Scientific expertise and role in the project

The von Karman Institute for Fluid Dynamics (VKI) has extensive expertise in the field of numerical techniques for the simulation of flows with shocks on unstructured grids, including advanced multi-dimensional upwind flow solvers, and hybrid and adaptive grid generation techniques. The Icarus-MHD code, which is being developed at VKI and K.U.Leuven, is a residual distribution code on unstructured grids with explicit or implicit time integration. The novel discretization technique employs compact numerical stencils which allow for efficient matrix inversions in an implicit integration scheme. The unstructured grid approach allows for flexible and adaptive gridding, such that different length scales can be covered efficiently.

The role of VKI in the project will be threefold. First the codes will be extended to allow for solution-adaptive refinement of tetrahedral 3D grids for steady flows. Three methods will be investigated. First isotropic refinement will be implemented, followed by extending the technique of interpolation error based anisotropic mesh refinement to 3D, and developing the technique of remeshing using feature detection. These techniques will be important to resolve the heliospheric and magnetotail current sheets. In a second phase an Arbitrary Lagrangian-Eulerian (ALE) formulation will be derived for the residual distribution schemes to allow for moving grids. This is an essential ingredient for the third contribution, namely dynamic grid refinement and coarsening for unsteady flow problems. This will be useful to track CME structures and shocks in their outward motion through the solar wind.