Simulation of Three-Dimensional Free-Surface Flows Using Two-Dimensional Multilayer Shallow Water Equations (Communications in Computational Physics, 2020)
We present an efficient and conservative Eulerian-Lagrangian method forsolving two-dimensional hydrostatic multilayer shallow water flows with mass exchange between the vertical layers. The method consists of a projection finite volumemethod for the Eulerian stage and a method of characteristics to approximate the numerical fluxes for the Lagrangian stage. The proposed method is simple to implement,satisfies the conservation property and it can be used for multilayer shallow waterequations on non-flat bathymetry including eddy viscosity and Coriolis forces. It offers a novel method of calculating stratified vertical velocities without the use of theNavier-Stokes equations. Numerical results are presented for several examples andthe obtained results for a free-surface flow problem are in close agreement with theanalytical solutions. We also test the performance of the proposed method for a testexample of wind-driven flows with recirculation
Keywords: Multilayer shallow water equations; incompressible hydrostatic flows; Eulerian-Lagrangian scheme; finite volume solver; projection method.