Numerical Simulation of Tidal Currents in an Island Basin with Variational Boundaries

Abstract

In this paper, we describe a numerical model that is called “the crevice method” using a triangular mesh difference to simulate tidal currents in an island basin with a large area of beach ; the land boundaries move with the shift of the tide, and with geometrically complex boundaries. This model is based on shallow water momentum and continuity equations. For simulating variational boundaries, crevices which are artificially imagined are erected all over the shallows where the bed elevations are not lower than the lowest tidal level and where the water depth in the crevices changes with the ascent and descent of the tidal levels. For simulating a flow field within geometrically complex island boundaries, especially in flow circumstances near the islands, the triangular mesh difference is adopted in this model. The second derivative of u, ν and ζ with respect to time and the semi-implicit scheme are used in the triangular mesh difference for the purpose of increasing stability and accuracy, Practical calculation of tidal currents shows that this model has the advantages of better stability, higher accuracy, shorter calculation time, and it saves computer memory. The calculated results coincide reasonably with the measured ones.