Spectral collocation methods and polar coordinate singularities
Journal of Computational Physics
A spectral method for polar coordinates
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Accurate Navier-Stokes investigation of transitional and turbulent flows in a circular pipe
Journal of Computational Physics
An efficient spectral-projection method for the Navier--Stokes equations in cylindrical geometries
Journal of Computational Physics
Spectral solvers for spherical elliptic problems
Journal of Computational Physics
Spectral radial basis functions for full sphere computations
Journal of Computational Physics
An optimal Galerkin scheme to solve the kinematic dynamo eigenvalue problem in a full sphere
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.46 |
A spectral tau-method is proposed for solving vector field equations defined in polar coordinates. The method employs one-sided Jacobi polynomials as radial expansion functions and Fourier exponentials as azimuthal expansion functions. All the regularity requirements of the vector field at the origin and the physical boundary conditions at a circumferential boundary are exactly satisfied by adjusting the additional tau-coefficients of the radial expansion polynomials of the highest order. The proposed method is applied to linear and nonlinear-dispersive time evolution equations of hyperbolic-type describing internal Kelvin and Poincare waves in a shallow, stratified lake on a rotating plane.