Adaptive semi-implicit FVEG methods for multidimensional systems of hyperbolic balance laws

The aim of the proposed project is the development of new adaptive semi-implicit finite volume
evolution Galerkin (FVEG) methods for two- and three-dimensional systems of hyperbolic balance
laws. These schemes are based on exact and approximate evolution operators, derived from
bicharacteristic theory of hyperbolic conservation laws. For a number of test problems conducted
over several years, these schemes have proven to be particularly accurate and efficient. The
proposal intends to develop the schemes further to make them suitable for a range of hydraulic,
geophysical and meteorological applications in two and three space dimensions. Key techniques
to be developed are semi-implicit time approximation, adaptivity and error control, as well as
multidimensional open boundary conditions.
To assure that the derived schemes are robust and reliable for such complex models, an in-depth
numerical analysis including stability, convergence and error control is necessary. The project is supported
by the DFG and realized in a cooperation with Prof. Noelle (RWTH Aachen).

Rising large warm air bubble with a small cold bubble on top, simulated on GPU by the DG evolution Galerkin method (computed by L. Yelash and B.J. Block)