Performance of Numerical Calculation of Transport Equations of Scrape-off Layer Plasma: Pressure Correction Algorithms

doi:10.19596/j.cnki.1001-246x.8525

Abstract

Abstract:

Test codes are programmed with C++ to study influence of pressure correction algorithms, including SIMPLE (Semi-Implicit Method for Pressure Linked Equations), SIMPLEC (SIMPLE Consistent), SIMPLER (SIMPLE Revised), SIMPLEX (SIMPLE Extrapolation) and PISO (Pressure-Implicit with Splitting of Operators), on numerical solution performance of Braginskii transport equation for scrape-off layer plasma. Plasma model equations of SOLPS (Scrape-Off Layer Plasma Simulation) are adopted in the test codes. Numerical calculations are carried out on a simplified slab model. It was found that all of the pressure correction algorithms make the program converge to correct results. The fastest convergence speed is achieved with PISO. There is no significant difference in the convergence speed of SIMPLE, SIMPLEC, SIMPLER and SIMPLEX algorithms.

Key words: tokamak, scrape-off layer, Braginskii equation, finite volume method, pressure correction algorithm

Renzhu ZHU, Jiafeng HE, Taihao HUANG, Xinglei RUAN, Yuchen XU, Jin GUO, Tianyuan LIU, Shifeng MAO, Minyou YE. Performance of Numerical Calculation of Transport Equations of Scrape-off Layer Plasma: Pressure Correction Algorithms[J]. Chinese Journal of Computational Physics, 2023, 40(1): 29-39.

Figures/Tables 8

Fig.1 A schematic of the simplified slab model

Table 1 Boundary condition settings

	密度/m^-3	平行速度	电子温度/eV	离子温度/eV
芯部(图 1中蓝色边界)	3×10¹⁹	$ \partial V_{\\|} / \partial y=0$	400	400
靶板(图 1中黄色边界)	$ \partial n / \partial x=0$	±6.189 938×10⁴ m·s^-1*	40	40
私有通量区/刮削层(图 1中红色边界)	3×10¹⁸	$ \partial V_{\\|} / \partial y=0$	40	40

Fig.2 Distributions of (a) ion density, (b) ion parallel velocity, (c) electron temperature, (d) ion temperature and (e) pressure calculated with SIMPLE algorithm on fine grid

Fig.3 Poloidal distributions of (a) ion density, (b) ion parallel velocity, (c) electron temperature and (d) ion temperature at y=-0.005 m calculated with SIMPLE algorithm and Richardson extrapolation (solid purple line)

Fig.4 Extrapolated results of (a) ion density, (b) ion parallel velocity, (c) electron temperature and (d) ion temperature with five pressure correction algorithms

Fig.5 Density residuals calculated with different pressure correction algorithms as functions of the number of iterations, while the pressure relaxation factors are (a) 0.3, (b) 0.5, (c) 0.7, and (d) 0.9, respectively

Fig.6 Parallel velocity residuals calculated with different pressure correction algorithms as function of the number of iterations, while the pressure relaxation factors are (a) 0.3, (b) 0.5, (c) 0.7, and (d) 0.9, respectively

Table 2 Convergence velocity using different pressure correction algorithms (Pressure relaxation factor is 0.5.)

算法	单轮计算时间/s	收敛迭代次数(密度残差低于10¹⁴)	计算收敛时间/s
SIMPLE	0.766	823	630.4
SIMPLEC	0.744	822	611.6
SIMPLER	0.823	822	676.5
SIMPLEX	0.795	825	655.9
PISO	0.813	466	378.9

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