{"title":"Using Piecewise Parabolic Reconstruction of Physical Variables\nin Rusanov’s Solver. II. Special Relativistic Magnetohydrodynamics Equations","authors":"I. M. Kulikov","doi":"10.1134/S1990478924010083","DOIUrl":null,"url":null,"abstract":"<p> Rusanov’s scheme for solving hydrodynamic equations is one of the most robust in the\nclass of Riemann solvers. It was previously shown that Rusanov’s scheme based on piecewise\nparabolic reconstruction of primitive variables gives a low-dissipative scheme relevant to Roe and\nHarten–Lax–Van Leer solvers when using a similar reconstruction. Moreover, unlike these solvers,\nthe numerical solution is free from artifacts. In the case of equations of special relativistic\nmagnetohydrodynamics, the spectral decomposition for solving the Riemann problem is quite\ncomplex and does not have an analytical solution. The present paper proposes the development of\nRusanov’s scheme using a piecewise parabolic reconstruction of primitive variables to use in the\nequations of special relativistic magnetohydrodynamics. The developed scheme was verified using\neight classical problems on the decay of an arbitrary discontinuity that describe the main features\nof relativistic magnetized flows.\n</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5800,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied and Industrial Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1134/S1990478924010083","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}
引用次数: 0
Abstract
Rusanov’s scheme for solving hydrodynamic equations is one of the most robust in the
class of Riemann solvers. It was previously shown that Rusanov’s scheme based on piecewise
parabolic reconstruction of primitive variables gives a low-dissipative scheme relevant to Roe and
Harten–Lax–Van Leer solvers when using a similar reconstruction. Moreover, unlike these solvers,
the numerical solution is free from artifacts. In the case of equations of special relativistic
magnetohydrodynamics, the spectral decomposition for solving the Riemann problem is quite
complex and does not have an analytical solution. The present paper proposes the development of
Rusanov’s scheme using a piecewise parabolic reconstruction of primitive variables to use in the
equations of special relativistic magnetohydrodynamics. The developed scheme was verified using
eight classical problems on the decay of an arbitrary discontinuity that describe the main features
of relativistic magnetized flows.
期刊介绍:
Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.