Mathematics of Computation

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ISSN 1088-6842(e) ISSN 0025-5718(p)

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

Author(s): Frédéric Coquel; Quang Long Nguyen; Marie Postel; Quang Huy Tran.
Journal: Math. Comp. 79 (2010), 1493-1533.
MSC (2010): Primary 65M08; Secondary 35L04
Posted: February 23, 2010
MathSciNet review: 2630001
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

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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