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

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, M2 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.

An Efficient Tide-Surge Interaction Model for the Coast of Bangladesh

The numerical method of lines(MOLs)in coordination with the classical fourth-order Runge Kutta(RK(4,4))method is used to solve shallow water equations(SWEs)for foreseeing water levels owing to the nonlinear interaction of tide and surge accompanying with a storm along the coast of Bangladesh.The SWEs are developed by extending the body forces with tide generating forces(TGFs).Spatial variables of the SWEs along with the boundary conditions are approximated by means of finite difference technique on an Arakawa C-grid to attain a system of ordinary differential equations(ODEs)of initial valued in time,which are being solved with the aid of the RK(4,4)method.Nested grid technique is adopted to solve coastal complexities closely with least computational cost.A stable tidal solution in the region of our choice is produced by applying the tidal forcing with the major tidal constituent M2(lunar semi-diurnal)along the southern open-sea boundary of the outer scheme.Numerical experimentations are carried out to simulate water levels generated by the cyclonic storm AILA along the coast of Bangladesh.The model simulated results are found to be in a reasonable agreement with the limited available reported data and observations.

An Efficient Approach for Simulation of Water Levels due to the Nonlinear Interaction of Tide and Surge Along the Coast of Bangladesh

The ultimate goal and highlight of this paper are to explore water levels along the coast of Bangladesh efficiently due to the nonlinear interaction of tide and surge by employing the method of lines(MOLs)with the aid of newly proposed RKAHeM(4,4)technique.In this regard,the spatial derivatives of shallow water equations(SWEs)were discretized by means of a finite difference method to obtain a system of ordinary differential equations(ODEs)of initial valued with time as an independent variable.The obtained system of ODEs was solved by the RKAHeM(4,4)technique.One-way nested grid technique was exercised to incorporate coastal complexities closely with minimum computational cost.A stable tidal oscillation was produced over the region of interest by applying the most influential tidal constituent M2 along the southern open boundary of the outer scheme.The newly developed model was applied to estimate water levels due to the non-linear interaction of tide and surge associated with the catastrophic cyclone April 1991 along the coast of Bangladesh.The approach employed in the study was found to perform well and ensure conformity with real-time observations.

Discretization of Complex Geometric Domain Through Computer-Based Stair-Step Representation Method for Estimating Water Levels Associated with A Storm

In this paper,an improvement has been made to the approximation technique of a complex domain through the stair-step approach to have a considerable accuracy,minimize computational cost,and avoid the hardship of manual work.A novel stair-step representation algorithm is used in this regard,where the entire procedure is carried out through our developed MATLAB routine.Arakawa C-grid is used in our approximation with(1/120)°grid resolution.As a test case,the method is applied to approximate the domain covering the area between 15°-23°N latitudes and 85°-95°E longitudes in the Bay of Bengal.Along with the approximation of the land-sea interface,coastal stations are also identified.Approximated land-sea interfaces and coastal stations are found to be in good agreement with the actual ones based on the similarity index,overlap fraction,and extra fraction criteria.The method can be used for approximating an irregular geometric domain to employ the finite difference method in solving problems related to long waves.As a test case,shallow water equations in Cartesian coordinates are solved on the domain of interest for simulating water levels due to the nonlinear tide-surge interaction associated with the storms April 1991 and AILA,2009 along the coast of Bangladesh.The same input except for the discretized domain and bathymetry as that of Paul et al.(2016)is used in our simulation.The results are found to be in reasonable agreement with the observed data procured from Bangladesh Inland Water Transport Authority.

A variety of novel closed-form soliton solutions to the family of Boussinesq-like equations with different types

This paper deals with the closed-form solutions to the family of Boussinesq-like equations with the effect of spatio-temporal dispersion.The sine-Gordon expansion and the hyperbolic function approaches are efficiently applied to the family of Boussinesq-like equations to explore novel solitary,kink,anti-kink,combo,and singular-periodic wave solutions.The attained solutions are expressed by the trigonometric and hyperbolic functions including tan,sec,cot,csc,tanh,sech,coth,csch,and of their combination.In addition,the mentioned two approaches are applied to the aforesaid models in the sense of Atangana conformable derivative or Beta derivative to attain new wave solutions.Three-dimensional and two-dimensional graphs of some of the obtained novel solutions satisfying the corresponding equations of interest are provided to understand the underlying mechanisms of the stated family.For the bright wave solutions in terms of Atangana’s conformable derivative,the amplitudes of the bright wave gradually decrease,but the smoothness increases when the fractional parametersαandβincrease.On the other hand,the periodicities of periodic waves increase.The attained new wave solutions can motivate applied scientists for engineering their ideas to an optimal level and they can be used for the validation of numerical simulation results in the propagation of waves in shallow water and other nonlinear cases.The performed approaches are found to be simple and efficient enough to estimate the solutions attained in the study and can be used to solve various classes of nonlinear partial differential equations arising in mathematical physics and engineering.