AN IMPROVED EFFICIENT SEMI-IMPLICIT FINITE ELEMENT SCHEME FOR TWO-DIMENSIONAL TIDAL FLOW COMPUTATIONS

In a recent paper, an efficient semi-implicit finite element scheme for 2-dimensional tidal flow computationsis proposed. In that scheme, each term of the governing equations, rather than each dependent variable, is ex-panded in terms of the unknown nodal values. Simpson’s rule ix used for numerical integration to make the massmatrix diagonal. The friction terms are represented semi-implicitly to improve stability, but no additional compu-tational effort is required. The shortcomings of this scheme are that the time-stepping scheme is only first-order ae-curate and artificial smoothing is required to control the numerical noise. In this paper, the previous scheme is im-proved by including the eddy viscosity terms in the governing equations to replace artificial smoothing in noise con-trol and the time-stepping scheme is modified to make it second-order accurate. These improvements can beachieved with only a slight increase in computational effort. The test cases used previously to validate the formerscheme are again employed to test the present scheme.