Calculation of natural convection within a heated enclosure using the method of second moments

The method of second moments is a quasi-Lagrangian, explicit numerical method which calculates the advection of a variable without numerical dispersion, damping, or phase error. The technique is particularly attractive for calculating temperatures and other scalar transport equations, and has been used primarily for environmental modeling. Application of the technique to free convection studies indicates that the method can also be adapted to calculate the transport of vorticity for low to moderate Rayleigh numbers. In fact, transport equations of the form similar to the vorticity equation can be solved with the technique, providing the equation can be quasi-linearized. Use of the technique for calculating highly nonlinear equations (e.g., shock fronts) can become troublesome. Instability can result in nonlinear self advection problems as a result of high wave number amplification and nonconservation of the integral relations.