Bienvenue - Laboratoire Jacques-Louis Lions

17 juin 2016 : 14h00-15h00
Eitan Tadmor (Université du Maryland)
Computation of entropy measure-valued solutions for Euler equations
(Colloquium dans le cadre des Leçons Jacques-Louis Lions 2016)

Exceptionnellement, ce Colloquium aura lieu dans l’amphithéâtre 25
(entrée face à la tour 25, niveau dalle Jussieu, Université Pierre et Marie Curie, Campus Jussieu, 4 place Jussieu, Paris 5ème)

Abstract
 Entropy stability plays an important role in the dynamics of nonlinear hyperbolic systems of conservation laws. But there are serious obstacles, most notably in multidimensional problems, where the persistence of oscillations at finer and finer scales prevents compactness. Indeed, these oscillations are an indication, consistent with recent theoretical results, of the possible lack of existence/uniqueness of entropy solutions within the standard framework of integrable functions. It is in this context that entropy measure-valued solutions offer the more general solution paradigm. Solutions are interpreted in an average sense as part of an ensemble average in configuration space.
 We revisit the general framework of numerical entropy stability. Our approach is based on comparing numerical viscosities with entropy conservative schemes. We demonstrate this approach with entropy conservative fluxes which serve as the building block for a class of non-oscillatory entropy stable schemes of arbitrarily high-order of accuracy, so-called TeCNO schemes.
 We then outline a viable numerical algorithm to compute entropy measure-valued solutions, based on realization of approximate measures as laws of Monte Carlo sampled random fields. Numerical experiments, including recent TeCNO-based computation of entropy measure-valued solutions, provide a convincing evidence for the viability of the new paradigm.