Scientific Computation and Applied & Industrial Mathematics: Martin Oberlack

The development of the new discontinuous Galerkin (DG) framework BoSSS (bounded support spectral solver) starting in 2007. Solvers for incompressible as well as compressible single and multi-phase flows were implemented. The code features a modern object-oriented design and is of course MPI-parallel. Within the development cycle, we use unit-testing to ensure software quality: this covers a wide range of tests, form very simple ones that test e.g. accuracy of implemented quadrature rules or the derivatives of a scalar field to complex MPI-parallel Navier-Stokes simulations and convergence tests. All these checks and tests are automatically executed by a dedicated server, whenever a developer commits changes to the GIT-repository.

BoSSS supports arbitrary partitioning of the grid, on an arbitrary number of compute-nodes at start-up time, which is an important perquisite for the adaptive meshing which is addressed by this proposal. Quite recently, support for mixed meshes (combining e.g. triangles and quads) and hanging nodes has been added. The most outstanding feature of the code is the support for multiphase-flows and immersed boundary methods. For both of these applications, the interface is described by a level-set-method. The novelty is that we can demonstrate arbitrarily high spectral convergence in the presence of curved interfaces. This becomes possible due to a novel numerical integration technique for implicitly defined surfaces, the so-called hierarchical moment fitting (HMF) technique.