A Monolithic Preconditioned Iterative Solver and Parallel Computing for Three-dimensional Thermal Radiation Transport Equation

doi:10.19596/j.cnki.1001-246x.8238

Abstract

Abstract:

We present a monolithic preconditioned iterative solver for implicit discrete ordinate equations of three-dimensional grey thermal radiation transport and parallel codes are developed. A strategy of assembling linear algebraic systems is used to obtain radiation intensity in all discrete directions simultaneously. With preconditioned Krylov subspace iterative methods, the solver avoids possible mesh cycles in complex grids associated with sweep algorithms, which improves robustness and computational efficiency. First order upwind finite volume scheme is used for space discretization. Numerical experiments verify convergence rate on distorted hexahedral grids and assess performance of preconditioned iterative methods. Problems with coupled radiation and matter are simulated. Simulation results of three-dimensional crooked pipe and hohlraum problems are shown. It shows validity of the codes and flexibility of the method.

Key words: three-dimensional radiation transport equations, preconditioned Krylov subspace methods, discrete ordinate method, parallel computing

CLC Number:

O242.1

Lingxiao LI, Chuanlei ZHAI, Hui XIE, Yi SHI. A Monolithic Preconditioned Iterative Solver and Parallel Computing for Three-dimensional Thermal Radiation Transport Equation[J]. Chinese Journal of Computational Physics, 2021, 38(3): 269-279.

Figures/Tables 17

Fig.1 Illustration of distorted hexahedral mesh

Table 1 Convergence rate of space discretization

网格	六面体个数	‖ϕ-ϕ_h‖_L²	收敛率	‖T-T_h‖_L²	收敛率
G1	512	4.48 × 10^-2		3.27 × 10^-2
G2	4 096	2.25 × 10^-2	0.994	1.64 × 10^-2	0.996
G3	32 768	1.13 × 10^-2	0.994	8.19 × 10^-3	1.002
G4	262 144	5.68 × 10^-3	0.992	4.10 × 10^-3	0.998

Fig.2 Illustration of stretched mesh

Fig.3 Distribution of material temperature on z = 0.5 at end time

Fig.4 1D Marshak wave test: Comparison of material temperature (a) S4, (b) S8

Table 2 Parallel scalability of the solver

网格/进程数	S2 build	S2 solve	S4 build	S4 solve
G1/1	9.33 s	1.85 s	59.18 s	8.80 s
G2/8	10.87 s	3.77 s	73.90 s	22.73 s
G3/64	12.12 s	6.63 s	85.37 s	46.06 s
G4/512	14.65 s	11.33 s	103.27 s	70.18 s

Fig.5 The mesh used in 3D crooked pipe problem

Table 3 Comparison of iteration number for different preconditioned Krylov methods

S8角度离散			GMRES		BiCGSTAB
时间步	τ/ns	NonIter	Jacobi	ASM	Jacobi	ASM
88	0.2	3	123	25	70	14
			117	24	62	13
			128	23	70	14
89	0.085 6	3	109	23	61	13
			104	22	55	12
			109	20	55	10

Table 4 Comparison of solving time for different preconditioned Krylov methods with 32 MPI ranks

	GMRES+Jacobi	BiCGSTAB+Jacobi	GMRES+ASM	BiCGSTAB+ASM
S4	236.4 s	197.1 s	158.4 s	126.1 s
S8	2 458.2 s	2 285.4 s	2 118.1 s	1 864.7 s

Table 5 Comparison of solving time for different Krylov methods with 64 MPI ranks

	GMRES+Jacobi	BiCGSTAB+Jacobi
S4	126.1 s	103.6 s
S8	1 221.9 s	1 029.4 s

Fig.6 Distribution of material temperature on x-z cross section

Fig.7 Distribution of radiation temperature on x-z cross section

Fig.8 Computational domain for 3D holaraum problem

Fig.9 Material temperature at t= 0.461 138 ns

Fig.10 Material temperature at t= 1 ns

Fig.11 Radiation temperature at t= 0.006 105 1 ns

Fig.12 Radiation temperature at t= 0.057 275 ns

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