Method for predicting natural convection in closed vessels

A numerical technique is presented which predicts the transient, two-dimensional, laminar natural convection within closed vessels. The finite difference analogs of the Navier-Stokes and the thermal energy equations are solved in an Eulerian stream function-vorticity framework. The parabolic transport equations (vorticity and thermal energy) are solved by a method, which is called a hybrid, that combines desirable features from both explicit and Alternating Direction Implicit methods. By treating the advection terms explicitly and the diffusion terms as in an ADI scheme, a very efficient solution algorithm can be employed. Conservative windward differencing, which accounts for the direction of the fluid motion, is used for the nonlinear advection terms. The elliptic stream function equation is solved by an iterative ADI method.