Compactly supported radial basis functions for shallow water equations

This paper presents the application of the compactly supported radial basis functions (CSRBFs) in solving a system of shallow water hydrodynamics equations. The proposed scheme is derived from the idea of piecewise polynomial interpolation using a function of Euclidean distance. The compactly supported basis functions consist of a polynomial which are non-zero on [0,1) and vanish on [1,∞). This reduces the original resultant full matrix to a sparse matrix. The operation of the banded matrix system could reduce the ill-conditioning of the resultant coefficient matrix due to the use of the global radial basis functions. To illustrate the computational efficiency and accuracy of the method, the difference between the globally and CSRBF schemes is compared. The resulting banded matrix has shown improvement in both ill-conditioning and computational efficiency. The numerical solutions are verified with the observed data. Excellent agreement is shown between the simulated and the observed data.