The calculation of the evolution of perturbations of the free surface using the finite element method for various variants of the shallow water equations

Abstract

The calculation of the evolution of perturbations of the free surface using the finite element method for various variants of the shallow water equations

Zhukov M.Yu., Malakhovskaya V.B., Shiryaeva E.V.

Incoming article date: 25.11.2015

The shallow water equations on the plane, the sphere, and in the approximation the beta–plane are investigated numerically using the finite element method. It is shown that the semi-implicit time approximation allows to obtain a stable solution in the case of localized initial perturbation of the free surface for a rotating fluid.

Keywords: finite elements, shallow water equations, beta–plane, the perturbation of the free surface