Abstract
The author presented a new spectral method to solve shallow-water equation on the unit disk domain numerically in the previous first part paper (Ishioka, 2003, J. Japan Soc. of Fluid Mech., vol. 22, pages 345-358). This method uses Jacobi polynomials as a basis of expansion to avoid the singularity at the origin which often appears when the polar coordinate is adopted. The novelty of the method is in expanding vector fields directly. In this paper, numerical examples based on the formulaton given by the first part paper are shown to discuss the usability of the spectral method. The examples include linear eigenvalue analyses and nonlinear time evolutions of shallow-water equation. Furthermore, a time integration method is proposed to deal with gravity wave components which makes nonlinear time integration difficult.
