Fully Implicit Finite Volume Scheme for Transient Conductive-Radiative Heat Transfer: Discrete Existence, Uniqueness, Maximum Principle

Peter Philip

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arXiv · 1407.1757

Fully Implicit Finite Volume Scheme for Transient Conductive-Radiative Heat Transfer: Discrete Existence, Uniqueness, Maximum Principle

Peter Philip

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Abstract

This article studies a fully implicit finite volume scheme for transient nonlinear heat transport equations coupled by nonlocal interface conditions modeling diffuse-gray radiation between the surfaces of (both open and closed) cavities. The model is considered in three space dimensions; modifications for the axisymmetric case are indicated. Extending previous results, where a similar, but not fully implicit, finite volume scheme was considered, a discrete maximum principle is established, yielding discrete $L^\infty$-$L^\infty$ a priori bounds as well as a unique discrete solution to the finite volume scheme.

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Peter Philip. 2014-07-04. Fully Implicit Finite Volume Scheme for Transient Conductive-Radiative Heat Transfer: Discrete Existence, Uniqueness, Maximum Principle. https://arxiv.org/abs/1407.1757

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