Entropy-satisfying relaxation method with large time-steps for Euler IBVPs

Coquel, Frédéric; Nguyen, Quang; Postel, Marie; Tran, Quang

doi:10.1090/S0025-5718-10-02339-2

Entropy-satisfying relaxation method with large time-steps for Euler IBVPs
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by Frédéric Coquel, Quang Long Nguyen, Marie Postel and Quang Huy Tran PDF

Math. Comp. 79 (2010), 1493-1533 Request permission

Abstract:

This paper could have been given the title: “How to positively and implicitly solve Euler equations using only linear scalar advections.” The new relaxation method we propose is able to solve Euler-like systems—as well as initial and boundary value problems—with real state laws at very low cost, using a hybrid explicit-implicit time integration associated with the Arbitrary Lagrangian-Eulerian formalism. Furthermore, it possesses many attractive properties, such as: (i) the preservation of positivity for densities; (ii) the guarantee of min-max principle for mass fractions; (iii) the satisfaction of entropy inequality, under an expressible bound on the CFL ratio. The main feature that will be emphasized is the design of this optimal time-step, which takes into account data not only from the inner domain but also from the boundary conditions.

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