Relaxation algorithms for the Euler equations

Abstract

The alternating direction implicit central-difference scheme algorithms may be replaced by successive-line-relaxation (SLR) procedures that are stable in three dimensions. Several Beamand Warming-type codes are presently modified on the basis of SLR solution procedures in order to compute the flows over a cylinder, a NACA-0012 airfoil, and a shock wave reflecting off a plate. Since the codes are written in a 'delta form', the implementation of relaxation procedures that rely only on the corrections is relatively easy; the steady state residual computation and any artificial viscosity terms may be left unchanged.