Multiquadric solution for shallow water equations

A computational algorithm based on the multiquadric, which is a continuousl y differentiable radial basis function, is devised to solve the shallow wat er equations. The numerical solutions are evaluated at scattered collocatio n points and the spatial partial derivatives are formed directly from parti al 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-eleme nt method and allows easy editing and refinement of the numerical model. To increase confidence in the multiquadric solution, a sensitivity and conver gence analysis is performed using numerical models of a rectangular channel . Applications of the algorithm are made to compute the sea surface elevati ons and currents in Tolo Harbour, Hong Kong, during a typhoon attack. The n umerical solution is shown to be robust and stable. The computed results ar e compared with measured data and good agreement is indicated.