Improved FVM for two-layer shallow-water models: Application to the Strait of Gibraltar

This paper deals with the numerical simulation of flows of stratified fluids through channels with irregular geometry. Channel cross-sections are supposed to be symmetric but not necessarily rectangular. The fluid is supposed to be composed of two shallow layers of immiscible fluids of constant densities, and the flow is assumed to be one-dimensional. Therefore, the equations to be solved are a coupled system composed of two Shallow Water models with source terms involving depth and breadth functions. Extensions of Roe’s Q-scheme are proposed where a suitable treatment of the coupling and source terms is performed by adapting the techniques developed in [Vázquez-Cendón ME. Improved treatment of source terms in upwind schemes for the shallow water equations in channels with irregular geometry. J Comp Phys 1999;148:497–526; García-Navarro P, Vázquez-Cendón ME. On numerical treatment of the source terms in the shallow water equations. Comput Fluids 2000;29(8):17–45; Castro MJ, Macías J, Parés C. A Q-Scheme for a class of systems of coupled conservation laws with source term. Application to a two-layer 1-D shallow water system. Math Model Numer An 2001;35(1):107–27]. Finally we apply the numerical scheme to the simulation of the flow through the Strait of Gibraltar. Real bathymetric and coast-line data are considered to include in the model the main features of the abrupt geometry of this natural strait connecting the Atlantic Ocean and the Mediterranean Sea. A steady state solution is obtained from lock-exchange initial conditions. This solution is then used as initial condition to simulate the main semidiurnal and diurnal tidal waves in the Strait of Gibraltar through the imposition of suitable boundary conditions obtained from observed tidal data. Comparisons between numerical results and observed data and some tests on friction sensitivity are also presented.