Maximum-Principle-Preserving, Steady-State-Preserving and Large Time-Stepping High-Order Schemes for Scalar Hyperbolic Equations with Source Terms

IF 2.6 3区 物理与天体物理 Q1 PHYSICS, MATHEMATICAL Communications in Computational Physics Pub Date : 2024-03-01 DOI:10.4208/cicp.oa-2023-0143
Lele Liu,Hong Zhang,Xu Qian, Songhe Song
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Abstract

In this paper, we construct a family of temporal high-order parametric relaxation Runge–Kutta (pRRK) schemes for stiff ordinary differential equations (ODEs), and explore their application in solving hyperbolic conservation laws with source terms. The new time discretization methods are explicit, large time-stepping, delay-free and able to preserve steady state. They are combined with fifth-order weighted compact nonlinear schemes (WCNS5) spatial discretization and parametrized maximum-principle-preserving (MPP) flux limiters to solve scalar hyperbolic equations with source terms. We prove that the fully discrete schemes preserve the maximum principle strictly. Through benchmark test problems, we demonstrate that the proposed schemes have fifth-order accuracy in space, fourth-order accuracy in time and allow for large time-stepping without time delay. Both theoretical analyses and numerical experiments are presented to validate the benefits of the proposed schemes.
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有源项的标量双曲方程的最大原则保留、稳态保留和大时间步进高阶方案
在本文中,我们为刚性常微分方程(ODEs)构建了一系列时间高阶参数松弛 Runge-Kutta (pRRK) 方案,并探讨了它们在求解带源项的双曲守恒定律中的应用。新的时间离散化方法是显式的、大时间步长的、无延迟的,并且能够保持稳定状态。它们与五阶加权紧凑非线性方案(WCNS5)空间离散化和参数化最大原理保持(MPP)通量限制器相结合,用于求解带有源项的标量双曲方程。我们证明了完全离散方案严格保留了最大原则。通过基准测试问题,我们证明了所提出的方案在空间上具有五阶精度,在时间上具有四阶精度,并且允许无时间延迟的大时间步进。理论分析和数值实验都验证了所提方案的优势。
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来源期刊
Communications in Computational Physics
Communications in Computational Physics 物理-物理:数学物理
CiteScore
4.70
自引率
5.40%
发文量
84
审稿时长
9 months
期刊介绍: Communications in Computational Physics (CiCP) publishes original research and survey papers of high scientific value in computational modeling of physical problems. Results in multi-physics and multi-scale innovative computational methods and modeling in all physical sciences will be featured.
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