Numerical modeling of long waves in shallow water using Incremental Differential Quadrature Method

Incremental Differential Quadrature Method (IDQM) as a rapid and accurate method for numerical simulation of Nonlinear Shallow Water (NLSW) waves is employed. To the best of authors’ knowledge, this is the first endeavor to exploit DQM in coastal hydraulics. The one-dimensional NLSW equations and related boundary conditions are discretized in space and temporal directions by DQM rules and the resulting system of equations are used to compute the state variables in the entire computational domain. It was found that the splitting of total simulation time into a number of smaller time increments, could significantly enhance the performance of the proposed method. Furthermore, results of this study show two main advantages for IDQM compared with other conventional methods, namely; unconditional stability and minimal computational effort. Indeed, using IDQM, one can use a few grid points (in spatial or time direction) without imposing any stability condition on the time step to obtain an accurate convergent solution.