| Abstract: | A fourth-order method, without using extrapolation, is developed for the steady-state solution of a non-linear system of three simultaneous partial differential equations for the flow of a fluid in a heated closed cavity. The method is a finite difference method which has converged for all Rayleigh numbers Ra of physical interest and all Prandtl numbers Pr attempted. The results are presented and compared with some of the accurate results available in de Vahl Davis and Jones, Shay and Schultz, and Dennis and Hudson. The method used to develop the fourth-order method presented in this paper can be used to develop high-order methods for other partial differential equations. The method was developed to be stable without using the upwinding technique. |
