Computing oscillatory solutions of the Euler system via $\mathcal{K}$-convergence

Abstract

We develop a method to compute effectively the Young measures associated to sequences of numerical solutions of the compressible Euler system. Our approach is based on the concept of $\mathcal{K}$-convergence adapted to sequences of parametrized measures. The convergence is strong in space and time (a.e.~pointwise or in certain $L^q$ spaces) whereas the measures converge narrowly or in the Wasserstein distance to the corresponding limit.

arXiv comment35 pages, 8 figures

References in corpus (4)

• On admissibility criteria for weak solutions of the Euler equations
• Construction of approximate entropy measure valued solutions for hyperbolic systems of conservation laws
• On oscillatory solutions to the complete Euler system
• On the convergence of a finite volume method for the Navier-Stokes-Fourier system