Summary: Construction of second-order accurate monotone and
stable residual distribution schemes for steady problems
Remi Abgrall *,1
, Mohamed Mezine
Mathematiques Appliquees de Bordeaux, Universite Bordeaux I, 351 cours de la Liberation, 33 405 Talence Cedex, France
Received 25 April 2003; received in revised form 9 September 2003; accepted 10 September 2003
Abstract
After having recalled the basic concepts of residual distribution (RD) schemes, we provide a systematic construction
of distribution schemes able to handle general unstructured meshes, extending the work of Sidilkover. Then, by using
the concept of simple waves, we show how to generalize this technique to symmetrizable linear systems. A stability
analysis is provided. We formally extend this construction to the Euler equations. Several test cases are presented to
validate our approach.
Ó 2003 Elsevier Inc. All rights reserved.
AMS: 65C99; 65M60; 76N10
Keywords: Compressible flow solvers; Residual schemes; Unstructured meshes; Multidimensional up-winding
1. Introduction
The numerical simulation of compressible flows is generally done via some generalization of the one-
dimensional Lax­Wendroff scheme. It is well known that this scheme is stable in the energy norm, but does
not have any stability property in the maximum norm. The simulation of flows with strong discontinuities
can only be performed with schemes having properties in the maximum norm, because we want solutions

Source: Abgrall, Rémi - Institut de Mathematiques de Bordeaux, Université Bordeaux

Collections: Mathematics