Implicit methods in CFD

Abstract

A class of implicit approximate factorization schemes is examined for stability and convergence characteristics. These schemes include Newton's method, factorization, and flux-vector splitting. Examples are used to show that all practical methods suffer from some limited stability or asymptotic convergence restriction. A three-dimensional factored scheme is shown which suffers from unconditional instability which can only be ameliorated by added artificial dissipation. An F3D + or - flux split scheme is described which avoids unconditional instability, but in the end has similar convergence characteristics.