A Comparison of positivity preserving techniques without time step restriction for the DG scheme applied to shallow water flows

Positivity preservation in the context of shallow water flows is important as soon as wet regions become dry or a dry region is flooded. However, positivity preserving explicit time stepping of DG semi-discretizations can not be applied in a straigthforward manner to the case of implicit time integration as the enforcement of non-negativity generally demands rather restrictive time step constraints. In this context, we compare two different modifications to the strategy of positivity preservation based on a production-destruction splitting of the DG scheme for the cell means of water height. One strategy uses the so-called Patankar trick while the other one is based on an iterative redistribution of the water level. Both modifications guarantee non-negativity of the water height for any time step size while still preserving conservativity. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)