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
Journal of Computational Physics
Journal of Computational Physics
Generalized Roe schemes for 1D two-phase, free-surface flows over a mobile bed
Journal of Computational Physics
FORCE schemes on unstructured meshes I: Conservative hyperbolic systems
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Solving the depth-integrated solute transport equation with a TVD-MacCormack scheme
Environmental Modelling & Software
An Exner-based coupled model for two-dimensional transient flow over erodible bed
Journal of Computational Physics
A Riemann solver for unsteady computation of 2D shallow flows with variable density
Journal of Computational Physics
Hi-index | 31.45 |
The numerical solution of advection-reaction-diffusion transport problems in two-dimensional shallow water flow is split in three subproblems in order to analyze them separately. In the first part, the advection component is solved with the help of an extended Jacobian matrix for the coupled system of flow and advection conservation laws and focusing on the correct definitions of the approximate or weak solutions. Considering that one of the conserved quantities is the solute volume, nonphysical solutions for the solute concentration may appear in complex situations and a solute fix is proposed. This is formulated for first and second order schemes. In the second part of this work, the solution of problems with volumetric reaction terms is studied and the results of single-step as well as multi-step pointwise and upwind approaches are compared in order to establish their relative performance. The upwind treatment is done in 2D cases dividing cell volumes to transform reacting terms in singular source terms. The third part is concerned with the diffusion term. The focus of this part is put on the interference between numerical and physical diffusion. A simple form to estimate the magnitude of the numerical diffusion is proposed and it is shown to improve the accuracy of the results in first and second order approaches.