A semi-implicit, semi-Lagrangian, p-adaptive Discontinuous Galerkin method for the shallow water equations

Keywords

Advanced Numerical Methods for Scientific Computing
SC4I/Digitization, Innovation, and Competitiveness of the Production System
Code:
04/2012
Title:
A semi-implicit, semi-Lagrangian, p-adaptive Discontinuous Galerkin method for the shallow water equations
Date:
Wednesday 18th January 2012
Author(s):
Tumolo, G.; Bonaventura, L.; Restelli, M.
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Abstract:
A semi-implicit and semi-Lagrangian Discontinuous Galerkin (SISLDG) method for the shallow water equations is proposed, for applications to geophysical scale flows. A non conservative formulation of the advection equation is employed, in order to achieve a more treat- able form of the linear system to be solved at each time step. 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 show that the method captures well the main features of gravity and inertial gravity waves, as well as reproducing correct solutions in nonlinear test cases with analytic solutions. The accuracy and effectiveness of the method are also demonstrated by numerical results obtained at high Courant numbers and with automatic choice of the local approximation degree.
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Journal of Computational Physics, Vol. 232, pp. 46-67, 2013