Haar-type stochastic Galerkin formulations for hyperbolic systems with Lipschitz continuous flux function

TL;DR

This paper extends Haar-type stochastic Galerkin methods to multi-dimensional hyperbolic systems with Lipschitz continuous flux functions, providing theoretical insights and numerical validation for complex nonlinear stochastic problems.

Contribution

It generalizes previous Haar-based stochastic Galerkin formulations to multi-dimensional systems with non-polynomial flux functions, enhancing applicability.

Findings

Theoretical analysis of the generalized formulation.

Numerical validation using multidimensional CWENO reconstruction.

Demonstration of the method's effectiveness on complex systems.

Abstract

This work is devoted to the Galerkin projection of highly nonlinear random quantities. The dependency on a random input is described by Haar-type wavelet systems. The classical Haar sequence has been used by Pettersson, Iaccarino, Nordstroem (2014) for a hyperbolic stochastic Galerkin formulation of the one-dimensional Euler equations. This work generalizes their approach to several multi-dimensional systems with Lipschitz continuous and non-polynomial flux functions. Theoretical results are illustrated numerically by a genuinely multidimensional CWENO reconstruction.