Numerical Calculation of Transient Response of Natural Convection in a Cavity

This paper presents the effect of some kinds of methods for the numerical solution of natural convection in a cavity at Pr=0.7 and Gr=10^6 on the transient responses and converged values of stream function and temperature. The governing equation was discretized by explicit, Crank-Nicolson and fully implicit methods. ADI, Line by Line and Incomplete LU decomposition conjugate residual (CR) algorithms were used to solve the discretization equation by fully implicit method. Further, the effect of time interval and grid size on the results was also investigated. It was concluded that all solution methods agree as time interval and grid size approach to 0. ADI is the most reasonable method in this study, and CR is most stable in fully implicit methods for time interval