A Coarse Grid Projection Method for Accelerating Free and Forced Convection Heat Transfer Computations

Abstract

Coarse grid projection (CGP) methodology is used to accelerate the computations of sets of decoupled nonlinear evolutionary and linear static equations. In CGP, the linear equations are solved on a coarsened mesh compared to the nonlinear equations, leading to a reduction in central processing unit time. The accuracy of CGP has been assessed for the advection–diffusion equation along with the pressure Poisson equation. Here we add another decoupled equation to this set: the energy equation. In this article, we examine the influence of CGP methodology for the first time on thermal fields. CGP is validated with two different test cases: first, natural convection induced by a hot circular cylinder located in the center of a cold square cylinder, and second, the flow over a circular cylinder with the condition of constant cylinder temperature. For the first test case, the velocity and temperature fields as well as the local Nusselt number on the surface of the inner hot cylinder calculated by CGP reveal good agreement with the non-CGP data. For the second test case, the Nusselt number and the spatial structure of the temperature field obtained by CGP are in a good agreement with the non-CGP data for different Prandtl numbers. In general, CGP is able to maintain excellent to reasonable accuracy of the temperature filed, while achieves speedup factors ranged approximately from 1.7 to 3.7.