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A Novel Finite Volume Scheme with Geometric Average Method for Radiative Heat Transfer Problems

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Author: Cunyun Nie, Haiyuan Yu

Abstract: We construct a novel finite volume scheme by innovatively introducing the weighted geometric average method for solving three multi-material radiative heat transfer problems, and compare it with the weighted arithmetic and harmonic average methods, respectively. We also put forward the effect of the convexity of nonlinear diffusion functions. Then, we present a cylinder symmetric finite volume element (SFVE) scheme for the three-dimensional problem by transferring it to a two-dimensional one with the axis symmetry. Numerical experiments reveal that the convergent order is less than two, and numerical stimulations are valid and rational, and confirm that the new scheme is agreeable for solving radiative heat transfer problems.

Keywords: Finite volume scheme ; Weighted geometric average method ; Radiative heat transfer problems; Convexity of diffusion functions.

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