The Benard problem: A comparison of finite difference and spectral collocation eigen value solutions
Abstract
The application of spectral methods, using a Chebyshev collocation scheme, to solve hydrodynamic stability problems is demonstrated on the Benard problem. Implementation of the Chebyshev collocation formulation is described. The performance of the spectral scheme is compared with that of a 2nd order finite difference scheme. An exact solution to the MarangoniBenard problem is used to evaluate the performance of both schemes. The error of the spectral scheme is at least seven orders of magnitude smaller than finite difference error for a grid resolution of N = 15 (number of points used). The performance of the spectral formulation far exceeded the performance of the finite difference formulation for this problem. The spectral scheme required only slightly more effort to set up than the 2nd order finite difference scheme. This suggests that the spectral scheme may actually be faster to implement than higher order finite difference schemes.
 Publication:

6th Annual Thermal and Fluids Analysis Workshop
 Pub Date:
 January 1995
 Bibcode:
 1995tfla.work..275S
 Keywords:

 Benard Cells;
 Chebyshev Approximation;
 Collocation;
 Finite Difference Theory;
 Flow Stability;
 Fluid Flow;
 Spectral Methods;
 Computational Grids;
 Difference Equations;
 Eigenvalues;
 Hydrodynamics;
 Fluid Mechanics and Heat Transfer