Computational magnetohydrodynamics (MHD) for space physics has become an essential area in understanding the multiscale dynamics of geophysical and astrophysical plasma processes, partially motivated by the lack of space data. Full MHD simulations are typically very demanding and may require substantial computational efforts. In particular, computational space-weather forecasting is an essential long-term goal in this area, motivated for instance by the needs of modern satellite communication technology. We present a new feature of a recently developed compressible two-and three-dimensional MHD solver, which has been successfully implemented into the parallel AMROC (Adaptive Mesh Refinement in Object-oriented C++) framework with improvements concerning the mesh adaptation criteria based on wavelet techniques. The developments are related to computational efficiency while controlling the precision using dynamically adapted meshes in space-time in a fully parallel context.

We present an adaptive parallel solver for the numerical simulation of ideal magnetohydrodynamics in two and three space dimensions. The discretisation uses a finite volume scheme based on a Cartesian mesh and an explicit compact Runge-Kutta scheme for time integration. Numerically, a generalized Lagrangian multiplier approach with a mixed hyperbolic-parabolic correction is used to guarantee a control on the incompressibility of the magnetic field. We implement the solver in the AMROC (Adaptive Mesh Refinement in Object-oriented C++) framework that uses a structured adaptive mesh refinement (SAMR) method discretisation-independent and is fully parallelised for distributed memory systems. Moreover, AMROC is a modular framework providing manageability, extensibility and efficiency. In this paper, we give an overview of the ideal magnetohydrodynamics solver developed in this framework and its capabilities. We also include an example of this solver's verification with other codes and its numerical and computational performance.

Plasma disturbances affect satellites, spacecraft and can cause serious problems to telecommunications and sensitive sensor-systems on Earth. Considering the huge scale of the plasma phenomena, data collection at individual locations is not sufficient to cover this entire relevant environment. Therefore, computational plasma modelling has become a significant issue for space sciences, particularly for the near-Earth magnetosphere. However, the simulations of these disturbances present many physical as well as numerical and computational challenges. In this work, we discuss our recent magnetohydrodynamic solver, realised within the MPI-parallel AMROC (Adaptive Mesh Refinement in Object-oriented C ++ ) framework, in which particular physical models and automatic mesh generation procedures have been implemented. A performance analysis using a selection of significant space applications validates the solvers capabilities and confirms the technical importance of our approach.

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