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

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In this paper,we develop new high-order numerical methods for hyperbolic systems of non-linear 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 essen-tially 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.

Hyperbolic conservation and balance laws with uncertaintiesFinite-volume methodsCentral-upwind schemesWeighted essentially non-oscillatory(WENO)interpolations

Alina Chertock、Michael Herty、Arsen S.Iskhakov、Safa Janajra、Alexander Kurganov、Mária Lukáčová-Medvid'ová

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Department of Mathematics,North Carolina State University,Raleigh,NC,USA

Department of Mathematics,RWTH Aachen University,Aachen,Germany

Department of Mathematics,Shenzhen International Center for Mathematics,and Guangdong Provincial Key Laboratory of Computational Science and Material Design,Southern University of Science and Technology,Shenzhen 518055,Guangdong,China

Institute of Mathematics,Johannes Gutenberg University Mainz,Mainz,Germany

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2024

10.1007/s42967-024-00392-z

应用数学与计算数学学报
上海大学

应用数学与计算数学学报

影响因子：0.165
ISSN：1006-6330
年,卷(期)：2024.6(3)