Exact solution for Riemann problems of the shear shallow water model

TL;DR

This paper derives exact solutions for the Riemann problem in the shear shallow water model, a complex hyperbolic system including shear effects, and compares these solutions with numerical approximations.

Contribution

The paper constructs exact solutions assuming a linear path in conserved variables for the shear shallow water model, aiding in understanding wave interactions.

Findings

Exact solutions for Riemann problems are derived.

Comparison shows good agreement with numerical schemes.

Provides insights into wave structures in shear shallow flows.

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.