Using Piecewise Parabolic Reconstruction of Physical Variables in Rusanov’s Solver. II. Special Relativistic Magnetohydrodynamics Equations

IF 0.58 Q3 Engineering
I. M. Kulikov
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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.

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在鲁萨诺夫求解器中使用物理变量的分段抛物线重构。II.特殊相对论磁流体动力学方程
摘要 Rusanov 的流体力学方程求解方案是黎曼求解器中最稳健的方案之一。以前的研究表明,当使用类似的重构时,Rusanov 基于基元变量的片断抛物线重构的方案给出了与 Roe 和 Harten-Lax-Van Leer 求解器相关的低损耗方案。此外,与这些求解器不同的是,数值解法没有人工痕迹。对于特殊相对论磁流体力学方程,求解黎曼问题的谱分解非常复杂,而且没有解析解。本文提出利用原始变量的片断抛物线重构来发展鲁萨诺夫方案,并将其用于特殊相对论磁流体动力学方程。本文利用关于任意不连续性衰减的八个经典问题验证了所开发的方案,这些问题描述了相对论磁流体的主要特征。
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来源期刊
Journal of Applied and Industrial Mathematics
Journal of Applied and Industrial Mathematics Engineering-Industrial and Manufacturing Engineering
CiteScore
1.00
自引率
0.00%
发文量
16
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.
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