An alternating direction implicit (ADI) numerical model for two-dimensional hydrodynamic equations

A two-dimensional computational model is developed for the calculation of tides, storm surges and other long-period waves in coastal and shelf waters.The partial differential equations are approximated by two sets of difference equations on a space-staggered grid system.Both sets are implicit with one set for water level and x-component velocity, and another for water level and y-component velocity.These two sets are used successively for step-by-step solution in time.An analytical investigation on the linearized sets of the difference equations indicates that the computational scheme is unconditionally stable.The model is of second order accuracy both in space and in time and conserves mass and momentum.Simulations of surface elevation caused by periodic forcing in one-opening rectangular basin with flat topography and by steady wind stress in the basin with flat or slope topography show that the computed results are in excellent agreement with the corresponding analytic solutions.The steady-tate wind-induced setup in a closed basin with discontinuous topography rnmputed with the present model are also in exceVent agreement with the results from Leendertse's model.Finally, the model is applied to hindcast a storm surge in the South China Sea and reproduces the surge elevation satisfactorily.