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We explore the performance and advantages/disadvantages of usingunconditionally stable explicit super time-stepping (STS) algorithms versusimplicit schemes with Krylov solvers for integrating parabolic operators inthermodynamic MHD models of the solar corona. Specifically, we compare thesecond-order Runge-Kutta Legendre (RKL2) STS method with the implicit backwardEuler scheme computed using the preconditioned conjugate gradient (PCG) solverwith both a point-Jacobi and a non-overlapping domain decomposition ILU0preconditioner. The algorithms are used to integrate anisotropic Spitzerthermal conduction and artificial kinematic viscosity at time-steps much largerthan classic explicit stability criteria allow. A key component of thecomparison is the use of an established MHD model (MAS) to compute a real-worldsimulation on a large HPC cluster. Special attention is placed on the parallelscaling 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 solversin performance and scaling, but suffers from some accuracy limitations. Theselimitations, and the applicability of RKL methods are briefly discussed.

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