Evaluation of a finite element formulation for the shallow water equations with numerical smoothing in the Gulf of San Jorge

Abstract

The shallow water equations (SWE) are a time-dependent system of non-linear partial differential equations utilized for fluid motion where the horizontal length scales are much greater than the fluid depth. The numerical solution of the SWE usually requires complex schemes and methods to deal with the instabilities proper to the system. This paper is concerned with a simple method to solve the SWE, utilizing continuous linear finite elements, no-slip closed boundary, and nested open boundary conditions, and a stabilization technique known as numerical smoothing. First, we describe the governing equations, the finite element model and the chosen discretization. Then we solve a 2D test case of an elliptical paraboloid and analyze its convergence comparing with provided analytical solutions. Finally, we apply the model to the northern region of the Gulf of San Jorge (Argentina), optimize parameters, and validate it with collected data from an acoustic Doppler current profiler (ADCP) of two spatial points during one tidal M2 period.