New High-Order Numerical Methods for Hyperbolic Systems of Nonlinear PDEs with Uncertainties
Alina Chertock , Michael Herty , Arsen S. Iskhakov , Safa Janajra , Alexander Kurganov , Mária Lukáčová-Medvid’ová
Communications on Applied Mathematics and Computation ›› 2024, Vol. 6 ›› Issue (3) : 2011 -2044.
New High-Order Numerical Methods for Hyperbolic Systems of Nonlinear PDEs with Uncertainties
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.
Division of Mathematical Sciences(DMS-2208438)
Deutsche Forschungsgemeinschaft(20021702/GRK2326)
Germany’s Excellence Strategy EXC-2023 Internet of Production(390621612)
National Natural Science Foundation of China(12171226)
Guangdong Provincial Key Laboratory Of Computational Science And Material Design(2019B030301001)
Deutsche Forschungsgemeinschaft(SFB/TRR 146 Multiscale Simulation Methods for Soft Matter Systems)
LeRoy B. Martin, Jr. Distinguished Professorship Foundation
LeRoy B. Martin, Jr. Distinguished Professorship Foundation
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