A Coupled Prediction Scheme for Solving the Navier-Stokes and Convection-Diffusion Equations

Abstract. 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 Coupled Prediction Scheme (CPS). 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.