拉格朗日方法中减小非物理熵增的方法

doi:10.19596/j.cnki.1001-246x.8384

计算物理 ›› 2022, Vol. 39 ›› Issue (2): 179-190.DOI: 10.19596/j.cnki.1001-246x.8384

拉格朗日方法中减小非物理熵增的方法

王丽吉¹^,²(), 郭虹平¹^,³, 沈智军¹^,*()

1. 北京应用物理与计算数学研究所，北京 100088
2. 中国工程物理研究院研究生院，北京 100088
3. 包头师范学院，内蒙古包头 014030

收稿日期:2021-04-21 出版日期:2022-03-25 发布日期:2022-06-24
通讯作者: 沈智军
作者简介:
Wang Liji (1995-), female, postgraduate student, research in computational fluid dynamics, E-mail: 13843154502@163.com

Reducing Entropy Production in a Lagrangian Method

Liji WANG¹^,²(), Hongping GUO¹^,³, Zhijun SHEN¹^,*()

1. Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
2. Graduate School of China Academy of Engineering Physics, Beijing 100088, China
3. Faculty of Mathematics, Baotou Teachers′ College, Baotou, Inner Mongolia 014030, China

Received:2021-04-21 Online:2022-03-25 Published:2022-06-24
Contact: Zhijun SHEN
Supported by:
National Natural Science Foundation of China(11971071); Foundation of LCP

摘要/Abstract

摘要：

为了减少Godunov方法在计算等熵流动问题时的非物理现象, 研究单元中心型拉格朗日方法的离散熵增问题。通过对传统数值方法进行压力修正, 提出一种基于完全离散熵不等式的通量修正方法。数值实验表明: 改进后的通量算法在计算包含膨胀波的问题时能够有效地减少原拉格朗日方法的非物理误差。

关键词: Godunov方法, 黎曼求解器, 稀疏波, 熵

Abstract:

We investigate entropy production in a cell centered Lagrangian method. The motivation is to reduce intrinsic entropy dissipation of a Godunov method in calculating isentropic flow problems. By implementing pressure modification to the original scheme, a flux fix approach is proposed based on the fully discrete entropy inequality. Numerical experiments show that for problems with expansion waves the modified flux algorithm has better solution behaviors than the original Lagrangian method.

Key words: Godunov methods, Riemann solver, rarefaction wave, entropy

王丽吉, 郭虹平, 沈智军. 拉格朗日方法中减小非物理熵增的方法[J]. 计算物理, 2022, 39(2): 179-190.

Liji WANG, Hongping GUO, Zhijun SHEN. Reducing Entropy Production in a Lagrangian Method[J]. Chinese Journal of Computational Physics, 2022, 39(2): 179-190.

图/表 9

Fig.1 One-dimensional grid and notations

Fig.2 Notations on generic polygonal grid

Fig.3 Density and internal energy at t=0.15 in the 1-2-3 problem (The grid resolution is 200-cell grid.)

Fig.4 Density and internal energy at t=0.15 in the 1-2-3 problem (The grid resolution is 400-cell grid.)

Fig.5 Density and internal energy at t=0.2 in the Sod shock tube problem

Fig.6 Grid and density of the modified approach at time t=1 in the Sedov problem

Fig.7 Density and pressure at t=1 in Maire′s method and the modified approach in the Sedov problem (Every cell center value in the mesh is plotted. Horizontal axis is the distance between the cell center to the origin $ r = \sqrt {{x^2} + {y^2}} $.)

Fig.8 Enlarged pressure plot at t=1 in Maire′s method and the modified approach in the Sedov problem (Every cell center value in the mesh is plotted. Horizontal axis is distance between the cell center to the origin $ r = \sqrt {{x^2} + {y^2}} $.)

Fig.9 3D functions of Δ at λ=0.3 and λ=0.7

参考文献 18

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拉格朗日方法中减小非物理熵增的方法

Reducing Entropy Production in a Lagrangian Method

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