A Multi-component Mie-Grüneisen Mixture Model Based on HLLC Algorithm

doi:10.19596/j.cnki.1001-246x.7979

CHINESE JOURNAL OF COMPUTATIONAL PHYSICS ›› 2020, Vol. 37 ›› Issue (1): 55-62.DOI: 10.19596/j.cnki.1001-246x.7979

Previous Articles Next Articles

A Multi-component Mie-Grüneisen Mixture Model Based on HLLC Algorithm

WU Zongduo¹, YAN Jin¹, ZONG Zhi², ZHAO Yong³

1. College of Ocean Engineering, Guangdong Ocean University, Zhanjiang, Guangdong 524088, China;
2. Department of Naval Architecture, Dalian University of Technology, Dalian, Liaoning 116024, China;
3. Transportation Engineering Postdoctoral Research Station, Dalian Maritime University, Dalian, Liaoning 116026, China

Received:2018-10-10 Revised:2018-11-30 Online:2020-01-25 Published:2020-01-25

Abstract

Abstract: A revised robust HLLC(Harten-Lax-Van Leer-Contact) solver for multi-component Mie-Grüneisen mixture model is established. In Mie-Grüneisen mixture model, flux can be divided into conservative part and non-conservative part. Original HLLC scheme can well adapt to conservative part. As the original HLLC solver is directly extended to non-conservative part, oscillation is hard to be controlled. In original scheme, moving speed of discontinuous section refers to velocity at left or right side of the gird. It is replaced by average velocity within the grid. After the revision, the HLLC scheme is deduced again and extended to 2D problem. Numerical tests show that Mie-Grüneisen mixture model is robust and accurate with the help of modified HLLC solver.

Key words: multicomponent Riemann problem, HLLC solver, Mie-Grüneisen equation, non-conservative model

CLC Number:

WU Zongduo, YAN Jin, ZONG Zhi, ZHAO Yong. A Multi-component Mie-Grüneisen Mixture Model Based on HLLC Algorithm[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2020, 37(1): 55-62.

References

[1] TORO E F. Riemann solvers and numerical methods for fluid dynamics[M]. Berlin Heidelberg:Springer-Verlag 2009.
[2] HARTEN A,LAX P D,van LEER B. On upstream differencing and Godunov-type schemes for hyperbolic conservation laws[J].SIAM Review,1983,25(1):35-61.
[3] TORO E F, SPRUCE M, SPEARES M. Restoration of the contact surface in the HLL-Riemann solver[J].Shock Waves, 1994, 4(1):25-34.
[4] LIANG Shan, LIU Wei, YUAN Li. Solving seven-equation model for compressible two-phase flow using multiple GPUs[J]. Computers and Fluids, 2014, 99:156-171.
[5] 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.
[6] 丁岩, 袁礼, 杨莉. 虚拟流体方法的显隐算法[J]. 计算物理, 2013, 30(1):27-34.
[7] TIAN Baolin, TORO E F, CASTRO C E. A path-conservative method for a five-equation model of two-phase flow with an HLLC-type Riemann solver[J]. Computers and Fluids, 2011, 46:122-132.
[8] REN Jian, SHEN Zhijun, YAN Wei, et al. A robust Riemann solver without artificial intervention[J]. Chinese Journal of Computational Physics, 2018, 35(1):1-12.
[9] LIU Jingjing, ZENG Xianyang, NI Guoxi. 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.
[10] KEH-MING Shyue. A fluid-mixture type algorithm for compressible multicomponent flow with Mie-Grüneisen equation of states[J]. Journal of Computational Physics, 2001, 171(2):678-707.
[11] WARD G M, PULLIN D I. A hybrid, center-difference, limiter method for simulations of compressible multicomponent flows with Mie-Grüneisen equation of state[J]. Journal of Computational Physics. 2010, 229(8):2999-3018.
[12] 吴宗铎, 宗智. Mie-Grüneisen状态方程下多介质守恒型欧拉方程组的数值计算[J]. 计算物理, 2011,28(6):803-809.
[13] LIU Zhongyu, ZHANG Mingfeng, ZHENG Guannan, et al. Preconditioning HLLEW scheme for flows at all Mach numbers[J]. Chinese Journal of Computational Physics, 2016, 33(3):273-282.
[14] 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.

A Multi-component Mie-Grüneisen Mixture Model Based on HLLC Algorithm

RichHTML

PDF

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 2

Recommended Articles

Metrics

Authors

Reviewers

Journal Online

About Journal

[1]	JI Meixuan, YU Xijun, SONG Mingyang. ALE Discontinuous Finite Element Method for One-dimensional Fluid Dynamics Equations with Chemical Reactions [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2020, 37(1): 1-9.
[2]	LIU Jingjing, ZENG Xianyang, NI Guoxi. 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.