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

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 enjoys many desirable 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 design of this optimal time-step, which takes into account data not only from the inner domain but also from the boundary conditions, is the main novel feature we emphasize on. Keywords Euler equations, multiphase flow, initial boundary value problems, explicit-implicit, relaxation methods, Lagrange-projection, ...

• Type: Journal
• Year: 2010
• Where: MOC
• Authors: Frédéric Coquel, Quang Long Nguyen, Marie Postel, Quang-Huy Tran
• Keywords: Boundary Value Problems, Euler Equations, MOC 2010, Relaxation Methods, Security Privacy