Volume 54, Number 2, March-April 2020
|Page(s)||465 - 492|
|Published online||18 February 2020|
Up-wind difference approximation and singularity formation for a slow erosion model
Dipartimento di Meccanica, Matematica e Management, Politecnico di Bari, Via Orabona 4, 70125 Bari, Italy
2 Dipartimento di Ingegneria, Università degli Studi di Palermo, Viale delle Scienze, Ed. 8, 90128 Palermo, Italy
3 Dipartimento di Matematica e Informatica, Università degli Studi di Palermo, Via Archirafi 34, 90123 Palermo, Italy
* Corresponding author: firstname.lastname@example.org
Accepted: 10 September 2019
We consider a model for a granular flow in the slow erosion limit introduced in . 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.
Mathematics Subject Classification: 35A20 / 35L65 / 65M12 / 65M06 / 76S05
Key words: Entropy solutions / up-wind scheme / Engquist–Osher scheme / spectral analysis / complex singularities / granular flows
© EDP Sciences, SMAI 2020
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.