Three-Dimensional Finite-Element Model for Stratified Coastal Seas

Abstract

An efficient semi-implicit finite-element model for stratified coastal seas is proposed. Nine-node Lagrangian quadratic isoparametric elements are employed for spatial discretization in the horizontal domain and a three-mode Lagrangian interpolation formula is used to approximate the vertical gradients of the two horizontal velocity components. The distinguishing feature of the proposed numerical scheme is that only nodal values on the same vertical line are coupled, resulting in a drastic reduction of computer time. The model is applicable even in situations where there are great variabilities in the water depth in the computational domain, which leads to orders of magnitude difference in the thicknesses of the different water layers in the water body. The model is first verified by a test case for which analytic solutions are available and then applied to simulate the flow in a stratified sea for which solution by a combined finite-difference–Galerkin method is available in the literature for comparison.