Implicit solution methods in computational fluid dynamics

Abstract

A class of implicit finite difference schemes of the Beam and Warming approximate factorization type will be addressed. The development and analysis of various aspects of this class of schemes will be given along with the motivations behind many of the choices. Various acceleration and efficiency modifications such as matrix reduction, diagonalization and flux split schemes will be presented. The methods are demonstrated in fully vectorized codes for a CRAY type architecture. The emphasis will be on the Euler equations in generalized coordinates.