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Mathematics > Numerical Analysis

arXiv:2108.08648 (math)
[Submitted on 19 Aug 2021 (v1), last revised 7 Apr 2022 (this version, v2)]

Title:Exact solution for Riemann problems of the shear shallow water model

Authors:Boniface Nkonga, Praveen Chandrashekar
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Abstract: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.
Subjects: Numerical Analysis (math.NA); Computational Physics (physics.comp-ph)
Cite as: arXiv:2108.08648 [math.NA]
  (or arXiv:2108.08648v2 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2108.08648

Submission history

From: Praveen Chandrashekar [view email]
[v1] Thu, 19 Aug 2021 12:21:32 UTC (216 KB)
[v2] Thu, 7 Apr 2022 14:13:45 UTC (302 KB)
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