Numerical experiments with the pseudospectral method in spherical coordinates

Residual Potential Method in Spherical Coordinates and Related Approximations

The Residual Potential Method, introduced by Geers [ l ] , appears to be a very promising technique in the solution of sol id-f luid interaction problems. The theoretical development of the method in cylindrical coordinates was presented in [1,2]. In [3], Geers presents some numerical results obtained using the Residual Potential Method in spherical coordinates; however, the theoretical treatme...

Incorporating directivity in the Pseudospectral time-domain method by using spherical harmonics

A technique to incorporate directivity in the Pseudospectral time-domain method (PSTD) for auralization purposes is presented. The Pseudospectral time-domain method is a numerical method for solving the wave equation that requires only two spatial points per wavelength, making it more efficient compared to other wave based methods. The effect of source directivity as well as the head-related di...

A 3D pseudospectral method for cylindrical coordinates. Application to the simulations of rotating cavity flows

The present work proposes a collocation spectral method for solving the three-dimensional Navier-Stokes equations using cylindrical coordinates. The whole diameter −R ≤ r ≤ R is discretized with an even number of radial Gauss-Lobatto collocation points and an angular shift is introduced in the Fourier transform that avoid pole and parity conditions usually required. The method keeps the spectra...

The Laplacian in Spherical Polar Coordinates

A Hybrid Radial Basis Function-Pseudospectral Method for Thermal Convection in a 3-D Spherical Shell

A novel hybrid spectral method that combines radial basis function (RBF) and Chebyshev pseudospectral (PS) methods in a “2+1” approach is presented for numerically simulating thermal convection in a 3D spherical shell. This is the first study to apply RBFs to a full 3D physical model in spherical geometry. In addition to being spectrally accurate, RBFs are not defined in terms of any surface ba...