Numerical Method for Computing Nonlinear, Time Dependent, Buoyant Circulation of Air in Rooms

A method is described which solves the dynamic equations for air circulation at Grashof numbers that are in the range of environmental temperatures of rooms. Previous two-dimensional computation techniques were limited to G ≈ 10
⁵
but environmental conditions require G ≈ 10
¹²
. The higher Grashof numbers become calculable through the design of a mixed system of nonlinear difference equations which has purely leading-phase-error properties. In addition provision is made for nonlinear stability by explicitly programming cross derivative terms in lieu of employing “time splitting.” The isotropic behavior achieved through time splitting is retained by the system of difference equations. Details of the required algorithms are included.