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Multidimensional Upwinding. Part I. The Method of Transport for Solving the Euler Equations

โœ Scribed by Michael Fey

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
486 KB
Volume
143
Category
Article
ISSN
0021-9991

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โœฆ Synopsis

The aim of this paper is to show a new approach towards the discretization of multidimensional conservation laws. The idea of transport associated with the solution of a scalar equation is used for the convective part of the compressible Euler equations. A multidimensional wave structure is derived to model the acoustic part of this non-linear system, that allows infinitely many propagation directions in the numerical method. This provides the basic knowledge to construct a numerical method that does not rely on Riemann solvers. A more general definition of the waves, together with the concept of consistency, enables the design of a number of effective, genuinely multidimensional, methods.

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