Maximum principle and positivity-preserving high order spectral volume schemes with parametrized flux limiters for solving hyperbolic conservation laws

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NSTL
Elsevier

外文摘要：In this paper, we use maximum principle preserving (MPP) and positivity-preserving (PP) parametrized flux limiters to achieve strict maximum principle and positivity-preserving property for the high order spectral volume (SV) scheme for solving hyperbolic conservation laws. This research is based on a generalization of the MPP and PP parametrized flux limiters in Xu (2014) and Christlieb et al. (2015) with Runge-Kutta (RK) time discretizations. For constructing MPP (PP) RK-SV schemes for hyperbolic conservation laws, we first focus on the RK-SV schemes to discuss how to apply MPP or PP parametrized flux limiters. Then we design and analyze high order MPP RK-SV schemes for scalar conservation laws, and high order PP RK-SV schemes for compressible Euler systems. The efficiency and effectiveness of the proposed schemes are demonstrated via a set of numerical experiments. Both the analysis and numerical experiments indicate that the proposed scheme without any additional time step restriction, not only preserves the maximum principle of the numerical approximation, but also maintains the designed high-order accuracy of the SV scheme for linear advection problems. (C) 2021 Published by Elsevier B.V.

外文关键词：

Hyperbolic conservation lawsSpectral volume schemesMaximum principle preservingPositivity-preservingParametrized flux limiterESSENTIALLY NONOSCILLATORY SCHEMESFINITE-ELEMENT-METHODDISCONTINUOUS GALERKIN METHODSHIGH-RESOLUTION SCHEMESWEIGHTED ENO SCHEMESCENTRAL WENO SCHEMESUNSTRUCTURED GRIDSEFFICIENT IMPLEMENTATIONEXTENSIONTRANSPORT

作者：

Yeganeh, S. Mousavi、Farzi, J.

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作者单位：

Sahand Univ Technol

出版年：

2022

DOI：

10.1016/j.cam.2021.113893

Journal of Computational and Applied Mathematics

EISCI

ISSN：0377-0427

年,卷(期)：2022.404

参考文献量83