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

Stephan Gerster; Aleksey Sikstel; Giuseppe Visconti

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arXiv · 2203.11718

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

Stephan Gerster·Aleksey Sikstel·Giuseppe Visconti

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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.

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Stephan Gerster, Aleksey Sikstel, Giuseppe Visconti. 2022-03-22. Haar-type stochastic Galerkin formulations for hyperbolic systems with Lipschitz continuous flux function. https://arxiv.org/abs/2203.11718

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