A COUPLED PREDICTION SCHEME FOR SOLVING THE NAVIER–STOKES AND CONVECTION-DIFFUSION EQUATIONS

This paper presents a new algorithm for the numerical solution of the Navier–Stokes equations coupled with the convection-diffusion equation. After establishing convergence of the semi-discrete formulation at each time step, we introduce a new iterative scheme based on a projection method called the coupled prediction scheme. We show that even though the predicted temperature is advected by a velocity prediction which is not necessarily divergence free, the theoretical time accuracy of the global scheme is conserved. From a numerical point of view, this new approach gives a faster and more efficient algorithm compared to the usual fixed-point approaches.