Advancing parabolic operators in thermodynamic MHD models: Explicit super time-stepping versus implicit schemes with Krylov solvers

11th International Conference on Numerical Modeling of Space Plasma Flows

Caplan, R.M.^1 ; Miki, Z.^1 ; Linker, J.A.^1 ; Lionello, R.^1

Predictive Science Inc., 9990 Mesa Rim Road, San Diego

CA

92121, United States^1

关键词: Accuracy limitations;    Backward Euler scheme;    Nonoverlapping domain decomposition;    Preconditioned conjugate gradient solvers;    Real-world simulation;    Super time stepping;    Thermal conduction;    Unconditionally stable;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/837/1/012016/pdf
DOI  :  10.1088/1742-6596/837/1/012016

来源: IOP

【 摘 要 】

We explore the performance and advantages/disadvantages of using unconditionally stable explicit super time-stepping (STS) algorithms versus implicit schemes with Krylov solvers for integrating parabolic operators in thermodynamic MHD models of the solar corona. Specifically, we compare the second-order Runge-Kutta Legendre (RKL2) STS method with the implicit backward Euler scheme computed using the preconditioned conjugate gradient (PCG) solver with both a point-Jacobi and a non-overlapping domain decomposition ILU0 preconditioner. The algorithms are used to integrate anisotropic Spitzer thermal conduction and artificial kinematic viscosity at time-steps much larger than classic explicit stability criteria allow. A key component of the comparison is the use of an established MHD model (MAS) to compute a real-world simulation on a large HPC cluster. Special attention is placed on the parallel scaling of the algorithms. It is shown that, for a specific problem and model, the RKL2 method is comparable or surpasses the implicit method with PCG solvers in performance and scaling, but suffers from some accuracy limitations. These limitations, and the applicability of RKL methods are briefly discussed.