Improved finitedifference methods based on a critical evaluation of the approximation errors
Abstract
When finitedifference methods are used to solve the benchmark problem of natural convection in a square cavity, a very fine grid is required to obtain predictions that are accurate to 12%. The derivation of the finitedifference equations requires the introduction of many approximations; this study systematically evaluates these approximations to establish which are mainly responsible for the finegrid requirement. The poorest approximations are then improved one by one, resulting in a scheme that yields highly accurate predictions using a relatively coarse grid. The method of evaluating the accuracy of the approximations, the improved approximations themselves, and the solution method used all contain novel features. Storage and computing time requirements for a new sparse matrix solver, which was used in the current study to simultaneously solve for stream function and vorticity, are presented.
 Publication:

Numerical Heat Transfer
 Pub Date:
 June 1979
 Bibcode:
 1979NumHT...2..139W
 Keywords:

 Convective Heat Transfer;
 Error Analysis;
 Finite Difference Theory;
 Free Convection;
 Diffusion;
 Rayleigh Number;
 Stream Functions (Fluids);
 Vorticity;
 Fluid Mechanics and Heat Transfer