A Fast and Stable Well-Balanced Scheme with Hydrostatic Reconstruction for Shallow Water Flows
SIAM Journal on Scientific Computing
Journal of Computational Physics
Hydrodynamics of Free Surface Flows: Modelling with the finite element method
Hydrodynamics of Free Surface Flows: Modelling with the finite element method
Efficient well-balanced hydrostatic upwind schemes for shallow-water equations
Journal of Computational Physics
A multilayer shallow water system for polydisperse sedimentation
Journal of Computational Physics
A simple multi-layer finite volume solver for density-driven shallow water flows
Mathematics and Computers in Simulation
Hi-index | 31.46 |
We present a multilayer Saint-Venant system for the numerical simulation of free surface density-stratified flows over variable topography. The proposed model formally approximates the hydrostatic Navier-Stokes equations with a density that varies depending on the spatial and temporal distribution of a transported quantity such as temperature or salinity. The derivation of the multilayer model is obtained by a Galerkin-type vertical discretization of the Navier-Stokes system with piecewise constant basis functions. In contrast with classical multilayer models in the literature that assume immiscible fluids, we allow here for mass exchange between layers. We show that the multilayer system admits a kinetic interpretation, and we use this result to formulate a robust finite volume scheme for its numerical approximation. Several numerical experiments are presented, including simulations of wind-driven stratified flows.