Numerical simulation of 2D shallow water flow equations using RBF-DQ

Numerical simulation of long waves based on 2D Shallow Water Equations (SWEs) is considered as an important issue in coastal and river hydrodynamics. In this paper, a numerical model is developed to solve 2D SWEs using Radial Basis Function-based Differential Quadrature (RBF-DQ) technique. The method is meshfree, suitable for irregular domains, and easy to add or remove nodes. To increase the degree of confidence in model development, a sensitivity and convergence analysis is carried out for a simplified version of 2D linear SWEs with analytical solution. The numerical results are compared with existing analytical/numerical schemes and are found to be in good agreement even by using a few nodes. It is also shown that the two methods so called "RBF-Collocation" and "RBF-DQ" are basically the same.

Keywords:

Differental Quadrature , Radial Basis Functions , Tidal modeling , 2D Shallow water equations