Continuation Methods in Computational Fluid Dynamics

Abstract

Continuation methods are extremely powerful techniques that aid in the numerical solution of nonlinear problems. Their use in computational fluid dynamics has, until very recently, been minimal. This is somewhat surprising, since they are rather well known in solid mechanics. Furthermore, their mathematical foundations—homotopy methods—were laid by mathematicians very much concerned with fluid-dynamical problems and in particular with the construction of existence proofs for the Navier-Stokes equations. We shall attempt here to recall or expose some of these ideas and to indicate some of their current uses in computational fluid dynamics. Brief remarks on their relevance to the papers on numerical fluid dynamics in this meeting are made in Section 2.