PLASMA-FEMmE: An adaptive Shallow Water Model on the Sphere

PLASMA-FEMmE solves on the sphere the shallow water equations, a prototype for partial differential equations in atmospheric modelling, using a semi-implicit semi-Lagrangian time step and linear finite elements. Grid generation is done by the grid generator amatos.

In our talk we present results using statically and dynamically adapted grids and compare them with the predecessor model FEMmE that uses a static uniform grid. Steady state flow regimes and more complex ones, e.g. flow over a mountain, are demonstrated.
The outcome shows the capability of the chosen approach as well as its limits. Grid adaptation can easily be achieved with amatos. No reflexions at the grid interfaces are observed.
The numerical errors are reduced without a considerable enhancement of the computational effort in the steady state test case. In respect to the conservation properties the results are more sophisticated. In contrast to conservation of mass that cannot improved in any investigated test case, this is achieved for conservation of energy. In case of complex flow regimes this statement only holds for static grid adaption. Here, with dynamic grid adaption, all conservation properties fade in the second half of a 15-day simulation period.
Nevertheless it can be concluded that the investigated scheme works out fine within the expectations. With additional research effort and using conservative advection schemes as well as more sophisticated adaption criteria there is hope that the aforementioned problems can be overcome.