Comparison of measured and predicted thermal mixing tests using improved finite difference technique

Abstract

The numerical diffusion introduced by the use of upwind formulations in the finite difference solution of the flow and energy equations for thermal mixing problems was examined. The relative importance of numerical diffusion in the flow equations, compared to its effect on the energy equation was demonstrated. The flow field equations were solved using both first order accurate upwind, and second order accurate differencing schemes. The energy equation was treated using the conventional upwind and a mass weighted skew upwind scheme. Results presented for a simple test case showed that, for thermal mixing problems, the numerical diffusion was most significant in the energy equation. The numerical diffusion effect in the flow field equations was much less significant. A comparison of predictions using the skew upwind and the conventional upwind with experimental data from a two dimensional thermal mixing test are presented. The use of the skew upwind scheme showed a significant improvement in the accuracy of the steady state predicted temperatures.