical study considers five two-dimensional problems with distinct features. Four implicit time stepping schemes and five Rosenbrock methods are involved.