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Comparison of different spatial/angular agglomeration multigrid schemes for radiative heat transfer computations

Lygidakis Georgios, Nikolos Ioannis

Πλήρης Εγγραφή

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Περίληψη

During the past decade the 3D unstructured grids have become an important tool for radiative heat transfer simulations, extending their applications to even more complex enclosures. Nevertheless, the corresponding solvers appear to be inferior in terms of efficiency, compared to those for structured meshes. One remedy to this shortcoming appears to be the agglomeration multigrid method, based on the solution of the numerical problem on successively coarser spatial and angular resolutions, derived from the initial finest ones through the fusion of their neighbouring control volumes and control angles respectively. Considering this state, the enhancement of an in-house academic solver with different spatial/angular agglomeration multigrid schemes to accelerate the finite-volume method for the prediction of radiative heat transfer, is reported in this study. The incorporated multigrid methods are based on the relaxation of radiative transfer equation with the FAS approach, considering though different types of sequentially coarser spatial and angular resolutions, as well as different V-cycle types. More specifically, a nested, a uniform and an alternate scheme were developed, while they were examined in conjunction with the V(1,0), V(1,1), V(2,0) and V(2,1) V-cycles types. To further accelerate the numerical solution, a combined FMG-FAS strategy was included, according to which the whole procedure begins from the coarsest discretization (spatial and angular) and as the number of iterations is increased the FAS extends to the finer resolutions, up to the initial finest one. The proposed numerical schemes were validated against a benchmark test case, considering radiative heat transfer through a strongly scattering medium in a cubic enclosure with highly reflecting surfaces. The obtained results reveal the superiority of the nested scheme along with the V(2,0)-cycle type strategy, while they highlight the significant contribution of the angular extension of the multigrid technique.

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