Transient conductive-radiative heat transfer: Discrete existence and uniqueness for a finite volume scheme
- Klein, Olaf
- Philip, Peter
2010 Mathematics Subject Classification
- 45K05 65M99 35K05 35K55 65N22 47H10 80A20
- Integro-partial differential equations. Finite volume method. Nonlinear parabolic PDEs. Integral operators. Nonlocal interface conditions. Diffuse-gray radiation. Maximum principle
This article presents a 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. Proving a maximum principle as well as existence and uniqueness for roots to a class of discrete nonlinear operators that can be decomposed into a scalar-dependent sufficiently increasing part and a benign rest, we establish a discrete maximum principle for the finite volume scheme, yielding discrete $L^infty$-$L^infty$ a priori bounds as well as a unique discrete solution to the finite volume scheme.
- Mathematical Models and Methods in Applied Sciences, 15 (2005), 227-258