The 3D MHD code GOEMHD3 for astrophysical plasmas with large Reynolds numbers - Code description, verification, and computational performance

摘要

Context. The numerical simulation of turbulence and flows in almost ideal astrophysical plasmas with large Reynolds numbers motivates the implementation of magnetohydrodynamical (MHD) computer codes with low resistivity. They need to be computationally efficient and scale well with large numbers of CPU cores, allow obtaining a high grid resolution over large simulation domains, and be easily and modularly extensible, for instance, to new initial and boundary conditions. Aims. Our aims are the implementation, optimization, and verification of a computationally efficient, highly scalable, and easily extensible low-dissipative MHD simulation code for the numerical investigation of the dynamics of astrophysical plasmas with large Reynolds numbers in three dimensions (3D). Methods. The new GOEMHD3 code discretizes the ideal part of the MHD equations using a fast and efficient leap-frog scheme that is second-order accurate in space and time and whose initial and boundary conditions can easily be modified. For the investigation of diffusive and dissipative processes the corresponding terms are discretized by a DuFort-Frankel scheme. To always fulfill the Courant-Friedrichs-Lewy stability criterion, the time step of the code is adapted dynamically. Numerically induced local oscillations are suppressed by explicit, externally controlled diffusion terms. Non-equidistant grids are implemented, which enhance the spatial resolution, where needed. GOEMHD3 is parallelized based on the hybrid MPI-OpenMP programing paradigm, adopting a standard two-dimensional domain-decomposition approach. Results. The ideal part of the equation solver is verified by performing numerical tests of the evolution of the well-understood Kelvin-Helmholtz instability and of Orszag-Tang vortices. The accuracy of solving the (resistive) induction equation is tested by simulating the decay of a cylindrical current column. Furthermore, we show that the computational performance of the code scales very efficiently with the number of processors up to tens of thousands of CPU cores. This excellent scalability of the code was obtained by simulating the 3D evolution of the solar corona above an active region (NOAA AR1249) for which GOEMHD3 revealed the energy distribution in the solar atmosphere in response to the energy influx from the chromosphere through the transition region, taking into account the weak Joule current dissipation and viscosity in the almost dissipationless solar corona. Conclusions. The new massively parallel simulation code GOEMHD3 enables efficient and fast simulations of almost ideal astrophysical plasma flows with large Reynolds numbers well resolved and on huge grids covering large domains. Its abilities are verified by comprehensive set of tests of ideal and weakly dissipative plasma phenomena. The high-resolution (20483 grid?points) simulation of a large part of the solar corona above an observed active region proves the excellent parallel scalability of the code up to more than 30?000 processor cores.