Computing oscillatory solutions of the Euler system via 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 K-convergence adapted to sequences of parameterized measures.

The convergence is strong in space and time (a.e. pointwise or in certain Lq spaces) whereas the measures converge narrowly or in the Wasserstein distance to the corresponding limit.

Keywords

• Young measure
• dissipative solutions
• K-convergence
• compressible Euler system
• Wasserstein distance
• finite volume methods
• consistent approximate solutions