Numerical storm surge model with higher order finite difference method of lines for the coast of Bangladesh

• Published in: Acta oceanologica Sinica Vol. 38; no. 6; pp. 100 - 116
• Main Authors: Paul, Gour Chandra, Ali, Md. Emran
• Format: Journal Article
• Language: English
• Published: Beijing The Chinese Society of Oceanography 01.06.2019; Springer Nature B.V; Department of Mathematics, University of Rajshahi, Rajshahi 6205, Bangladesh%Department of Textile Engineering, Northern University Bangladesh, Dhaka 1230, Bangladesh
• Subjects: Approximation; Approximation method; Cartesian coordinates; Climatology; Coastal environments; Coastal storms; Computer simulation; Coordinate systems; Cyclones; Differential equations; Earth and Environmental Science; Earth Sciences; Ecology; Engineering Fluid Dynamics; Environmental Chemistry; Finite difference method; Fresh water; Freshwater; Independent variables; Initial conditions; Inland water environment; Inland waters; Lines; Marine & Freshwater Sciences; Mathematical models; Method of lines; Momentum; Numerical experiments; Oceanography; Ordinary differential equations; Rivers; Runge-Kutta method; Shallow water; Shallow water equations; Storm surges; Storms; Tidal constituents; Water discharge; Water levels; Water transport; Bangladesh; nested scheme; surge; shallow water equations; method of lines; higher order finite difference approximation method
• ISSN: 0253-505X; 1869-1099
• DOI: 10.1007/s13131-019-1385-7

In this study, the method of lines (MOLs) with higher order central difference approximation method coupled with the classical fourth order Runge-Kutta (RK(4,4)) method is used in solving shallow water equations (SWEs) in Cartesian coordinates to foresee water levels associated with a storm accurately along the coast of Bangladesh. In doing so, the partial derivatives of the SWEs with respect to the space variables were discretized with 5-point central difference, as a test case, to obtain a system of ordinary differential equations with time as an independent variable for every spatial grid point, which with initial conditions were solved by the RK(4,4) method. The complex land-sea interface and bottom topographic details were incorporated closely using nested schemes. The coastal and island boundaries were rectangularized through proper stair step representation, and the storing positions of the scalar and momentum variables were specified according to the rules of structured C-grid. A stable tidal regime was made over the model domain considering the effect of the major tidal constituent, M 2 along the southern open boundary of the outermost parent scheme. The Meghna River fresh water discharge was taken into account for the inner most child scheme. To take into account the dynamic interaction of tide and surge, the generated tidal regime was introduced as the initial state of the sea, and the surge was then made to come over it through computer simulation. Numerical experiments were performed with the cyclone April 1991 to simulate water levels due to tide, surge, and their interaction at different stations along the coast of Bangladesh. Our computed results were found to compare reasonable well with the limited observed data obtained from Bangladesh Inland Water Transport Authority (BIWTA) and were found to be better in comparison with the results obtained through the regular finite difference method and the 3-point central difference MOLs coupled with the RK(4,4) method with regard to the root mean square error values.