Adaptive mesh refinement method. Part 2: Application to tsunamis propagation

Kévin Pons (1, 2) , Mehmet Ersoy (2) , Frederic Golay (2) , Richard Marcer (1)

1 Pincipia
2 IMATH - Institut de Mathématiques de Toulon - EA 2134

As an extension of " Adaptive mesh refinement method. Part 1: Automatic thresholding based on a distribution function. " , we propose to show the efficiency of the automatic thresholding method for a large variety of real life test problems such as the propagation of tsunamis. The numerical simulations of multi dimensional large variety scale fluid-flows such as tsunami modeling, is still nowadays a challenging and a difficult problem. To this purpose, a parallel finite volume scheme on adaptive unstructured meshes for multi dimensional Saint-Venant system is presented. The adaptive mesh refinement method is based on a block-based decomposition (called BB-AMR) which allows quick meshing and easy parallelization. The main difficulty addressed here concerns the selection of the mesh refinement threshold which is certainly the most important parameter in the AMR method. Usually, the threshold is calibrated according to the test problem to balance the accuracy of the solution and the computational cost. To avoid " hand calibration " , we propose to apply the automatic threshold method based on the decreasing rearrangement function of the mesh refinement criterion. The robustness was shown in the first part of

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Kévin Pons, Mehmet Ersoy, Frederic Golay, Richard Marcer. Adaptive mesh refinement method. Part 2: Application to tsunamis propagation. 2016. ⟨hal-01330680v1⟩