Efficient construction and utilisation of approximate riemann solutions
Proc. of the sixth int'l. symposium on Computing methods in applied sciences and engineering, VI
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
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
Variable density bore interaction with block obstacles
International Journal of Computational Fluid Dynamics
Improved Riemann solvers for complex transport in two-dimensional unsteady shallow flow
Journal of Computational Physics
Energy balance numerical schemes for shallow water equations with discontinuous topography
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.46 |
A novel 2D numerical model for vertically homogeneous shallow flows with variable horizontal density is presented. Density varies according to the volumetric concentration of different components or species that can represent suspended material or dissolved solutes. The system of equations is formed by the 2D equations for mass and momentum of the mixture, supplemented by equations for the mass or volume fraction of the mixture constituents. A new formulation of the Roe-type scheme including density variation is defined to solve the system on two-dimensional meshes. By using an augmented Riemann solver, the numerical scheme is defined properly including the presence of source terms involving reaction. The numerical scheme is validated using analytical steady-state solutions of variable-density flows and exact solutions for the particular case of initial value Riemann problems with variable bed level and reaction terms. Also, a 2D case that includes interaction with obstacles illustrates the stability and robustness of the numerical scheme in presence of non-uniform bed topography and wetting/drying fronts. The obtained results point out that the new method is able to predict faithfully the overall behavior of the solution and of any type of waves.