We consider a model for a granular flow in the slow erosion limit introduced in [31]. We propose an up-wind numerical scheme for this problem and show that the approximate solutions generated by the scheme converge to the unique entropy solution. Numerical examples are also presented showing the reliability of the scheme. We study also the finite time singularity formation for the model with the singularity tracking method, and we characterize the singularities as shocks in the solution.
Giuseppe Maria, C., Francesco, G., Vincenzo, S. (2020). Up-wind difference approximation and singularity formation for a slow erosion model. MODÉLISATION MATHÉMATIQUE ET ANALYSE NUMÉRIQUE, 54(2), 465-492 [10.1051/m2an/2019068].
Up-wind difference approximation and singularity formation for a slow erosion model
Francesco, Gargano;Vincenzo, Sciacca
2020-03-01
Abstract
We consider a model for a granular flow in the slow erosion limit introduced in [31]. We propose an up-wind numerical scheme for this problem and show that the approximate solutions generated by the scheme converge to the unique entropy solution. Numerical examples are also presented showing the reliability of the scheme. We study also the finite time singularity formation for the model with the singularity tracking method, and we characterize the singularities as shocks in the solution.
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