A high-resolution shallow water model using unstructured quadrilateral grids

A two-dimensional cell-centred finite volume model for quadrilateral grids is presented. The solution methodology of the depth-averaged shallow water equations is based upon a Godunov-type upwind finite volume formulation, whereby the inviscid fluxes of the system of equations are obtained using the HLL Riemann solver. A simple yet precise analytical expression is presented to compute hydrostatic flux through an interface of a quadrilateral cell in order to achieve exact balance between flux gradient and bed slope source terms under still water condition. A multidimensional gradient reconstruction procedure and a continuously differentiable multidimensional slope limiter based on a wide computational stencil are proposed to maintain second-order spatial accuracy. The proposed second-order scheme is shown to be more accurate even when distorted grids are used and is therefore more suitable for practical applications. The presented model is verified and validated by solving a wide variety of test cases having analytical solutions and laboratory measurements.

► Describes balancing of hydrostatic pressure and bed slope terms for quadrilateral grid.
► Simple second-order reconstruction method is presented for quadrilateral grid.
► The reconstruction method can reduce computations when viscous terms are considered.
► A multi-dimensional limiter is presented for unstructured quadrilateral grid.
► The model gives better results when the grids are distorted.