Numerical modeling of long waves in shallow water using LRBF-DQ and hybrid DQ/LRBF-DQ

A computational algorithm based on coupling the differential quadrature (DQ) method and the local radial basis function-based differential quadrature (LRBF-DQ) method is used to solve the shallow water equations. The proposed method that is named ‘hybrid DQ/LRBF-DQ’ has the advantages of DQ such as simplicity and low computational cost and the advantages of LRBF-DQ, like mesh free and Kronecker delta function properties. Contrary to the DQ method, this method can be used in problems with irregular domain with less computational cost and less sensitivity to shape parameter(s) compared to the LRBF-DQ method. The proposed method is employed to simulate the complex and irregularly shaped waterway of the Oresund strait which is located between Sweden and Denmark. Implementation of the proposed method leads to good results for water depth. In comparison with the LRBF-DQ method, the results show that the proposed method is less sensitive to the shape parameter and the range of acceptable shape parameter in the proposed method is wider.