3D Lagrangian Methods for Ideal Magnetohydrodynamics on Unstructured Meshes

CHINESE JOURNAL OF COMPUTATIONAL PHYSICS ›› 2020, Vol. 37 ›› Issue (4): 403-412.

Special Issue: 第十届全国青年计算物理会议优秀论文

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3D Lagrangian Methods for Ideal Magnetohydrodynamics on Unstructured Meshes

XU Xiao^1,2, GAO Zhiming¹, DAI Zihuan¹

1. Institute of Applied Physics and Computational Mathematics, Beijing 100088, China;
2. Graduate School of China Academy of Engineering Physics, Beijing 100088, China

Received:2019-08-14 Revised:2019-11-19 Online:2020-07-25 Published:2020-07-25

Abstract

Abstract: Interaction between magnetic field and fluids is crucial in Z pinch process. Since Z pinch involves with multi materials and severe deformation, we develop 3D compatible Lagrangian staggered and cell-centered schemes for ideal MHD on unstructured meshes. Both of the schemes are of first order in space and time discretization. Accuracy and robustness of the schemes are validated with typical numerical tests.

Key words: 3D Lagrangian magnetohydrodynamics, staggered scheme, cell-centered scheme

CLC Number:

O241

XU Xiao, GAO Zhiming, DAI Zihuan. 3D Lagrangian Methods for Ideal Magnetohydrodynamics on Unstructured Meshes[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2020, 37(4): 403-412.

References

[1] 贾祖朋, 张树道, 蔚喜军. 多介质流体动力学计算方法[M]. 北京:科学出版社, 2014, 1-17.
[2] TOTH G. The Δ·B=0 constraint in shock-capturing magnetohydrodynamics codes[J]. Comput Phys, 2000, 161(2):605-652.
[3] WENSENBURG M. Efficient MHD Riemann solvers for simulations on unstructured triangular grids[J]. J Numer Math, 2002, 10(1):37-71.
[4] GALLICE G. Positive and entropy stable Godunov-type schemes for gas dynamicsand MHD equations in Lagrangian or Eulerian coordinates[J]. Numer Math, 2003, 94(4):673-713.
[5] Von NEUMANN J, RICHTMYER R D. A method for the numerical calculations of hydrodynamical shocks[J]. J Appl Phys, 1950, 21(3):232-238.
[6] CARAMANA E J, BURTON D E, SHASHKOV M J, et al. The construction of compatible hydrodynamics algorithms utilizing conservation of total energy[J]. J Comput Phys, 1998, 146(1):227-262.
[7] CARAMANA E J, SHASHKOV M J, WHALEN P P. Formulations of artificial viscosity for multi-dimensional shock wave computations[J]. J Comput Phys, 1998, 144(1):70-97.
[8] CAMPBELL J C, SHASHKOV M J. A tensor artificial viscosity using a mimetic finite difference algorithm[J]. J Comput Phys, 2001, 172(2):739-765.
[9] KOLEV T V, RIEBEN R N. A tensor artificial viscosity using a finite element approach[J]. J Comput Phys, 2009, 228:8336-8366.
[10] DAI Z, WU J, LIN Z, et al. Subzonal pressure methods in Lagrangian algorithm of two-dimensional three-temperature radiation hydrodynamics[J]. Chinese Journal of Computational Physics, 2010, 27(3):326-334.
[11] GODUNOV S K. A difference scheme for numerical computation of discontinue solution of hydrodynamic equations[J]. Mathematics Sbornik, 1959, 47:271-306.
[12] MAIRE P H, ABGRALL R, BREIL J, et al. A cell-centered Lagrangian scheme for two-dimensional compressible flows problems[J]. SIAM J Sci Comput, 2007, 29:1782-1824.
[13] GEORGES G, BREIL J, MAIRE P H. A 3D GCL compatible cell-centered Lagrangian scheme for solving gas dynamics equations[J]. J Comput Phys, 2016, 305:921-941.
[14] LOUBERE R, MAIRE P H, VACHAL P, 3D staggered Lagrangian hydrodynamics scheme with cell-centered Riemann solver-based artificial viscosity[J]. Int J Numer Meth Fluids, 2013, 72(1):22-42.
[15] SUN Y, YU M, REN Y, et al. A finite volume method for 2D Lagrangian hydrodynamics based on characteristics theory[J]. Chinese Journal of Computational Physics, 2011, 28(1):19-26.
[16] SUN Y, JIA A, YU M, et al. A second order Lagrangian scheme based on characteristics theory for two-dimensional compressible flows[J]. Chinese Journal of Computational Physics, 2012, 29(6):791-798.
[17] XU X, GAO Z, DAI Z. A 3D staggered Lagrangian scheme for ideal magnetohydrodynamics equations on unstructured meshes[J]. Int J Numer Meth Fluids, 2019, 90:584-602.
[18] XU X, DAI Z, GAO Z. A 3D cell centered Lagrangian scheme for the ideal magnetohydrodynamics equations on unstructured meshes[J]. Comput Methods Appl Mech Engrg, 2018, 342:490-508.
[19] BENSON D J. Computational methods in Lagrangian and Eulerian hydrocodes[J]. Comput Method Appl Mech Eng, 1992, 99(2-3):235-394.
[20] MAIRE P H, NKONGA B. Multi-scale Godunov-type method for cell-centered discrete Lagrangian hydrodynamics[J]. J Comput Phys, 2008, 228:799-821.
[21] BRIO M, WU C C. An upwind difference scheme for the equations of ideal magnetohydrodynamics[J]. J Comput Phys, 1988, 75(2):400-422.
[22] BALSARA D S, SPICER D. A staggered mesh algorithm using high order Godunov fluxs to ensure solenoidal magnetic fields in magnetohydrodynamic simulations[J]. J Comput Phys, 1999, 149(1):270-292.
[23] BALSARA D S. Self-adjusting, positivity preserving high order schemes for hydrodynamics and magnetohydrodynamics[J]. J Comput Phys, 2012, 231:7504-7517.

3D Lagrangian Methods for Ideal Magnetohydrodynamics on Unstructured Meshes

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