# American Institute of Mathematical Sciences

September  2010, 5(3): 507-524. doi: 10.3934/nhm.2010.5.507

## Theoretical and numerical aspects of the interfacial coupling: The scalar Riemann problem and an application to multiphase flows

 1 CEA-Saclay, DEN/DANS/DM2S/SFME/LETR, F-91191 Gif-sur-Yvette, France

Received  January 2010 Revised  April 2010 Published  July 2010

This paper is devoted to the study of the one dimensional interfacial coupling of two PDE systems at a given fixed interface, say $x=0$. Each system is posed on a half-space, namely $x<0$ and $x>0$. As an interfacial model, a coupling condition whose objective is to enforce the continuity (in a weak sense) of a prescribed variable is generally imposed at $x=0$.
We first focus on the coupling of two scalar conservation laws and state an existence result for the coupled Riemann problem. Numerical experiments are also proposed. We then consider, both from a theoretical and a numerical point of view, the coupling of two-phase flow models namely a drift-flux model and a two-fluid model. In particular, the link between both models will be addressed using asymptotic expansions.
Citation: Christophe Chalons. Theoretical and numerical aspects of the interfacial coupling: The scalar Riemann problem and an application to multiphase flows. Networks and Heterogeneous Media, 2010, 5 (3) : 507-524. doi: 10.3934/nhm.2010.5.507
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