Journal of Computational Physics
Flux difference splitting and the balancing of source terms and flux gradients
Journal of Computational Physics
Generalized Roe schemes for 1D two-phase, free-surface flows over a mobile bed
Journal of Computational Physics
Journal of Computational Physics
An Exner-based coupled model for two-dimensional transient flow over erodible bed
Journal of Computational Physics
Improved Riemann solvers for complex transport in two-dimensional unsteady shallow flow
Journal of Computational Physics
Journal of Computational Physics
A Riemann solver for unsteady computation of 2D shallow flows with variable density
Journal of Computational Physics
Hi-index | 31.48 |
An explicit finite volume model to simulate two-dimensional shallow water flow with multi-component transport is presented. The governing system of coupled conservation laws demands numerical techniques to avoid unrealistic values of the transported scalars that cannot be avoided by decreasing the size of the time step. The presence of non conservative products such as bed slope and friction terms, and other source terms like diffusion and reaction, can make necessary the reduction of the time step given by the Courant number. A suitable flux difference redistribution that prevents instability and ensures conservation at all times is used to deal with the non-conservative terms and becomes necessary in cases of transient boundaries over dry bed. The resulting method belongs to the category of well-balanced Roe schemes and is able to handle steady cases with flow in motion. Test cases with exact solution, including transient boundaries, bed slope, friction, and reaction terms are used to validate the numerical scheme. Laboratory experiments are used to validate the techniques when dealing with complex systems as the @k-@e model. The results of the proposed numerical schemes are compared with the ones obtained when using uncoupled formulations.