| Issue |
ESAIM: M2AN
Volume 56, Number 4, July-August 2022
|
|
|---|---|---|
| Page(s) | 1115 - 1150 | |
| DOI | https://doi.org/10.1051/m2an/2022032 | |
| Published online | 27 June 2022 | |
Exact solution for Riemann problems of the shear shallow water model
1
Université Côte d’Azur, INRIA, CNRS and LJAD, 06108 Nice Cedex 2, France
2
Centre for Applicable Mathematics, Tata Institute of Fundamental Research, Bangalore 560065, India
* Corresponding author: praveen@math.tifrbng.res.in
Received:
19
August
2021
Accepted:
27
March
2022
The shear shallow water model is a higher order model for shallow flows which includes some shear effects that are neglected in the classical shallow models. The model is a non-conservative hyperbolic system which can admit shocks, rarefactions, shear and contact waves. The notion of weak solution is based on a path but the choice of the correct path is not known for this problem. In this paper, we construct exact solution for the Riemann problem assuming a linear path in the space of conserved variables, which is also used in approximate Riemann solvers. We compare the exact solutions with those obtained from a path conservative finite volume scheme on some representative test cases.
Mathematics Subject Classification: 35L03 / 65M08
Key words: Shear shallow water model / non-conservative system / path conservative scheme / approximate Riemann solver / finite volume method
© The authors. Published by EDP Sciences, SMAI 2022
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