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A coupled approach to compute approximate solutions of a compressible immiscible three-phase flow model with fast transient and stiff source terms
Jean-Marc Hérard1; Guillaume Jomée1
1 EDF Lab Chatou, 6 quai Watier, 78400, Chatou, France
The SMAI Journal of computational mathematics, Volume 11 (2025), pp. 405-434.

This paper aims at developing a new numerical coupled approach to compute solutions of a compressible immiscible three-phase flow model with stiff source terms. The targeted applications involve flows with fast transient and shock waves. Thus, a well-posed model with respect to the initial conditions that embarks an entropy inequality is considered. A preliminary work on the underlying relaxation process of the model is conducted. Then the new numerical scheme is presented and numerically tested.

Published online:
DOI: 10.5802/smai-jcm.129
Classification: 76T30, 65M08, 34C26
Keywords: Multiphase flows, Hyperbolic Systems, Relaxation, Compressible fluids, Transient flows, Steam explosion

Jean-Marc Hérard 1; Guillaume Jomée 1

1 EDF Lab Chatou, 6 quai Watier, 78400, Chatou, France 
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     title = {A coupled approach to compute approximate solutions of a compressible immiscible three-phase flow model with fast transient and stiff source terms},
     journal = {The SMAI Journal of computational mathematics},
     pages = {405--434},
     publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
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Jean-Marc Hérard; Guillaume Jomée. A coupled approach to compute approximate solutions of a compressible immiscible three-phase flow model with fast transient and stiff source terms. The SMAI Journal of computational mathematics, Volume 11 (2025), pp. 405-434. doi : 10.5802/smai-jcm.129. https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.129/

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