A numerical algorithm is developed for solving the three dimensional shallow water equations that frequently used in oceanography. The governing equations based on CJ-coordinatesare discretized by the three time levels Leapfrog/Crank-Nicholson method on three dimensional staggered grids. Second order accuracy in space and time is achieved. The discretized equations are then split into two time stages by the approximate operator factorization method. The most distinctive feature of this splitting method is that only tridiagonal systems should be solved at each stage. Therefore, efficiency and accuracy of this algorithm is better than most existing methods for solving the same system of equations. The resulting algorithm is tested with the case of wind-induced flow in a rectangular basin...[ Read more ]

A numerical algorithm is developed for solving the three dimensional shallow water equations that frequently used in oceanography. The governing equations based on CJ-coordinatesare discretized by the three time levels Leapfrog/Crank-Nicholson method on three dimensional staggered grids. Second order accuracy in space and time is achieved. The discretized equations are then split into two time stages by the approximate operator factorization method. The most distinctive feature of this splitting method is that only tridiagonal systems should be solved at each stage. Therefore, efficiency and accuracy of this algorithm is better than most existing methods for solving the same system of equations. The resulting algorithm is tested with the case of wind-induced flow in a rectangular basin that was used by many researchers for the same purpose. The algorithm is shown to be efficient and reliable.