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Coarse Grid Projection (CGP) methodology is used to accelerate thecomputations of sets of decoupled nonlinear evolutionary and linear staticequations. In CGP, the linear equations are solved on a coarsened mesh comparedto the nonlinear equations, leading to a reduction in central processing unit(CPU) time. The accuracy of the CGP scheme has been assessed for theadvection-diffusion equation along with the pressure Poisson equation. Here weadd another decoupled equation to this set: the energy equation. In thisarticle, we examine the influence of CGP methodology for the first time onthermal fields. To this purpose, a semi-implicit-time-integrationunstructured-triangular-finite-element CGP version is selected. The CGPplatform is validated with two different test cases: first, natural convectioninduced by a hot circular cylinder located in the center of a cold squarecylinder, and second, the flow over a circular cylinder with the condition ofconstant cylinder temperature. Regarding the first test case, the CGP andnon-CGP simulations are carried out for different Rayleigh numbers. Thevelocity and temperature fields as well as the local Nusselt number on thesurface of the inner hot cylinder calculated by CGP reveal good agreement withthe non-CGP data. Concerning the second test case, the temperature variable isused as the passive scalar. For different Prandtl numbers, we compare the CGPand non-CGP configurations according to the Nusselt number and the spatialstructure of the scalar field obtained. The phase lag between the standard andCGP approaches is transmitted from the velocity field into the temperaturefiled, and thus into the local transient Nusselt number. For one and two levelsof coarsening, the numerical predictions by CGP for the unsteady local heattransfer coefficients agree well with available data in the literature.

A coarse grid projection method for accelerating heat transfer computations