| Issue |
ESAIM: M2AN
Volume 54, Number 2, March-April 2020
|
|
|---|---|---|
| Page(s) | 465 - 492 | |
| DOI | https://doi.org/10.1051/m2an/2019068 | |
| Published online | 18 February 2020 | |
Up-wind difference approximation and singularity formation for a slow erosion model
1
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: vincenzo.sciacca@unipa.it
Received:
30
July
2018
Accepted:
10
September
2019
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.
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
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