, Volume 50, Issue 2, pp 331-376

Front tracking for a model of immiscible gas flow with large data

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Abstract

In this paper we study front tracking for a model of one dimensional, immiscible flow of several isentropic gases, each governed by a gamma-law. The model consists of the p-system with variable gamma representing the different gases. The main result is the convergence of a front tracking algorithm to a weak solution, thereby giving existence as well. This convergence holds for general initial data with a total variation satisfying a specific bound. The result is illustrated by numerical examples.

Communicated by Anders Szepessy.
This paper was written as part of the international research program on Nonlinear Partial Differential Equations at the Centre for Advanced Study at the Norwegian Academy of Science and Letters in Oslo during the academic year 2008–09. Supported in part by the Research Council of Norway through the project “Integro-PDEs: Numerical methods, Analysis, and Applications to Finance”.