{"title":"Maximum-Principle-Preserving, Steady-State-Preserving and Large Time-Stepping High-Order Schemes for Scalar Hyperbolic Equations with Source Terms","authors":"Lele Liu,Hong Zhang,Xu Qian, Songhe Song","doi":"10.4208/cicp.oa-2023-0143","DOIUrl":null,"url":null,"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\nwith source terms. The new time discretization methods are explicit, large time-stepping, delay-free and able to preserve steady state. They are combined with\nfifth-order weighted compact nonlinear schemes (WCNS5) spatial discretization and\nparametrized 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\nanalyses and numerical experiments are presented to validate the benefits of the proposed schemes.","PeriodicalId":50661,"journal":{"name":"Communications in Computational Physics","volume":null,"pages":null},"PeriodicalIF":2.6000,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Computational Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.4208/cicp.oa-2023-0143","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
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.
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.