A Multiquadric Solution for the Shallow Water Equations

A computational algorithm based on the multiquadric, which is a continuously diierentiable 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 diierence scheme. The method does not require the generation of a grid as in the nite element method and allows easy editing or reenement of the numerical model. To increase the conndence on 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 free of spurious oscillations. The computed results are compared with the measured data and good agreement is indicated.