Numerical Approximation of Hyperbolic Systems Containing an Interface

In this paper we present an approach to approximate numerically the solution of coupled hyperbolic conservation laws. The coupling is achieved through a fixed interface, in which interface conditions are linking the traces of both sides. The numerical solver is based on central methods, like the Rus...

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Bibliographic Details
Published in:arXiv.org 2016-03
Main Authors: Aguillon, Nina, Borsche, Raul
Format: Article
Language:English
Subjects:
Conservation laws
Hyperbolic systems
Mathematical models
Online Access:Get full text
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Summary:In this paper we present an approach to approximate numerically the solution of coupled hyperbolic conservation laws. The coupling is achieved through a fixed interface, in which interface conditions are linking the traces of both sides. The numerical solver is based on central methods, like the Rusanov scheme, and does not use the structure of the Riemann Problem. It consists in balancing the effects of the waves that enter the interface. The scheme is well balanced with respect to all the piecewise constant equilibria associated with the interface condition and is able to maintain exactly conservation properties of the interface conditions. A detailed analysis and several numerical tests show the quality of the method. Different applications, including sonic and transsonic flows and a multiphysic model are studied.
ISSN:2331-8422