An Artificial Viscosity Based on the Subcell-Edged Approximate Riemann Solver
-
摘要: 在交错网格型Lagrange(拉格朗日)流体力学算法中,通常采用人为粘性捕捉激波,人为粘性的好坏对于计算结果至关重要.研究了一种基于子网格边界处近似Riemann解的新型人为粘性.新人为粘性能够满足动量守恒和熵不等式.利用子网格边界速度差中引入的限制器,新人为粘性能够区分激波和等熵压缩,并能满足球对称问题中的波面不变性.新人为粘性在典型模型数值模拟及惯性约束聚变黑腔整体数值模拟中取得了较好的结果.
-
关键词:
- Lagrange流体力学 /
- 人为粘性 /
- 近似Riemann解 /
- 大长宽比网格 /
- 惯性约束聚变
Abstract: The artificial viscosity method is generally used to capture shock waves in the Lagrangian hydrodynamics algorithms, and the properties of the artificial viscosity influence the simulation results essentially. A new artificial viscosity based on the subcell-edged approximate Riemann solver was presented. This new method was prove to have the merits of momentum conservation and satisfaction of entropy inequality. With the introduced limiters for the differences of velocities on the subcell edges, the presented artificial viscosity is able to distinguish the shock wave from the isoentropic compression and satisfy the wave front invariance in the spherical symmetric problems. Various numerical examples demonstrate the robustness and effectiveness of the new artificial viscosity. -
[1] 葛全文. Lagrange非结构网格高阶交错型守恒气体动力学格式[J]. 应用数学和力学, 2014,35(1): 92-101.(GE Quan-wen. Lagrangian high-order staggered conservative gasdynamics scheme on unstructured meshes[J].Applied Mathematics and Mechanics,2014,35(1): 92-101.(in Chinese)) [2] von Neumann J, Richtmyer R D. A method for the numerical calculation of hydrodynamic shocks[J].Journal of Applied Physics,1950,21(3): 232-237. [3] Landshoff R. A numerical method for treating fluid flow in the presence of shocks[R]. Los Alamos, New Mexico: Los Alamos National Laboratory, LA-1930, 1955. [4] Kuropatenko V F.Difference Methods for Solutions of Problems of Mathematical Physics I[M]. Janenko N N, ed. USA: Amer Mathematical Society, 1967: 116. [5] Caramana E J, Burton D E, Shashkov M J, Whalen P P. The construction of compatible hydrodynamics algorithms utilizing conservation of total energy[J].Journal of Computational Physics,1998,146(1): 227-262. [6] Caramana E J, Shashkov M J, Whalen P P. Formulations of artificial viscosity for multi-dimensional shock wave computations[J].Journal of Computational Physics,1998,144(1): 70-97. [7] Campbell J C, Shashkov M J. A tensor artificial viscosity using a mimetic finite difference algorithm[J].Journal of Computational Physics,2011,172(2): 739-765. [8] Loubère R, Maire P H, Váchalc P. A second-order compatible staggered Lagrangian hydrodynamics scheme using a cell-centered multidimensional approximate Riemann solver[J].Procedia Computer Science,2010,1(1): 1931-1933. [9] Maire P H, Loubère R, Váchal P. Staggered Lagrangian discretization based on cell-centered Riemann solver and associated hydro-dynamics scheme[J].Communications in Computational Physics,2011,10(4): 940-978. [10] Barlow A, Burton D, Shashkov M. Compatible, energy and symmetry preserving 2D Lagrangian hydrodynamics inrz -cylindrical coordinates[J].Procedia Computer Science,2010,1(1): 1893-1901. [11] Dukowicz J K. A general, non-iterative Riemann solver for Godunov’s method[J].Journal of Computational Physics,1985,61(1): 119-137. [12] Noh W F. Errors for calculations of strong shocks using an artificial viscosity and an artificial heat flux[J]. Journal of Computational Physics,1987,72(1): 78-120. [13] Dukowicz J K, Meltz B J A. Vorticity errors in multidimensional Lagrangian codes[J].Journal of Computational Physics,1992,99(1): 115-134. [14] 江少恩, 丁永坤, 缪文勇, 刘慎业, 郑志坚, 张保汉, 张继彦, 黄天晅, 李三伟, 陈家斌, 蒋小华, 易荣清, 杨国洪, 杨家敏, 胡昕, 曹柱荣, 黄翼翔. 我国激光惯性约束聚变实验研究进展[J]. 中国科学, G辑:物理学, 力学, 天文学, 2009,39(11): 1571-1583.(JIANG Shao-en, DING Yong-kun, MIAO Wen-yong, LIU Shen-ye, ZHENG Zhi-jian, ZHANG Bao-han, ZHANG Ji-yan, HUANG Tian-xuan, LI San-wei, CHEN Jia-bin, JIANG Xiao-hua, YI Rong-qing, YANG Guo-hong, YANG Jia-min, HU Xin, CAO Zhu-rong, HUANG Yi-xiang. Recent progress of inertial confinement fusion experiments in China[J].Science in China, Series G: Physics, Mechanics & Astronomy,2009,39(11): 1571-1583.(in Chinese)) [15] 翟传磊, 李双贵, 勇珩, 古培俊. 靶丸变形实验的多群扩散整体数值模拟[J]. 强激光与粒子束, 2013,25(5): 1157-1160.(ZHAI Chuan-lei, LI Shuang-gui, YONG Heng, GU Pei-jun. Integrated simulation of capsule compression distortion experiments in radiation multi-group diffusion approximation[J].High Power Laser and Particle Beams,2013,25(5): 1157-1160.(in Chinese))
点击查看大图
计量
- 文章访问数: 1398
- HTML全文浏览量: 47
- PDF下载量: 887
- 被引次数: 0