Coupling Radiation, Ion and Electron Energy Equations with Second-order Time Discretization

doi:10.19596/j.cnki.1001-246x.8858

Abstract

Abstract:

Based on second-order time discretization of BDF2, this paper presents a simpler approach for designing algorithms for coupling radiation, ion and electron energies via operator splitting method. Numerical results show the error and computational cost of iterative operator splitting method is less than that of operator splitting method with the same time discretization order, and while compared with first-order backward Euler method, time steps of second-order BDF2 can be ten times lager for obtaining the same computational accuracy. This new proposed second-order time discretization iterative operator splitting method can be used for simulating ICF physical models, and promoting the computational efficiency.

Key words: radiative transfer, three-temperature (electron; ion; and radiation) model, second-order time discretization, iterative operator splitting method, operator splitting method

Shuanggui LI, Rong YANG. Coupling Radiation, Ion and Electron Energy Equations with Second-order Time Discretization[J]. Chinese Journal of Computational Physics, 2025, 42(2): 202-210.

Figures/Tables 9

References 32

1	常铁强, 张钧, 张家泰, 等. 激光等离子体相互作用与激光聚变[M]. 长沙: 湖南科学技术出版社, 1991.
2	LAN Ke. Dream fusion in octahedral spherical hohlraum[J]. Matter and Radiation at Extremes, 2022, 7(5): 055701. DOI
3	GUO Yi, ZHANG Xiaomei, XU Dirui, et al. Suppression of stimulated Raman scattering by angulary incoherent light, towards a laser system of incoherence in all dimensions of time, space, and angle[J]. Matter and Radiation at Extremes, 2023, 8(3): 035902. DOI
4	李纪伟, 王立锋, 李志远, 等. 混合驱动下高熵高内爆速度中心点火靶设计[J]. 计算物理, 2023, 40(2): 181- 188. DOI
5	BOWERS R L, WILSON J R. Numerical modeling in applied physics and astrophysics[M]. Sudbury: Jones and Bartlerr Publishers, 1991.
6	PORMRANING G C. The equations of radiation hydrodynamics[M]. NewYork: Pergamon Press, 1973.
7	CASTOR J I. Radiation hydrodynamics[M]. Cambridge: Cambridge University Press, 2004.
8	GRAZIANI F R. Computational methods in transport[M]. Granlibakken: Springer, 2004.
9	杜书华, 张数发, 王元璋, 等. 输运问题的计算机模拟[M]. 长沙: 湖南科学技术出版社, 1989.
10	GEISER J. Iterative splitting methods for differential equations[M]. New York: CRC Press, 2011.
11	MOREL J E, LARSEN E W, MATZEN M K. A synthetic acceleration scheme for radiative diffusion calculations[J]. Journal of Quantitative Spectroscopy & Radiative Transfer, 1984, 34(3): 243- 261.
12	EVANS T M, DENSMORE J D. Methods for coupling radiation, ion, and electron energies in grey implicit Monte Carlo[J]. Journal of Computational Physics, 2007, 225, 1695- 1720. DOI
13	OLSON G L. Efficient solution of multi-dimensional flux-limited nonequilibrium radiation diffusion coupled to material conduction with second-order time discretization[J]. Journal of Computational Physics, 2007, 226(1): 1181- 1195. DOI
14	OBER C C, SHADID J N. Studies on the accuracy of time integration methods for radiation-diffusion equations[J]. Journal of Computational Physics, 2004, 195(2): 743- 772. DOI
15	KNOLL D A, RIDERD W J, OLSON G L. Nonlinear convergence, accuracy, and time step control in non-equilibrium radiation diffusion[J]. Journal of Quantitative Spectroscopy and Radiative Transfer, 2001, 70(1): 25- 36. DOI
16	KNOLL D A, LOWRIE R B, MOREL J E. Numerical analysis of time integration errors for nonequilibrium radiation diffusion[J]. Journal of Computational Physics, 2007, 226(2): 1332- 1347. DOI
17	BROWN P N, SHUMAKER D E, WOODWARD C S. Fully implicit solution of large-scale nonequilibrium radiation diffusion with high order time integration[J]. Journal of Computational Physics, 2005, 204(2): 760- 783. DOI
18	LOWRIE R B. A comparision of implicit time integration methods for nonlinear relaxation and diffusion[J]. Journal of Computational Physics, 2004, 196(2): 566- 590. DOI
19	MOUSSEAU V A, KNOLL D A, RIDER W J. Physics-based preconditioning and the Newton-Krylov method for non-equilibrium radiation diffusion[J]. Journal of Computational Physics, 2000, 160(2): 743- 765. DOI
20	KNOLL D A, CHACON L, MARGOLIN L G, et al. On balanced approximations for time integration of multiple time scale systems[J]. Journal of Computational Physics, 2003, 185(2): 583- 611. DOI
21	李双贵, 杨容, 杭旭登. 多群辐射输运计算的输运综合加速方法[J]. 计算物理, 2014, 31(5): 505- 513. DOI
22	李若, 李蔚明, 宋鹏. 辐射输运与电子能量强耦合源项的一种高效计算方法[J]. 计算物理, 2017, 34(3): 253- 260. DOI
23	FAN Zhengfeng, LIU Yuanyuan, LIU Bin, et al. Non-equilibrium between ions and electrons inside hot spots from national ignition facility experiments[J]. Matter and Radiation at Extremes, 2017, 2(1): 3- 8. DOI
24	HU Xiaoyan, NI Guoxi, FAN Zhengfeng, et al. Algorithm of radiation hydrodynamics with nonorthogonal mesh for 3D implosion problem[J]. Journal of Computational Physics, 2021, 437, 110309. DOI
25	冯庭桂, 赖东显, 许琰, 等. X光辐射输运计算的一种算子分裂方法[J]. 中国工程物理研究院科技年报: 内部通讯, 1998, 176- 187.
26	李双贵, 冯庭桂. 辐射输运菱形差分SN方程的扩散综合加速方法[J]. 计算物理, 2008, 25(1): 1- 6. DOI
27	李双贵, 杭旭登, 李敬宏. 辐射与物质强耦合问题的二维输运数值模拟[J]. 计算物理, 2009, 26(2): 247- 253. DOI
28	李双贵, 杭旭登, 杨容, 等. LARED集成程序辐射输运模拟的性能优化[J]. 计算物理, 2017, 34(3): 320- 326. DOI
29	翟传磊, 李双贵, 勇珩, 等. 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.
30	李双贵, 翟传磊, 杭旭登, 等. 激光腔靶耦合二维辐射输运数值模拟[J]. 强激光与粒子束, 2014, 26(8): 082002. DOI
31	宋鹏, 翟传磊, 李双贵, 等. 激光间接驱动惯性约束聚变二维总体程序——LARED集成程序[J]. 强激光与粒子束, 2015, 27(3): 032007. DOI
32	EVANS K J, KNOLL D A, PERNICE M. Development of a 2-D algorithm to simulate convection and phase transition efficiently[J]. Journal of Computational Physics, 2006, 219(1): 404- 417. DOI

