A study of the effects of grid non-orthogonality on the solution of shallow water equations in boundary-fitted coordinate systems
Date of Original Version
In the present study, an existing two-dimensional boundary-fitted model [J. Hydraul. Eng.-ASCE 122 (9) (1996) 512] is used to study the effect of grid non-orthogonality on the solution of shallow water equations using boundary-fitted grids. The linearized two-dimensional shallow water equations are expressed in terms of the grid angle and aspect ratio. The truncation errors of the finite difference approximations used in the solution of the governing equations are shown to be dependent on the grid angle and the aspect ratio. The coefficient of the truncation error was shown to increase, with the decrease in the grid angle. The RMS errors in model predicted surface elevations and velocities for the case of seiching in a rectangular basin are found to increase gradually, as the grid resolution decreases from 174 to 80 gridpoints per wavelength or as the grid angle decreases from 90° to 50° and increases rather sharply for a grid angle of 30° at grid resolutions less than 80 gridpoints per wavelength. The model predicted surface elevations for the case of tidal forcing in a rectangular basin are found to be insensitive to the grid angle at grid resolutions higher than 600 gridpoints per wavelength. The RMS error in the model predicted velocities is found to increase gradually as the grid angle decreases from 90° to 30° or as the grid resolution decreases from 1400 gridpoints per wavelength to 400 gridpoints per wavelength and increases sharply as the grid resolution decreases from 400 to 150 gridpoints per wavelength. Two-dimensional depth averaged hydrodynamic modeling of tidal circulation in Narragansett Bay, using three different boundary-fitted grids showed that the model predicted surface elevations are insensitive to the grid angle at grid resolutions as low as 200 gridpoints per wavelength. However, the model predicted velocities were found to increase as the grid resolution decreases from 600 to 200 gridpoints per wavelength. We conclude from this study that grid angle and grid resolution affects the accuracy of the model predicted currents and the numerical dispersion increases with the decrease in grid angle or grid resolution and these are in agreement with that reached by Sankaranarayanan and Spaulding [Dispersion and Stability Analyses of Shallow Water Equations in Boundary-fitted Coordinates, Department of Ocean Engineering, University of Rhode Island, 2001, p. 33] through a Fourier analysis of the discretized equations in boundary-fitted coordinates. © 2002 Elsevier Science B.V. All rights reserved.
Journal of Computational Physics
Sankaranarayanan, S., and Malcolm L. Spaulding. "A study of the effects of grid non-orthogonality on the solution of shallow water equations in boundary-fitted coordinate systems." Journal of Computational Physics 184, 1 (2003): 299-320. doi:10.1016/S0021-9991(02)00042-6.