A control volume finite element method for radiative heat transfer problems in irregular geometries

摘要

The purpose of this paper is to present a Control Volume Finite Element Method (CVFEM) for the solution of the Radiative Transfer Equation (RTE). The objectives of the research were to: (1) implement several interpolation schemes to decide whichones should be retained in the context of a coupling of the CVFEM with a comprehensive numerical method for the predictions of turbulent combustion. Three spatial schemes are presented in the paper and two are compared. Two angular discretizations arealso presented; and (2) provide an assessment of the CVFEM which incorporates these interpolation schemes in selected irregular geometries.The upwind (step) scheme was found to yield the best accuracy/cost ratio when spatial interpolation was concerned. In terms of accuracy, the upwind scheme always produced results that were within 2% of those obtained with an exponential scheme. Whenangular interpolation was considered, the analytical integration of the dot productΩ·n over solid angles was retained along with the azimuthal discretization.The results obtained with the CYFEM compare well with those found in the literature (from exact or approximate methods) for the same test cases. The key feature of the CVFEM, when compared with a Finite Volume Method, is that it is based on triangulartwo-dimensional and tetrahedral three-dimensional elements which are more amenable for the discretization of complex irregular geometries.