An anti-singularity Mie-Grüneisen mixture model based on isentropic and hugoniot curves

WU Zongduo; YAN Jin; PANG Jianhua; SUN Yifang; ZHANG Dapeng

doi:10.11883/bzycj-2025-0102

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WU Zongduo, YAN Jin, PANG Jianhua, SUN Yifang, ZHANG Dapeng. An anti-singularity Mie-Grüneisen mixture model based on isentropic and hugoniot curves[J]. Explosion And Shock Waves. doi: 10.11883/bzycj-2025-0102

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WU Zongduo, YAN Jin, PANG Jianhua, SUN Yifang, ZHANG Dapeng. An anti-singularity Mie-Grüneisen mixture model based on isentropic and hugoniot curves[J]. Explosion And Shock Waves. doi: 10.11883/bzycj-2025-0102

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An anti-singularity Mie-Grüneisen mixture model based on isentropic and hugoniot curves

doi: 10.11883/bzycj-2025-0102

1.
Ship and Marine College, Guangdong Ocean University，Guangdong 524088, China
2.
Ocean intelligence technology center, Shenzhen Institute of Guangdong Ocean university，Shenzhen 518055, China

Received Date: 2025-04-01
Rev Recd Date: 2025-09-15

Available Online: 2025-09-17

Abstract

Abstract

The Mie-Grüneisen mixture model is conveniently used in the multi-component problem with Mie-Grüneisen EOS (equation of states). In the Mie-Grüneisen EOS, the isentropic and Hugoniot curves are two typical reference states curves. However, the curves of these two reference states contain singularity points and cause difficulty when the interface is treated by volume fraction, which is accustomed used as a color function in traditional model. The difficulty lies in that the volume fraction model produces fragments of fluid volumes near the interface due to its diffused style, these volume fragments may encounter the singularity points and make the sound velocity abnormally high at the interface in some isentropic reference curves. On the other side, the singularity points may cause the sound velocity negative for some Hugoniot reference states and interrupt the calculation. To avoid volumes fragments near the interface area, the volume fraction is replaced by mass fraction, and the relative volume is defined by the reciprocal of proportional density of fluid component. This definition makes the relative volume no less than which of fluids mixture. Thanks to the reconstructed relative volume, the sound velocity forms a trough shape at the interface and does not cause high peak value. Moreover, some equations in Mie-Grüneisen mixture model contains the derivatives items of reference states parameters, when these items are defined as weighted average mixture at the interface, they often become negative if weighted average of mass fraction are directly used. To prevent the negative value at the interface, the reference states are optimized at the interface. Numerical examples show that the mass fraction has tiny improvement on the accuracy of results, it makes the sound velocity steady on the isentropic reference states of medium and spend less time steps than volume fraction model. And the mass fraction can be used to correct the negative sound velocity in Hugoniot reference states. Then the calculation is kept smooth and accurate.
- Mie-Grüneisen mixture model,
- Mie-Grüneisen equation of states,
- anti-singularity,
- reference states

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References(16)

