A new finite element method for Navier-Stokes equations coupled with a temperature equation

An algorithm for the numerical solution of coupled Navier-Stokes and temperature equations is developed and demonstrated. The finite-element method described by Benque et al. (1980), Ibler (1981), and Bristeau et al. (1978) is reviewed: the Boussinesq approximation is applied, and the resulting system is decomposed into advection, temperature-diffusion, and Stokes problems which are solved successively. The characteristic-curve approach to the critical advection problem is modified by applying a weak formulation, as suggested by Benque and Ronat (1981). Sample test results show that the convergence and accuracy of the method are improved by the weak formulation. An application to the calculation of flow and velocity fields in the closed cavity of an industrial fast-breeder reactor is illustrated.