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Adaptivity for Finite Volume Methods on Unstructured Meshes

Published by the American Society of Agricultural and Biological Engineers, St. Joseph, Michigan www.asabe.org

Citation:  Paper number  023022,  2002 ASAE Annual Meeting . (doi: 10.13031/2013.9614) @2002
Authors:   Marcio Arêdes Martins, Leandro Soares Oliveira
Keywords:   unstructured triangular meshes; adaptive refinement; heat transfer

This paper presents a new and reliable error estimate and adaptive procedure for finite volume methods on unstructured meshes. The error estimate belongs to the class of truncation error estimates and its major feature is that its formulation results in an algebraic discrete form. An adaptive time stepping procedure is also employed in order to solve nonlinear parabolic problem. Using the proposed methodology, a cooling problem is solved adaptively in time and space, and its selection is justified by the fact that high temperature gradients occur in specific regions of the computational domain. The simulation results demonstrate that the proposed error estimate and adaptive methodology is suitable and reliable for nonlinear parabolic problems.

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