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

TL;DR

This paper introduces a novel method leveraging $\\mathcal{K}$-convergence to accurately compute Young measures from numerical solutions of the compressible Euler system, enhancing the understanding of oscillatory behaviors.

Contribution

It develops a new approach based on $\\mathcal{K}$-convergence for effectively computing Young measures associated with Euler system solutions.

Findings

The method achieves strong convergence in space and time.

Measures converge narrowly or in Wasserstein distance to the limit.

Enables better analysis of oscillations in Euler solutions.

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.