A general formulation of the spherical harmonics (PN) methods was developed recently to expand the method to high orders of PN. The set of N(N + 1)/2 three-dimensional second-order elliptic PDEs formulation and their Marshak boundary conditions for arbitrary geometries are implemented in the openfoam finite volume based cfd software. The results are verified for four cases, including a 1D slab, a 2D square enclosure, a 3D cylindrical enclosure, and an axisymmetric flame. All cases have strongly varying radiative properties, and the results are compared with exact solutions and solutions from the photon Monte Carlo method (PMC).
Implementation of High-Order Spherical Harmonics Methods for Radiative Heat Transfer on openfoam
Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received August 19, 2014; final manuscript received December 29, 2014; published online February 10, 2015. Assoc. Editor: Zhuomin Zhang.
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Ge, W., Marquez, R., Modest, M. F., and Roy, S. P. (May 1, 2015). "Implementation of High-Order Spherical Harmonics Methods for Radiative Heat Transfer on openfoam." ASME. J. Heat Transfer. May 2015; 137(5): 052701. https://doi.org/10.1115/1.4029546
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