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arXiv · 2312.08280

New High-Order Numerical Methods for Hyperbolic Systems of Nonlinear PDEs with Uncertainties

Alina Chertock·Michael Herty·Arsen S. Iskhakov·Safa Janajra·Alexander Kurganov·Maria Lukacova-Medvidova
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Abstract

In this paper, we develop new high-order numerical methods for hyperbolic systems of nonlinear partial differential equations (PDEs) with uncertainties. The new approach is realized in the semi-discrete finite-volume framework and is based on fifth-order weighted essentially non-oscillatory (WENO) interpolations in (multidimensional) random space combined with second-order piecewise linear reconstruction in physical space. Compared with spectral approximations in the random space, the presented methods are essentially non-oscillatory as they do not suffer from the Gibbs phenomenon while still achieving high-order accuracy. The new methods are tested on a number of numerical examples for both the Euler equations of gas dynamics and the Saint-Venant system of shallow-water equations. In the latter case, the methods are also proven to be well-balanced and positivity-preserving.

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Alina Chertock, Michael Herty, Arsen S. Iskhakov, Safa Janajra, Alexander Kurganov, Maria Lukacova-Medvidova. 2024-07-03. New High-Order Numerical Methods for Hyperbolic Systems of Nonlinear PDEs with Uncertainties. https://doi.org/10.1007/s42967-024-00392-z

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