Liou–Steffen压力系统非线性守恒律双曲型系统的Riemann问题

IF 0.5 4区数学 Q4 MATHEMATICS, APPLIED

Journal of Hyperbolic Differential Equations Pub Date : 2022-09-01 DOI:10.1142/s021989162250014x

Hongjun Cheng, Hanchun Yang

{"title":"Liou–Steffen压力系统非线性守恒律双曲型系统的Riemann问题","authors":"Hongjun Cheng, Hanchun Yang","doi":"10.1142/s021989162250014x","DOIUrl":null,"url":null,"abstract":"This paper is devoted to a hyperbolic system of nonlinear conservation laws, that is, the pressure system independent of density and energy from the Liou–Steffen flux-splitting scheme on the compressible Euler equations. First, the one-dimensional Riemann problem is solved with eight kinds of structures. Second, the two-dimensional Riemann problem is discussed; the solution reveals a variety of geometric structures; by the generalized characteristic analysis method and studying the pointwise interactions of waves, we construct 29 kinds of structures of solution consisting of shocks, rarefaction waves and contact discontinuities; the theoretical analysis is confirmed by numerical simulations.","PeriodicalId":50182,"journal":{"name":"Journal of Hyperbolic Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Riemann problems for a hyperbolic system of nonlinear conservation laws from the Liou–Steffen pressure system\",\"authors\":\"Hongjun Cheng, Hanchun Yang\",\"doi\":\"10.1142/s021989162250014x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper is devoted to a hyperbolic system of nonlinear conservation laws, that is, the pressure system independent of density and energy from the Liou–Steffen flux-splitting scheme on the compressible Euler equations. First, the one-dimensional Riemann problem is solved with eight kinds of structures. Second, the two-dimensional Riemann problem is discussed; the solution reveals a variety of geometric structures; by the generalized characteristic analysis method and studying the pointwise interactions of waves, we construct 29 kinds of structures of solution consisting of shocks, rarefaction waves and contact discontinuities; the theoretical analysis is confirmed by numerical simulations.\",\"PeriodicalId\":50182,\"journal\":{\"name\":\"Journal of Hyperbolic Differential Equations\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2022-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Hyperbolic Differential Equations\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1142/s021989162250014x\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Hyperbolic Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s021989162250014x","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

本文研究了一个非线性守恒定律的双曲型系统，即可压缩Euler方程上Liou–Steffen通量分裂格式中与密度和能量无关的压力系统。首先，用八种结构求解一维黎曼问题。其次，讨论了二维黎曼问题；该解决方案揭示了各种几何结构；采用广义特征分析方法，研究了波的逐点相互作用，构造了29种由冲击、稀疏波和接触间断组成的解的结构；数值模拟验证了理论分析的正确性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Riemann problems for a hyperbolic system of nonlinear conservation laws from the Liou–Steffen pressure system

This paper is devoted to a hyperbolic system of nonlinear conservation laws, that is, the pressure system independent of density and energy from the Liou–Steffen flux-splitting scheme on the compressible Euler equations. First, the one-dimensional Riemann problem is solved with eight kinds of structures. Second, the two-dimensional Riemann problem is discussed; the solution reveals a variety of geometric structures; by the generalized characteristic analysis method and studying the pointwise interactions of waves, we construct 29 kinds of structures of solution consisting of shocks, rarefaction waves and contact discontinuities; the theoretical analysis is confirmed by numerical simulations.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of Hyperbolic Differential Equations 数学-物理：数学物理

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

24 months

期刊介绍： This journal publishes original research papers on nonlinear hyperbolic problems and related topics, of mathematical and/or physical interest. Specifically, it invites papers on the theory and numerical analysis of hyperbolic conservation laws and of hyperbolic partial differential equations arising in mathematical physics. The Journal welcomes contributions in: Theory of nonlinear hyperbolic systems of conservation laws, addressing the issues of well-posedness and qualitative behavior of solutions, in one or several space dimensions. Hyperbolic differential equations of mathematical physics, such as the Einstein equations of general relativity, Dirac equations, Maxwell equations, relativistic fluid models, etc. Lorentzian geometry, particularly global geometric and causal theoretic aspects of spacetimes satisfying the Einstein equations. Nonlinear hyperbolic systems arising in continuum physics such as: hyperbolic models of fluid dynamics, mixed models of transonic flows, etc. General problems that are dominated (but not exclusively driven) by finite speed phenomena, such as dissipative and dispersive perturbations of hyperbolic systems, and models from statistical mechanics and other probabilistic models relevant to the derivation of fluid dynamical equations. Convergence analysis of numerical methods for hyperbolic equations: finite difference schemes, finite volumes schemes, etc.