A NUMERICAL MODEL FOR INTERNAL WAVE PROPAGATION IN CONTINUOUSLY STRATIFIED OCEAN

Based on the Euler equations,the finite volume method is employed to develop a numerical model for the internal wave propagation in continuously stratified ocean with variable water depth.The convection terms are discretized with the total variation diminishing (TVD) scheme to make the numerical scheme accurate up to second order,and the SIMPLE algorithm is used in the present numerical scheme.In order to simplify the calculation process and easily adapt to different TVD schemes,the adopted semi-implicit method for pressure linked equations (SIMPLE) algorithm is modified.The predicted velocity fields are calculated with the explicit scheme,instead of the implicit scheme,which is traditionally adopted in the SIMPLE algorithm.Also,the varieties of the hydrostatic pressure due to the density disturbances are not involved in the original SIMPLE algorithm,but they are involved and resolved in this paper.Thus,the SIMPLE algorithm is further developed.The open boundary at the far end is dealt with a sponge layer combined with the Sommerfield's radiation condition.The numerical results with constant depth are compared to the analytical solutions and good agreements are found,and the calculated spatial distributions of the density fields with a submerged dike at different moments are analyzed in details.It is shown that the present numerical model can effectively simulate the propagation of internal wave.