A BOUNDARY-FITTED SHALLOW WATER MODEL OF SIMULATE TIDE AND SURGE FOR THE HEAD BAY OF BENGAL – APPLICATION TO CYCLONE SIDR (2007) AND AILA (2009)
Subject Areas : International Journal of Mathematical Modelling & Computations
1 - Assistant Professor Department of Mathematics Shahjalal University of Science and Technology, Sylhet -3114, Bangladesh
Bangladesh
Assistant Professor,
Department of Mathematics,
Shahjalal University of Science and Technology,
Sylhet -3114, Bangladesh
Keywords: Bay of Bengal, Cyclone Sidr, Cyclone Aila, Tropical Storms, Surge, Shallow water equations, Transformation of Coordinates,
Abstract :
Severe Tropical Cyclones associated with surges frequently hits the coastal region of Bangladesh. For a reliable hydrodynamic model to simulate the severity of such cyclones, it is necessary to incorporate the meteorological and hydrological inputs properly. In order to incorporate the coastlines and the island boundaries properly in the numerical scheme a very fine grid resolution along the coastal belts is necessary. Consideration of very fine resolution involves more memory, CPU time in the solution process and invites problem of complexity in the model or numerical instability. In this study we use the boundary-fitted curvilinear grids where the complete boundary of the analysis area and each Island are represented by four curves and they are defined by four functions. Using appropriate transformations of independent coordinates, the curvilinear physical domains are transformed to a square one and also each island boundary transforms to a rectangle within this square domain. The vertically integrated shallow water equations are transformed to the new space domain and then the regular explicit finite difference scheme is used to solve the shallow water equations, where the problem domain is divided into 100× 129 grid points. The model is applied to compute the water levels due to astronomical tide and surges associated with Cyclone Sidr (2007) and Cyclone Aila (2009) that hit the coast of Bangladesh. The computed results along the coastal belt of Bangladesh are found to be reasonably accurate.