Preprint 45-2003

A Fictitious Domain Method for the Numerical Solution of the Stationary Navier-Stokes Equations

Author(s) : Thomas Slawig

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 45-2003

MSC 2000

76D05 Navier-Stokes equations

65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods

Abstract :
An embedding domain method for the stationary incompressible Navier-Stokes equations is presented. The method is useful for solving the equations or complicated-shaped or varying domains. The original domain is embedded in a so-called fictitious one. On the latter an equivalent formulation of the Navier-Stokes equation is derived. Existence and uniqueness results of its solution(s) are presented. The structure of and solution methods for the discrete systems and numerical issues are discussed. An algorithm for finding the trace of the original boundary in the fictitious domain are given. Numerical results for the fictitious domain method are compared with those from computations on the original domain. As test case the 2-D flow around a circular cylinder in a channel is used.

Keywords : Navier-Stokes Equations, embedding domain method