A Diffused Interface Type Mass Fraction Model with Time Steps Saving Mixture Rules

doi:10.19596/j.cnki.1001-246x.8453

Abstract

Abstract:

We focused on effects of treatment of mixture model as the interface is in a diffused style. In order to seek a convenient way to treat the interface and keep strong adaptability, Mie-Grüneisen mixture model is used. The original Mie-Grüneisen mixture model in terms of volume fraction is modified. In the model, the mass fraction is employed as color function, and the optimization of sound speed is achieved with the help of the density of fluid components. The optimized sound speed reduces time steps under the convergence mechanism and promotes efficiency of the calculation. Meanwhile, the introduction of limiter make the pressure curves stable. Numerical tests show that the modified mass fraction model reduces the number of time steps under different numerical schemes. Effects of this reduction depend on physical conditions of case.

Key words: Mie-Grüneisen mixture model, mass fraction, time steps, limiter

Zongduo WU, Jin YAN, Zhi ZONG, Jianhua PANG. A Diffused Interface Type Mass Fraction Model with Time Steps Saving Mixture Rules[J]. Chinese Journal of Computational Physics, 2022, 39(5): 510-520.

Figures/Tables 9

Fig.1 Curves of reference pressure pref

Fig.2 ρ and p results of the interaction between detonation gaseous product and copper at 73 μs

Fig.3 Results of the sound velocity at 73 μs in Case 1

Fig.4 ρ and u results at 85 μs as an inert explosive suffers from the impact of copper

Fig.5 Results of the sound velocity at 85 μs in Case 2

Fig.6 Time evolutions of the positions of shock wave

Fig.7 200 μs和500 μs solutions for NM explosion problem

Fig.8 Pressure distribution at 140 μs for 2D NM explosion problem

Fig.9 Contrast of sound velocity contours for 2D NM explosion problem

References 26

1	TORO E F. Riemann solvers and numerical methods for fluid dynamics[M]. Springer-Verlag Berlin Heidelberg, 2009.
2	高斯, 刘铁钢. 多介质黎曼问题精确解解算器软件包MultiRP开发[J]. 数值计算与计算机应用, 2016, 37 (4): 245- 256.
3	LIU T G , KHOO B C , YEO K S . Ghost fluid method for strong shock impacting on material interface[J]. Journal of Computational Physics, 2003, 190 (2): 651- 681. DOI
4	XIAO F , HONMA Y , KONO T . A simple algebraic interface capturing scheme using hyperbolic tangent function[J]. International Journal for Numerical Methods in Fluids, 2005, 48 (9): 1023- 1040. DOI
5	XU L , FENG C L , LIU T G . Analysis of impact load on elastic plate in underwater explosions with modified ghost fluid method[J]. Chinese Journal of Computational Physics, 2017, 34 (1): 1- 9. DOI
6	赵海洋, 明平剑, 张文平, 等. 基于THINC/QQ格式的两相界面流动数值模拟[J]. 哈尔滨工程大学学报, 2020, 41 (12): 1804- 1810.
7	ALLAIRE G , CLERC S , KOKH S . A five-equation model for the simulation of interfaces between compressible fluids[J]. Journal of Computational Physics, 2002, 181 (2): 577- 616. DOI
8	刘铁钢, 许亮. 模拟模拟多介质界面问题的虚拟流体方法综述[J]. 气体物理, 2019, 4 (2): 1- 16.
9	ABGRALL R . How to prevent pressure oscillations in multicomponent flow calculations: A quasi-conservative approach[J]. Journal of Computational Physics, 1999, 25 (1): 150- 160.
10	SAUREL R , ABGRALL R . A simple method for compressible multifluid flows[J]. SIAM Journal on Scientific Computing, 1999, 21 (3): 1115- 1145. DOI
11	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
12	梁姗, 刘伟, 袁礼. 七方程可压缩多相流模型的HLLC格式及应用[J]. 力学学报, 2012, 44 (5): 884- 895.
13	XUE C , LI X D , SUN W J , et al. A multi-material five-equation-reduced model and artificial compression method for interface capture[J]. Chinese Journal of Computational Physics, 2021, 38 (03): 257- 268.
14	陈芳, 李平, 刘坤, 等. 基于PPM的界面压缩方法研究[J]. 高压物理学报, 2019, 33 (5): 052302.
15	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.
16	SHYUE K . A wave-propagation based volume tracking method for compressible multicomponent flow in two space dimensions[J]. Journal of Computational Physics, 2006, 215 (1): 219- 244.
17	张宝坪, 张庆民, 黄风雷. 爆轰物理学[M]. 第1版北京: 兵器工业出版社, 2001.
18	WANG Z , ZOU G Y , GONG J , et al. A pressure-based algorithm for numerical simulation of one-dimensional two-phase flow[J]. Chinese Journal of Computational Physics, 2019, 36 (4): 413- 420.
19	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.
20	任玉新, 陈海昕. 计算流体力学基础[M]. 北京: 清华大学出版社, 2006.
21	LIU Y , MAO D K . An ADRS approximated Riemann solver in compatible Lagrangian method[J]. Chinese Journal of Computational Physics, 2020, 37 (2): 140- 152.
22	WU Z D , YAN J , ZONG Z , et al. A multi-component Mie-Grüneisen mixture model based on HLLC algorithm[J]. Chinese Journal of Computational Physics, 2020, 37 (1): 55- 62.
23	SHREYAS B , SARMA L R . Investigation of numerical viscosities and dissipation rates of second-order TVD-MUSCL schemes for implicit large-eddy simulation[J]. Journal of Computational Physics, 2015, 281 (2): 1003- 1031.
24	LIU J J , ZENG X Y , NI G X . Euler numerical methods for reactive flow with general equation of states in two dimensions[J]. Chinese Journal of Computational Physics, 2018, 35 (1): 29- 38.
25	STEINBERG D J. Spherical explosion and the equation of state of water, UCID-20974[R]. Livermore: Lawrence Livermore National Laboratory, 1978.
26	LEE E, FINGER M, COLLINS W. JWL equation of state coefficients for high explosives, UCID-16189[R]. Livermore: Lawrence Livermore National Laboratory, 1973.

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[12]	Chen Liang, Yan Chao. INVESTIGATIONS AND APPLICATIONS OF ADVANCED UPWIND SCHEME (AUSM+) [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 1998, 15(5): 547-552.
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