Exact solution for Riemann problems of the shear shallow water model

Nkonga, Boniface; Chandrashekar, Praveen

ESAIM: Mathematical Modelling and Numerical Analysis , Tome 56 (2022) no. 4, pp. 1115-1150

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.

Classification : 35L03, 65M08
Keywords: Shear shallow water model, non-conservative system, path conservative scheme, approximate Riemann solver, finite volume method

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