QMR methods in computational fluid dynamics

Abstract

We examine the application of QMR methods to the solution of linear systems of equations arising from the use of implicit solution methods in computational fluid dynamics. We will deal with implicit finite difference schemes for solving the Euler equations. These schemes may arise from the implicit treatment of the time dependent equations or from the use of Newton`s method for the solution of the steady state equations. In both situations it is necessary to solve a large sparse nonsymmetric linear system of equations at each iteration. We will examine the effectiveness of QMR in the solution of these systems. W e compare the resulting methods to methods which rely on some other simplifying technique to solve the linear systems. Our goal is to show that the QMR method is a viable alternative to the more ad-hoc schemes for solving implicit computational fluid dynamics problems.