Mie-Grüneisen混合模型减小边界差商的重构算子

doi:10.19596/j.cnki.1001-246x.8712

计算物理 ›› 2024, Vol. 41 ›› Issue (3): 277-286.DOI: 10.19596/j.cnki.1001-246x.8712

Mie-Grüneisen混合模型减小边界差商的重构算子

吴宗铎¹(), 严谨¹^,², 庞建华²^,³^,*(), 孙一方¹, 满庆洋⁴

1. 广东海洋大学船舶与海运学院, 广东湛江 524088
2. 广东海洋大学广东省南海海洋牧场智能装备重点实验室, 广东湛江 524088
3. 广东海洋大学深圳研究院智能海洋工程中心, 广东深圳 518055
4. 广东海洋大学电子与信息工程学院, 广东湛江 524088

收稿日期:2023-02-20 出版日期:2024-05-25 发布日期:2024-05-25
通讯作者: 庞建华
作者简介:吴宗铎(1984-), 男, 博士, 副教授, 研究方向为激波间断问题数值计算, E-mail: wuzongduo0@aliyun.com
基金资助:
国家自然科学基金(11702066);广东省自然科学基金(2022A1515011562);广东省促进经济高质量发展专项(GDNRC[2021]56);广东省促进经济高质量发展专项(粤融办函[2020]161)

A Boundary Variation Diminishing Reconstructed Solver for Mie-Grüneisen Mixture Model

Zongduo WU¹(), Jin YAN¹^,², Jianhua PANG²^,³^,*(), Yifang SUN¹, Qingyang MAN⁴

1. Ship and maritime college, Guangdong Ocean University, Zhanjiang, Guangdong 524088, China
2. Guangdong Provinical Key Laboratory of Intelligent Equipment for South China Sea Marine Ranching, Guangdong Ocean University, Zhanjiang, Guangdong 524088, China
3. Shenzhen Institute of Guangdong Ocean University, Intelligence Center of Ocean Engineering, Shenzhen, Guangdong 518055, China
4. College of Electronic and Information Engineering, Guangdong Ocean University, Zhanjiang, Guangdong 524088, China

Received:2023-02-20 Online:2024-05-25 Published:2024-05-25
Contact: Jianhua PANG

摘要/Abstract

摘要：

将守恒型单调迎风格式(MUSCL)和双曲正切界面捕捉(THINC)算法组合到一起进行数值重构, 并通过重构建立新的算子。重构的算子主要作用是尽可能降低网格的边界差商。在MUSCL和THINC算法下, 网格左右边界处的状态可以导出一个优化算法的差商判定机制。再按照这一边界差商优化值最小(BVD)的原则, 对MUSCL和THINC进行二选一。在BVD重构算子的作用下, 数值断面变得平滑, 并且有效地限制振荡。BVD重构算子的计算性能将通过一维和二维数值算例来进行检验。

关键词: BVD重构, Mie-Grüneisen混合模型, 守恒型单调迎风格式, 双曲正切界面捕捉

Abstract:

A numerical reconstruction is implemented according to a combination of MUSCL(Monotonic Upstream-Centered Scheme for Conservation Laws) and THINC(Tangent of Hyperbola for Interface Capturing) methods. And a new constructed solver is derived by the combination. The main principle of this reconstruction solver is to keep the variation diminishing of every cell boundary to a low level. And a BVD(Boundary Variation Diminishing) principle is set according to the left and right boundary states in MUSCL method, as well as which in THINC methods. To obey the BVD principle, an alternative choice between the MUSCL and THINC is needed here. Thanks to the BVD solver, the discontinuous section becomes smooth and the oscillation is significantly controlled. The numerical performance of BVD reconstruction is then tested by 1D and 2D numerical examples.

Key words: boundary variation diminishing(BVD) reconstruction, Mie-Grüneisen mixture model, monotonic upstream-centered scheme for conservation laws, tangent of hyperbola for interface capturing

中图分类号:

O359+.1

吴宗铎, 严谨, 庞建华, 孙一方, 满庆洋. Mie-Grüneisen混合模型减小边界差商的重构算子[J]. 计算物理, 2024, 41(3): 277-286.

Zongduo WU, Jin YAN, Jianhua PANG, Yifang SUN, Qingyang MAN. A Boundary Variation Diminishing Reconstructed Solver for Mie-Grüneisen Mixture Model[J]. Chinese Journal of Computational Physics, 2024, 41(3): 277-286.

图/表 8

图1 MUSCL和THINC的网格特性

Fig.1 The grids property for MUSCL and THINC

图2 气水相互作用的数值解

Fig.2 Numerical solution of gas-water interaction

图3 气水相互作用的数值解

Fig.3 Numerical solution of gas-water interaction

图4 爆轰气体与铜作用算例计算结果

Fig.4 Results of gaseous products and copper interaction

图5 欧拉方程(1)中基本变量(a) ρ、(b) ρu、(c) ρE的差商分布

Fig.5 Variation dimishing distributions of basic variables (a) ρ, (b) ρu, (c) ρE in Euler formulation

表1 部分物质压缩状态下Hugoniot曲线参数

Table 1 Hugoniot curve parameters for some materials

	ρ₀/(kg·m^-3)	c₀/(m·s^-1)	s	Г₀
Mo(钼)	9 961	4 700	1.43	1.56
MORB	2 660	2 100	1.68	0.18

图6 钼和MORB作用问题中(a) 50 μs和(b) 100 μs时压力云图

Fig.6 Contours of pressure at (a) 50 μs and (b) 100 μs instant in molybdenum and MORB interaction

图7 钼和MORB作用问题中(a) 50 μs和(b) 100 μs时压力在y=0.4上的分布

Fig.7 Pressure distributions along y=0.4 at (a) 50 μs and (b) 100 μs instant in molybdenum-MORB problem

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Mie-Grüneisen混合模型减小边界差商的重构算子

A Boundary Variation Diminishing Reconstructed Solver for Mie-Grüneisen Mixture Model

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