References

[1]	张宝銔, 张庆民, 黄风雷. 爆轰物理学[M]. 2006年3月第1版. 北京市: 北京理工大学出版社, 2001: 156, 336–345, 375–390.
[2]	LEE E, FINGER M, COLLINS W. JWL equation of state coefficients for high explosives: UCID-16189[R]. Livermore: Lawrence Livermore National Laboratory, 1973. DOI: 10.2172/4479737.
[3]	焦俊杰, 单锋, 王晗程, 等. 基于水下爆炸的爆轰产物JWL状态方程确定方法研究 [J]. 爆炸与冲击, 2025, 45(9): 093401. DOI: 10.11883/bzycj-2024-0203. JIAO J J, Shan F, Wang H C, et al. Determination of JWL equation of state based on the detonation product form underwater explosion [J]. Explosion and Shock Waves, 2025, 45(9): 093401. DOI: 10.11883/bzycj-2024-0203.
[4]	MILLER G H, PUCKETT E G. A High-order Godunov method for multiple condensed phases [J]. Journal of Computational Physics., 1996, 128(1): 134–164. DOI: 10.1006/jcph.1996.0200.
[5]	刘益儒, 胡晓棉. 一种基于Hugoniot关系的爆轰产物等熵状态方程 [J]. 爆炸与冲击, 2018, 38(1): 60–65. DOI: 10.11883/bzycj-2016-0132. LIU Y R, HU X M. An isentropic equation of state of detonation product based on a Hugoniot relationship of detonation product [J]. Explosion and Shock Waves, 2018, 38(1): 60–65. DOI: 10.11883/bzycj-2016-0132.
[6]	张剑, 谢燕武, 潘跃武, 等. 铝的等温状态方程 [J]. 高压物理学报, 2004, 18(1): 75–77. DOI: 10.11858/gywlxb.2004.01.013. ZHANG J, XIE Y W, PAN Y W, et al. Isothermal Equation of State of Aluminium [J]. Chinese Journal of High Pressure Physics, 2004, 18(1): 75–77. DOI: 10.11858/gywlxb.2004.01.013.
[7]	SHYUE K M. A fluid-mixture type algorithm for compressible multicomponent flow with Mie-Grüneisen equation of state [J]. Journal of Computational Physics, 2001, 171(2): 678–707. DOI: 10.1006/jcph.2001.6801.
[8]	WU Z D, SUN L, Zong Z. A mass fraction based interface capturing method for multi-component flow [J]. International Journal for Numerical Methods in Fluids, 2013, 73(1): 74–102. DOI: 10.1002/fld.3805.
[9]	柏劲松, 陈森华, 李平, 等. 多介质可压缩流体动力学界面捕捉方法 [J]. 爆炸与冲击, 2004, 24(1): 37–43. BO J S, CHEN S H, LI P. Interface capturing method for compressible multi-fluid dynamics [J]. Explosion and Shock Waves, 2004, 24(1): 37–43.
[10]	WARD G M, PULLIN D I. A hybrid, center-difference, limiter method for simulations of compressible multicomponent flows with Mie-Grüneisen equation of state. Journal of Computational Physics 2010, 229(8): 2999–3018. DOI: 10.1016/j.jcp.2009.12.027.
[11]	吴宗铎, 赵勇, 严谨, 等. 球坐标系下多介质混合物模型的数值模拟 [J]. 爆炸与冲击, 2019, 39(5): 054204. DOI: 10.11883/bzycj-2018-0075. WU Z D, ZHAO Y, YAN J, et al. Numerical simulation about the multi-component mixture model under spherical coordinate system [J]. Explosion and Shock Waves, 2019, 39(5): 054204. DOI: 10.11883/bzycj-2018-0075.
[12]	吴宗铎, 严谨, 宗智, 等. 扩散界面形式下一种节约时间步的质量分数混合模型 [J]. 计算物理, 2022, 39(5): 510–520. DOI: 10.19565/j.cnki.1001-246x.8453. WU Z D, YAN J, ZONG Z, et al. A Diffused Interface Type Mass Fraction Model with Time Steps Saving Mixture Rules [J]. Chinese Journal of Computational Physics, 2022, 39(5): 510–520. DOI: 10.19565/j.cnki.1001-246x.8453.
[13]	KERLEY G I. The Linear u_s-u_p relation in shock-wave physics: KTS06-1[R]. Appomattox: Kerley Technical Services, 2006.
[14]	SAUREL R, ABGRALL R. A multiphase Godunov method for compressible multifluid and multiphase flows [J]. Journal of Computational Physics, 1999, 150(2): 425–467. DOI: 10.1006/jcph.1999.6187.
[15]	COCHRAN S G, CHAN J. Shock initiation and detonation models in one and two dimensions. UCID-18024[R]. Livermore: Lawrence Livermore National Laboratory, 1979.
[16]	STEINBERG D J. Spherical explosion and the equation of state of water, UCID-20974 [R]. Livermore: Lawrence Livermore National Laboratory, 1978.