{"title":"A third-order entropy condition scheme for hyperbolic conservation laws","authors":"Haitao Dong, Tong Zhou, Fujun Liu","doi":"10.1002/fld.5268","DOIUrl":null,"url":null,"abstract":"<p>Following the solution formula method given in Dong et al. (High order discontinuities decomposition entropy condition schemes for Euler equations. <i>CFD J</i>. 2002;10(4): 448–457), this article studies a type of one-step fully-discrete scheme, and constructs a third-order scheme which is written into a compact form via a new limiter. The highlights of this study and advantages of new third-order scheme are as follows: ① We proposed a very simple new methodology of constructing one-step, consistent high-order and non-oscillation schemes that do not rely on Runge–Kutta method; ② We systematically studied new scheme's theoretical problems about entropy conditions, error analysis, and non-oscillation conditions; ③ The new scheme achieves exact solution in linear cases and performing better in nonlinear cases when CFL → 1; ④ The new scheme is third order but high resolution with excellent shock-capturing capacity which is comparable to fifth order WENO scheme; ⑤ CPU time of new scheme is only a quarter of WENO5 + RK3 under same computing condition; ⑥ For engineering applications, the new scheme is extended to multi-dimensional Euler equations under curvilinear coordinates. Numerical experiments contain 1D scalar equation, 1D,2D,3D Euler equations. Accuracy tests are carried out using 1D linear scalar equation, 1D Burgers equation and 2D Euler equations and two sonic point tests are carried out to show the effect of entropy condition linearization. All tests are compared with results of WENO5 and finally indicate EC3 is cheaper in computational expense.</p>","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":null,"pages":null},"PeriodicalIF":1.7000,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal for Numerical Methods in Fluids","FirstCategoryId":"5","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/fld.5268","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
Following the solution formula method given in Dong et al. (High order discontinuities decomposition entropy condition schemes for Euler equations. CFD J. 2002;10(4): 448–457), this article studies a type of one-step fully-discrete scheme, and constructs a third-order scheme which is written into a compact form via a new limiter. The highlights of this study and advantages of new third-order scheme are as follows: ① We proposed a very simple new methodology of constructing one-step, consistent high-order and non-oscillation schemes that do not rely on Runge–Kutta method; ② We systematically studied new scheme's theoretical problems about entropy conditions, error analysis, and non-oscillation conditions; ③ The new scheme achieves exact solution in linear cases and performing better in nonlinear cases when CFL → 1; ④ The new scheme is third order but high resolution with excellent shock-capturing capacity which is comparable to fifth order WENO scheme; ⑤ CPU time of new scheme is only a quarter of WENO5 + RK3 under same computing condition; ⑥ For engineering applications, the new scheme is extended to multi-dimensional Euler equations under curvilinear coordinates. Numerical experiments contain 1D scalar equation, 1D,2D,3D Euler equations. Accuracy tests are carried out using 1D linear scalar equation, 1D Burgers equation and 2D Euler equations and two sonic point tests are carried out to show the effect of entropy condition linearization. All tests are compared with results of WENO5 and finally indicate EC3 is cheaper in computational expense.
期刊介绍:
The International Journal for Numerical Methods in Fluids publishes refereed papers describing significant developments in computational methods that are applicable to scientific and engineering problems in fluid mechanics, fluid dynamics, micro and bio fluidics, and fluid-structure interaction. Numerical methods for solving ancillary equations, such as transport and advection and diffusion, are also relevant. The Editors encourage contributions in the areas of multi-physics, multi-disciplinary and multi-scale problems involving fluid subsystems, verification and validation, uncertainty quantification, and model reduction.
Numerical examples that illustrate the described methods or their accuracy are in general expected. Discussions of papers already in print are also considered. However, papers dealing strictly with applications of existing methods or dealing with areas of research that are not deemed to be cutting edge by the Editors will not be considered for review.
The journal publishes full-length papers, which should normally be less than 25 journal pages in length. Two-part papers are discouraged unless considered necessary by the Editors.