Spectral methods for multidimensional diffusion problems
Abstract
The numerical calculation of diffusion processes in complex geometries in multidimensions is of current interest in many applications involving the solution of the coupled equations of radiation transport or thermal conduction, as well as in applications involving unstable hydrodynamic flows. The application of pseudospectral techniques to the implicit solution of the diffusion equation in a distorted twodimensional grid for both linear and nonlinear problems is considered. The implicit pseudospectral equations on a m x n mesh result in a full P x P matrix (where P equals the square of the product of m and n) which can be inverted by the methods introduced. The examples given illustrate the success of pseudospectral techniques applied to the solution of these problems. The computational and memory requirements for machine implementation of pseudospectral techniques for a given accuracy are shown to be superior to those standard finite difference techniques.
 Publication:

Advances in Computer Methods for Partial Differential Equations  III
 Pub Date:
 1979
 Bibcode:
 1979acmp.proc..417M
 Keywords:

 Computational Fluid Dynamics;
 Computer Programs;
 Diffusion Theory;
 Finite Difference Theory;
 Partial Differential Equations;
 Spectral Methods;
 Thermal Diffusion;
 Conductive Heat Transfer;
 Differential Geometry;
 Flow Stability;
 Nonlinear Equations;
 Radiative Heat Transfer;
 Fluid Mechanics and Heat Transfer