A coarse grid projection method for accelerating heat transfer computations

TL;DR

This paper introduces a Coarse Grid Projection (CGP) method to accelerate heat transfer simulations by solving linear equations on coarser meshes, demonstrating good accuracy and significant computational savings in natural convection and heat transfer cases.

Contribution

The study extends the CGP methodology to thermal fields, validating its effectiveness for unsteady heat transfer problems with unstructured finite element meshes.

Findings

CGP achieves good agreement with non-CGP results for velocity and temperature fields.

The phase lag in temperature and Nusselt number predictions is minimal with one or two levels of coarsening.

CGP significantly reduces CPU time while maintaining accuracy in heat transfer simulations.

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 (CPU) time. The accuracy of the CGP scheme 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. To this purpose, a semi-implicit-time-integration unstructured-triangular-finite-element CGP version is selected. The CGP platform 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. Regarding the first test case, the CGP and non-CGP simulations are carried out for different Rayleigh numbers. 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. Concerning the second test case, the temperature variable is used as the passive scalar. For different Prandtl numbers, we compare the CGP and non-CGP configurations according to the Nusselt number and the spatial structure of the scalar field obtained. The phase lag between the standard and CGP approaches is transmitted from the velocity field into the temperature filed, and thus into the local transient Nusselt number. For one and two levels of coarsening, the numerical predictions by CGP for the unsteady local heat transfer coefficients agree well with available data in the literature.