MPI-AMRVAC: A parallel, grid-adaptive PDE toolkit

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