Abstract

As a first step towards construction and analysis of a DG based dynamical core for high resolution atmospheric modeling, a semi-implicit and semi-Lagrangian Discontinuous Galerkin method for the shallow water equations with rotation is proposed and analyzed.

The method is equipped with a simple p-adaptivity criterion, that allows to adjust dynamically the number of local degrees of freedom employed to the local structure of the solution.

Numerical results in the framework of two dimensional test cases prove that the method captures accurately and effectively the main features of linear gravity and inertial gravity waves. Also the solution of nonlinear Stommel problem is correctly simulated. The effectiveness of the method is also demonstrated by numerical results obtained at high Courant numbers and with automatic choice of the local approximation degree.

The present research has been carried out during the PhD of the autor (supervisors F. Giorgi and L. Bonaventura) with financial support from the {it Abdus Salam International Center for Theoretical Physics} and in collaboration with L.Bonaventura and M. Restelli {it MOX - Politecnico di Milano}.

See MOX -Report 04/2012 Tumolo, G.; Bonaventura, L.; Restelli, M. A semi-implicit, semi-Lagrangian, p-adaptive Discontinuous Galerkin method for the shallow water equations.