Discrete models for the numerical analysis of time-dependent multidimensional gas dynamics
Journal of Computational Physics
Conservative multidimensional upwinding for the steady two-dimensional shallow water equations
Journal of Computational Physics
Journal of Computational Physics
Flux difference splitting and the balancing of source terms and flux gradients
Journal of Computational Physics
The surface gradient method for the treatment of source terms in the shallow-water equations
Journal of Computational Physics
A well-balanced gas-kinetic scheme for the shallow-water equations with source terms
Journal of Computational Physics
Journal of Computational Physics
On the partial difference equations of mathematical physics
IBM Journal of Research and Development
Journal of Scientific Computing
A Hybrid Second Order Scheme for Shallow Water Flows
Journal of Scientific Computing
A Numerical Scheme for a Viscous Shallow Water Model with Friction
Journal of Scientific Computing
On the well-balanced numerical discretization of shallow water equations on unstructured meshes
Journal of Computational Physics
Hi-index | 31.45 |
The finite volume discretisation of the shallow water equations has been the subject of many previous studies, most of which deal with a well-balanced conservative discretisation of the convective flux and bathymetry. However, the bed friction discretisation has not been so profusely analysed in previous works, while it may play a leading role in certain applications of shallow water models. In this paper we analyse the numerical discretisation of the bed friction term in the two-dimensional shallow water equations, and we propose a new unstructured upwind finite volume discretisation for this term. The new discretisation proposed improves the accuracy of the model in problems in which the bed friction is a relevant force in the momentum equation, and it guarantees a perfect balance between gravity and bed friction under uniform flow conditions. The relation between the numerical scheme used to solve the hydrodynamic equations and the scheme used to solve a scalar transport model linked to the shallow water equations, is also analysed in the paper. It is shown that the scheme used in the scalar transport model must take into consideration the scheme used to solve the hydrodynamic equations. The most important implication is that a well-balanced and conservative scheme for the scalar transport equation cannot be formulated just from the water depth and velocity fields, but has to consider also the way in which the hydrodynamic equations have been solved.