Development of a Two-Dimensional Estuarine Hydrodynamic Model in Cylindrical Co-ordinates

Abstract

Development of a novel two-dimensional estuarine hydrodynamic model in cylindrical co-ordinates is presented herein. The full non-linear Navier-Stokes equations are written in cylindrical co-ordinates with the advantage of the co-ordinate system fitting the estuary's shape. Thus the bending of the coastline can be more accurately described. Also, this way a fine mesh is obtained in the coastal area, while a coarse mesh is defined away from the coast provided that the position of the pole is appropriately chosen. The new model aims at improving the resolution of study areas and getting results without increasing computational costs.

Validation of the cylindrical co-ordinates numerical model is done by comparison with robust industry-standard models, tidal basin measurements and analytical solution. Three test cases are proposed for comparison with other numerical models: horizontal bed with constant value of the scale factors in the radial direction, horizontal bed with one variation of the scale factors in the radial direction, horizontal bed with two variations of the scale factors in the radial direction. Variation of the scale factors in the radial direction is done with an exponential function. Comparisons with results of the two numerical models show very good agreement. Comparison with tidal basin data is done in three cases: cylindrical co-ordinates (the rectangular geometry is generated from cylindrical co-ordinates), uniform Cartesian co-ordinates, and non-uniform Cartesian co-ordinates. Results showed that agreement was achieved in all cases. Finally, agreement between analytical solution and results of the numerical model shows the potential of the cylindrical co-ordinates numerical model for estuarine hydrodynamic modelling.

In terms of computational savings, the model proved to be four times faster than the Cartesian co-ordinates numerical model ran at the finest resolution in the cylindrical co-ordinates numerical model. Compared to the general orthogonal curvilinear co-ordinates model, the new model is three times slower since this is a preliminary development of the cylindrical co-ordinates model and further improvement is required.