A Space-Time Adaptation Scheme for Unsteady Shallow Water Problems


A Space-Time Adaptation Scheme for Unsteady Shallow Water Problems
Tuesday 1st June 2010
Porta, G.M.; Perotto, S.; Ballio, F.
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We provide a space-time adaptation procedure for the approximation of the Shallow Water Equations (SWE). This approach relies on a recovery based estimator for the global discretization error, where space and time contributions are kept separate. In particular we propose an ad hoc procedure for the recovery of the time derivative of the numerical solution and then employ this reconstruction to de ne the error estimator in time. Concerning the space adaptation, we move from an anisotropic error estimator, i.e., able to automatically identify the density, the shape and the orientation of the elements of the computational mesh. The proposed global error estimator turns out to share the good properties of each recovery based error estimator. The whole adaptive procedure is then combined with a suitable stabilized nite element SW solver. Finally the reliability of the coupled solution-adaptation procedure is successfully assessed on two unsteady test cases of interest for hydraulics applications.