We report on the latest additions to our open-source, block-grid adaptive framework MPI-AMRVAC, which is a general toolkit for especially hyperbolic/parabolic partial differential equations (PDEs). Applications traditionally focused on shock-dominated, magnetized plasma dynamics described by either Newtonian or special relativistic (magneto)hydrodynamics, but its versatile design easily extends to different PDE systems. Here, we demonstrate applications covering any-dimensional scalar to system PDEs, with e.g. Korteweg–de Vries solutions generalizing early findings on soliton behavior, shallow water applications in round or square pools, hydrodynamic convergence tests as well as challenging computational fluid and plasma dynamics applications. The recent addition of a parallel multigrid solver opens up new avenues where also elliptic constraints or stiff source terms play a central role. This is illustrated here by solving several multi-dimensional reaction–diffusion-type equations. We document the minimal requirements for adding a new physics module governed by any nonlinear PDE system, such that it can directly benefit from the code flexibility in combining various temporal and spatial discretization schemes. Distributed through GitHub, MPI-AMRVAC can be used to perform 1D, 1.5D, 2D, 2.5D or 3D simulations in Cartesian, cylindrical or spherical coordinate systems, using parallel domain-decomposition, or exploiting fully dynamic block quadtree-octree grids.

Adaptive mesh refinement, (magneto)Hydrodynamics, PDEs
Computers & Mathematics with Applications
Centrum Wiskunde & Informatica, Amsterdam, The Netherlands

Keppens, R, Teunissen, H.J, Xia, C, & Porth, O. (2020). MPI-AMRVAC: A parallel, grid-adaptive PDE toolkit. Computers & Mathematics with Applications. doi:10.1016/j.camwa.2020.03.023