Multiquadric Solution for Shallow Water Equations

Abstract

A computational algorithm based on the multiquadric, which is a continuously differentiable radial basis function, is devised to solve the shallow water equations. The numerical solutions are evaluated at scattered collocation points and the spatial partial derivatives are formed directly from partial derivatives of the radial basis function, not by any difference scheme. The method does not require the generation of a grid as in the finite-element method and allows easy editing and refinement of the numerical model. To increase confidence in the multiquadric solution, a sensitivity and convergence analysis is performed using numerical models of a rectangular channel. Applications of the algorithm are made to compute the sea surface elevations and currents in Tolo Harbour, Hong Kong, during a typhoon attack. The numerical solution is shown to be robust and stable. The computed results are compared with measured data and good agreement is indicated.