We have long experience working with various kinds of high-resolution schemes and are proficient in topics such as
- Godunov schemes and Riemann solvers
- Total-variation diminishing (TVD) schemes
- Slope- and flux-limiting methods
- Weigthed non-oscillatory schemes (WENO)
- Central schemes and in particular semi-discrete central-upwind schemes
- Discontinuous Galerkin schemes
- Front-tracking methods
- Well-balanced discretizations
Most of our research focus on shallow-water equations used in surface water applications and ocean modelling or transport equations for multiphase, multicomponent flows in porous media on complex polytopal grids, but we also have experience from more academic applications of gas dynamics, traffic flow, and magneto-hydrodynamics.
With over two decades of experience, we have honed our skills in implementing high-resolution schemes on GPU computing hardware, demonstrated through the development of software solutions like GPUOcean and Alsvinn.