Topical Problems of Fluid Mechanics


Institute of Thermomechanics AS CR, v.v.i.	CTU in Prague Faculty of Mech. Engineering Dept. Tech. Mathematics	MIO Université du Sud Toulon Var - AMU - CNRS - IRD	Czech Pilot centre ERCOFTAC

Nested Adaptive Vertex-Centred Finite Volume Methods for Diffusion Problems
T. Ghoudi, I. Kissami
Abstract:
The goal of this paper is to develop a new technique of mesh adaptation for ?nite volume solution of di?usion problems. Vertex-centered ?nite volume discretization is used for the elliptic operator and error estimates in the energy norm are considered for adaptation of meshes. In contrast to the conventional approach in which the di?usion equation is solved after each error estimation, the current method allows for multiple adaptations of meshes within a single error estimation. This nested adaptive ?nite volume method requires only treatment of conformity in meshes for multiple adaptations which is dealt with using the new bisection procedure. For a prescribed accuracy, the new method o?ers a substantial reduction of computational cost compared to standard adaptive ?nite volume methods.
Keywords:
Vertex-centered ?nite volume, Di?usion equations, Error estimates, Mesh adaptation, Adapt solver, Nested re?nement, Newest-vertex-bissection

Fulltext: PDF DOI: https://doi.org/10.14311/TPFM.2018.014

In Proceedings Topical Problems of Fluid Mechanics 2018, Prague, 2018 Edited by David Šimurda and Tomáš Bodnár, pp. 105-114 ISBN 978-80-87012-65-9 (Print) ISSN 2336-5781 (Print)