Anisotropic Mesh Adaptation Driven by a Recovery-Based Error Estimator for Shallow Water Flow Modeling
Wednesday 13th January 2010
Porta, G.M.; Perotto, S.; Ballio, F.
Focus of the paper is to propose an effective anisotropic mesh adaptation procedure for the solution of the shallow water equations. The hyperbolic partial differential equation system is solved via the streamline diffusion finite element method, suitably corrected by a shock capturing contribution. The proposed adaptation procedure relies on a recovery-based error estimator. In particular we look for an anisotropic error estimator able to select not only the size, but also the shape and the orientation of the mesh elements, with the aim of optimizing the computational advantages yielded by mesh adaptation. The robustness of the proposed estimator is tested first in a purely diffusive setting and then on two steady shallow water problems, with known analytical solution. Finally we discuss the reliability of the adaptation procedure on a real-scale unsteady configuration.