A vertex-centered finite volume scheme preserving the discrete maximum principle for anisotropic and discontinuous diffusion equations

2022 ◽  
Vol 402 ◽  
pp. 113785
Author(s):  
Jiangfu Wang ◽  
Zhiqiang Sheng ◽  
Guangwei Yuan
Keyword(s):  
Maximum Principle ◽  
Finite Volume ◽  
Diffusion Equations ◽  
Discrete Maximum Principle ◽  
Finite Volume Scheme ◽  
Volume Scheme ◽  
Discontinuous Diffusion

TRANSIENT CONDUCTIVE–RADIATIVE HEAT TRANSFER: DISCRETE EXISTENCE AND UNIQUENESS FOR A FINITE VOLUME SCHEME

2005 ◽  
Vol 15 (02) ◽  
pp. 227-258 ◽  
Author(s):  
OLAF KLEIN ◽  
PETER PHILIP
Keyword(s):  
Maximum Principle ◽  
Finite Volume ◽  
Existence And Uniqueness ◽  
Radiative Heat ◽  
A Priori ◽  
Discrete Maximum Principle ◽  
Finite Volume Scheme ◽  
Nonlinear Operators ◽  
Volume Scheme ◽  
Three Space

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∞-L∞a priori bounds as well as a unique discrete solution to the finite volume scheme. We present results of numerical experiments to illustrate the effectiveness of the considered scheme.

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