Numerical solution of the conservative form of the shallow water equations using sixth-order super compact scheme


1 Institute of Geophysics, University of Tehran, P.O. Box 14155-6466, Tehran, Iran

2 Associate Professor, Mechanical Engineering Department, University of Tehran


The super compact finite difference method is used for integrating the conservation-law form of the shallow water equations in the beta plane. The second-order delta formulation of the trapezoidal time differencing scheme is used. The sixth-order super compact finite-difference method is applied to discretize the spatial factored form of the equations obtained using the ADI method. Because of the large aliasing error introduced by the super compact scheme, the application of a very selective low-pass filter, based on compact schemes, is introduced to overcome the error generated by the interaction of the nonlinear terms of the equations. The integral invariants of the shallow water equations, i.e., the total energy and potential enstrophy are well conserved during the numerical integration. This fact shows that the nonlinear structure of the equations is correctly modeled. The validation of the sixth-order super compact results are investigated by comparing them with the results of the fourth-order compact and second-order finite-difference schemes for different grid resolutions.