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

TL;DR

This paper compares explicit super time-stepping and implicit Krylov solver schemes for parabolic operators in thermodynamic MHD models, highlighting performance, scalability, and accuracy trade-offs in solar corona simulations.

Contribution

It provides a detailed comparison of RKL2 super time-stepping and implicit Krylov methods in realistic MHD simulations, emphasizing their performance and scalability.

Findings

RKL2 can outperform implicit schemes in certain large-scale simulations.

Implicit schemes with Krylov solvers are more accurate but less scalable.

RKL2 exhibits some accuracy limitations compared to implicit methods.

Abstract

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.