| A finite-element-based numerical algorithm is developed to solve the two-dimensional incompressible Navier-Stokes equations with Coriolis force, which can be used to simulate the wind-driven barotropic ocean circulation on a beta-plane. The spatial discretization is performed via the standard Galerkin Finite Element Method, by using the classical isoparametric Taylor-Hood serendipity quadrilateral finite element. A variant of the Crank-Nicolson rule is employed for the temporal discretization, and the Picard iteration method deals with the nonlinearity of the advective terms. In an effort to remain faithful to the standard Galerkin Finite Element Method, the consistent mass matrix is used instead of the lumped mass matrix, and least-square best fits are calculated for the quantities derived in the postprocessing phase. The algorithm has been implemented into a program and successfully tested on three benchmark problems, flow past a cylinder, flow over a backward facing step, and mid-latitude wind-driven barotropic ocean circulation for an idealized flat-bottomed ocean. |
