Multidimensional Upwinding. Part I. The Method of Transport for Solving the Euler Equations
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...
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| Published in | Journal of computational physics Vol. 143; no. 1; pp. 159 - 180 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Inc
10.06.1998
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| Online Access | Get full text |
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| Summary: | 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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| ISSN: | 0021-9991 1090-2716 |
| DOI: | 10.1006/jcph.1998.5958 |