Preprints, Working Papers, ...
2019
- auteur
- Kévin Pons, Mehmet Ersoy
- titre
- Adaptive mesh refinement method. Part 1: Automatic thresholding based on a distribution function
- article
- 2019
- resume
- The accurate numerical simulation of large scale flows, together with the detailed modeling of flooding or drying of small-scale regions, is a difficult and a challenging problem. Adaptive mesh method allows, in principle, to solve accurately those scales. However in practice, on one hand, the lack of a priori or efficient a posteriori error estimates, especially for multidimensional hyperbolic problems, make the analysis harder. On the other hand, once a mesh refinement criterion is chosen, the difficult problem is to determine the mesh refinement threshold parameter which is certainly the most important part of the adaptive process. The smaller this parameter is, the higher the number of cells refined is at the expense of the computational cost. In this work, we numerically investigate different refinement criteria and we present a general procedure to determine automatically a mesh refinement threshold for any given mesh refinement criterion. To this end the decreasing rearrangement (distribution) function of the mesh refinement criterion is introduced to catch relevant scales. The efficiency of the automatic thresholding method is illustrated through the one dimensional Saint-Venant system. Multidimensional and real life applications such as Tsunamis propagations are dealt in the second part.
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2016
- auteur
- Kévin Pons, Richard Marcer, Mehmet Ersoy, Frederic Golay, Richard Marcer Principia
- titre
- Adaptive mesh refinement method. Part 2: Application to tsunamis propagation
- article
- 2016
- resume
- Numerical simulations of multi dimensional large scale fluid-flows such as tsunamis, are 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 apply an automatic threshold method based on the decreasing rearrangement function of the mesh refinement criterion. This method is applied and validated successfully to the one and two dimensional non homogeneous Saint-Venant system through several tsunamis propagation test cases.
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