Improving the Accuracy of a Finite-Volume Method for Computing Radiative Heat Transfer in Three-Dimensional Unstructured Meshes

Abstract eng:
In recent years, the Finite-Volume Method (FVM), being one of the most widely applied techniques in Computational Fluid Dynamics (CFD), has gained some popularity in solving radiative heat transfer problems. In order to avoid excessive amounts of false scattering and improve the accuracy of this method, two techniques, well established in CFD scientific field, were developed for a parallelized algorithm using FVM for the prediction of radiative heat transfer for absorbing, emitting and scattering gray media in hybrid unstructured grids. The first one considers a second order accurate spatial/temporal scheme for the calculation of radiative heat fluxes, while the second one uses a grid adaptation technique during the progress of the solution. The second order spatial scheme is based on the Monotonic Upstream Scheme for Conservation Laws (MUSCL) reconstruction of the radiative intensities, using additionally a slope limiter to control the total variation of the reconstructed field. A second order in time Runge-Kutta method is utilized for the solution of the time dependent Radiative Transfer Equation (RTE), avoiding the oscillations derived from the coupling of the higher order spatial scheme and the standard iterative solution of the non timedependent RTE. The second technique is the h-refinement, which enhances the algorithm with the capability of local grid adaptation, based on the splitting of the existing elements into new ones. Special treatment is needed for hybrid grids, due to the variety of element types (tetrahedral, prismatic and pyramidical) and their division alternatives. The algorithm is validated against benchmark test cases, proving its potential for improving the accuracy with the implementation of the afore-mentioned techniques.

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