The accuracy of the finite difference computations of recirculating free convective flows

The determination of natural flow and heat transfer in a square, two dimensional cavity, whose vertical boundaries are held at different but constant temperatures and whose horizontal walls are perfectly insulated, was used to assess numerical solutions of nonlinear elliptic differential equations. With a resonable grid density, the reduction of the diverging effects ascribed to standard finite difference solution procedures requires the means of their quantitative assessment. This can be achieved using the false transient method, whose convergence behavior makes it one of the most efficient algorithms to obtain solutions of the coupled system of elliptic equations.