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Residual distribution schemes: Current status and future trends Remi Abgrall *
 

Summary: Review
Residual distribution schemes: Current status and future trends
Re´mi Abgrall *
Institut Universitaire de France and Mathe´matiques Applique´es de Bordeaux, Universite´ Bordeaux I, 33 405 Talence Cedex, France
Received 1 August 2004; accepted 10 January 2005
Available online 10 February 2006
Abstract
In this paper, we discuss a new class of schemes, the residual distribution schemes, adapted to compressible flow problems. They can
be seen as a link between pure finite element methods such as the streamline diffusion method and the high order upwind method finite
volume schemes. In fact they borrow ideas from both classes and this results in very accurate compact schemes. Up to now, they are
mainly adapted to triangular type meshes, but can handle steady and unsteady problems. Since the philosophy is quite different form
standard schemes, we will provide a full description of the schemes and many numerical illustrations. Some still unsolved issues will also
be discussed.
Ó 2005 Elsevier Ltd. All rights reserved.
Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 642
2. Residual distribution for steady problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 643
2.1. Generalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 643
2.2. Accuracy, monotonicity and conservation issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 644
2.2.1. Monotonicity preserving schemes, scalar case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 644

  

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

 

Collections: Mathematics