Parallel Solution Schemes for the Navier–Stokes Equations

Volker John Otto-von-Guericke-Universität Magdeburg PSF 4120, D-39016 Magdeburg, FRG

Abstract

We consider a finite element discretization of the linearized incompressible Navier– Stokes equations using the non–conforming P_{1}/P_{0} element of Crouzeix/Raviart and upwind techniques for stabilization. This leads to a large linear system of the form

( \begin{matrix}A & B \\ B^{T} & 0 \end{matrix} ) ( \begin{matrix}u \\ p \end{matrix} ) = ( \begin{matrix}f \\ 0 \end{matrix} ) .

We present various algorithms to solve this system of linear equations, estimate their computational costs and discuss their implementation on a parallel computer.