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High order uctuation schemes on triangular meshes R. Abgrally and P.L. Roe z
 

Summary: High order uctuation schemes on triangular meshes
R. Abgrally and P.L. Roe z
y Mathematiques Appliquees de Bordeaux,
Universite Bordeaux I, 33 405 Talence Cedex, France
and Institut Universitaire de France
z W. M. Keck Laboratory for Computational Fluid Dynamics,
Department of Aerospace Engineering,
University of Michigan, Ann Arbor, MI 48109, USA
Draft May 3, 2002
Abstract
We develop a new class of schemes for the numerical solution of rst-order steady conservation laws.
The schemes are of the residual distribution, or uctuation-splitting type. These schemes have mostly
been developed in the context of triangular or tetrahedral elements whose degrees of freedom are their
nodal values. We work here with more general elements that allow high-order accuracy. We introduce,
for an arbitrary number of degrees of freedom, a simple mapping from a low-order monotone scheme
to a monotone scheme that is as accurate as the degrees of freedom will allow. Proofs of consistency,
convergence and accuracy are presented, and numerical examples from second, third and fourth-order
schemes.
1 Introduction
In this paper, we consider high order discretisations of the problem

  

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

 

Collections: Mathematics