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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2022, Vol. 39 ›› Issue (1): 93-106.doi: 10.3969/j.issn.1005-3085.2022.01.007

• • 上一篇    下一篇

一种求解一维理想磁流体方程组的保正拉氏方法

邹世俊1,   蔚喜军2,   戴自换2   

  1. 1. 中国工程物理研究院研究生院，北京 100088
    2. 北京应用物理与计算数学研究所，北京 100088
  • 出版日期:2022-02-15 发布日期:2022-04-15
  • 通讯作者: 戴自换 E-mail: dai_zihuan@iapcm.ac.cn
  • 基金资助:
    国家自然科学基金 (11671049; 91330107; 11571002; 11702028)；国防基础科研项目 (B1520133015).

A Positivity-preserving Lagrangian Method for Ideal Magnetohydrodynamics Equations in One-dimension

ZOU Shijun1,   YU Xijun2,   DAI Zihuan2   

  1. 1. Graduate School of China Academy of Engineering Physics, Beijing 100088
    2. Institute of Applied Physics and Computational Mathematics, Beijing 100088
  • Online:2022-02-15 Published:2022-04-15
  • Contact: Z. Dai. E-mail address: dai_zihuan@iapcm.ac.cn
  • Supported by:

    The National Natural Science Foundation of China (11671049; 91330107; 11571002; 11702028); the Defense Industrial Technology Development Program (B1520133015).

PDF (PC)

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摘要：

拉氏方法在计算流体力学中扮演了一个十分重要的角色，并且十分适合于处理含有强磁场的物理问题，例如 Z 箍缩、托卡马克、惯性约束聚变等等。在这些物理问题中密度和热力学压力总是非负的。然而，运用数值格式对上述方程进行逼近时，得到的近似解并不能总是保持这种正性。为了处理这一问题，首先构建了一种拉氏 HLLD 近似黎曼解，这一近似黎曼解在合适的信号速度下可以保持保正性质。运用这一黎曼解，提出了一种求解一维理想可压缩磁流体方程组的守恒保正拉氏格式。最后，给出一些数值算例来证明方法的保正性。

关键词: 保正拉氏方法, 理想可压缩磁流体方程组, 拉氏 HLLD 近似黎曼解

Abstract:

Lagrangian methods play a very important role in computational fluid dynamics and especially suitable for dealing with the physical problems related to high-intensity magnetic field such as Z-pinch, Tokamak, ICF, and so on. In these physical problems the density and thermal pressure are always non-negative. However, such positivity property is not always satisfied by approximated solutions which obtained by a numerical scheme. To deal with this problem, the paper develops a Lagrangian HLLD approximate Riemann solver which can keep positivity-preserving property under some appropriate signal speeds. With this solver, a conservative Lagrangian scheme for solving the ideal compressible magnetohydrodynamics equations in one-dimensional is proposed. At last, some numerical examples are presented to demonstrate the positivity-preserving property of our scheme.

Key words: positivity-preserving Lagrangian method, ideal compressible MHD equations, Lagrangian HLLD approximate Riemann solver

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