The Numerical Method For Shallow Water Equations

These recent years, significant effort has been oriented for the developmentof shallow water environments simulators, for various objectives. These simulatorsare efficient tools for understanding and modeling tidal fluction, bay and estuaryflows, flood in rivers. Based on the. information provided by the numerical sim-ulation, the decision can be made on flood control and the construction and thereinforce of the bank. The two-dimensional shallow water equations, as an impor-tant one of these simulators, privides a model to describe fluid flow m domainswhose bathymetic depth is much smaller than the characteristics length scale inthe horizontal direction.The two-dimensional shallow water equations are governed by the followingsystemWater continuity equationH_t+▽.(HU)=0. (1.1)Water dynamic equations(HU)_t+▽.(HU(?)U)-▽.(H_μ▽U)+gH▽Z=HF, (1.2)The shallow water equations given by [1]can be expressed as advection-diffusionproblem, so the characteristics-mixed finite element method is considered in[2] and the characteristics-Galerkin method is investigated in[4]. In this paper,undersome mild assuptions we simplify (1.1)-(1.2) to a more compact form then simu-late the simplified form of shallow water equations in two dimensional space byFinite Difference-Streamline Diffusion simulation and characteristics finite elementsimulation.By strict numerical analysis, relevant error estimates are obtained.