Effect of grid non -orthogonality on the solution of shallow water equations using boundary -fitted grids
Effect of grid orthogonality on the solution of two-dimensional depth averaged shallow water equations is studied by comparing model predictions using different grid configurations with analytical solutions, for the cases of tidal forcing in a rectangular channel and seiche oscillation in a closed rectangular basin. The grid angle and grid resolution were found to affect accuracy of the model predicted velocities. Fourier analysis of the discretized equations also confirmed that grid angle and the grid resolution affects the accuracy of the solution and that the numerical dispersion increases with a decrease in grid angle or decrease in grid resolution.
The first manuscript investigates the effect of grid non-orthogonality on the solution of shallow water equations, using an existing two-dimensional boundary-fitted model (Muin and Spaulding, 1996). The linearized two-dimensional shallow water equations are expressed in terms of the grid angle and the grid aspect ratio.
In the second manuscript, expressions for phase and group speeds for both continuous and discretized, linearized two dimensional shallow water equations, in Cartesian coordinates are developed using Fourier analysis. The phase and group speeds of the equations, discretized using a three-point scheme of second-order, a five-point scheme of fourth order and a three-point compact scheme of fourth-order in an Arakawa C grid are calculated and compared with the corresponding values obtained for the continuous system.
In the third manuscript, a Fourier analysis is used to study the dispersion and group velocity relations of linearized, two-dimensional shallow water equations, in a non-orthogonal boundary fitted coordinate system. The phase and group speeds for the spatially discretized equations, using the second order scheme in an Arakawa C grid, are calculated for grids with varying degrees of non-orthogonality and compared with those obtained from the continuous case. A two-dimensional wave deformation analysis, based on complex propagation factor developed by Leendertse, is used to estimate the amplitude and phase errors of the two time level Crank-Nicolson scheme. (Abstract shortened by UMI.)