Δt	L_∞ (Ios_Euler)	Order	L_∞ (Os_Euler)	Order
2.5×10^-3	6.98×10^-3		3.51×10^-2
5.0×10^-3	1.39×10^-2	0.99	6.93×10^-2	0.98
1.0×10^-2	2.76×10^-2	0.99	0.13	0.91
2.0×10^-2	5.40×10^-2	0.97	0.25	0.94
4.0×10^-2	0.11	1.03	failure

Δt	L_∞ (Ios_Euler)	Order	L_∞ (Os_Euler)	Order
2.5×10^-3	6.98×10^-3		3.51×10^-2
5.0×10^-3	1.39×10^-2	0.99	6.93×10^-2	0.98
1.0×10^-2	2.76×10^-2	0.99	0.13	0.91
2.0×10^-2	5.40×10^-2	0.97	0.25	0.94
4.0×10^-2	0.11	1.03	failure

Δt	L_∞ (Ios_Euler)	Order	L_∞ (Os_Euler)	Order
2.5×10^-3	5.29×10^-3		3.61×10^-2
5.0×10^-3	1.05×10^-2	0.99	7.33×10^-2	1.02
1.0×10^-2	2.10×10^-2	1.00	0.15	1.03
2.0×10^-2	4.13×10^-2	0.98	failure
4.0×10^-2	8.13×10^-2	0.98	failure

Δt	L_∞ (Ios_Euler)	Order	L_∞ (Os_Euler)	Order
2.5×10^-3	5.29×10^-3		3.61×10^-2
5.0×10^-3	1.05×10^-2	0.99	7.33×10^-2	1.02
1.0×10^-2	2.10×10^-2	1.00	0.15	1.03
2.0×10^-2	4.13×10^-2	0.98	failure
4.0×10^-2	8.13×10^-2	0.98	failure

Δt	L_∞ (Ios_Euler)	Order	L_∞ (Os-Euler)	Order
2.5×10^-3	6.72×10^-3		3.53×10^-2
5.0×10^-3	1.34×10^-2	1.00	6.96×10^-2	0.98
1.0×10^-2	2.66×10^-2	0.99	0.14	1.01
2.0×10^-2	5.21×10^-2	0.97	0.25	0.84
4.0×10^-2	failure		failure