Random compressible Euler flows

TL;DR

This paper introduces a stochastic collocation finite volume method for solving the random Euler system, providing rigorous convergence proofs under boundedness assumptions, and combines deterministic and stochastic analysis techniques.

Contribution

It presents a novel finite volume stochastic collocation approach for the Euler system with rigorous convergence analysis incorporating stochastic compactness methods.

Findings

Proves convergence of the proposed method under boundedness assumptions.

Integrates deterministic FV convergence with stochastic compactness arguments.

Establishes a rigorous theoretical foundation for stochastic Euler flow simulations.

Abstract

We propose a finite volume stochastic collocation method for the random Euler system. We rigorously prove the convergence of random finite volume solutions under the assumption that the discrete differential quotients remain bounded in probability. Convergence analysis combines results on the convergence of a deterministic FV method with stochastic compactness arguments due to Skorokhod and Gy\"ongy-Krylov.