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Summary: INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
Int. J. Numer. Meth. Engng 2000; 00:16 Prepared using nmeauth.cls [Version: 2002/09/18 v2.02]
P1-conservative solution interpolation on unstructured triangular
meshes
F. Alauzet1, and M. Mehrenberger2
1INRIA, Projet Gamma, Domaine de Voluceau, Rocquencourt, BP 105, 78153 Le Chesnay Cedex, France.
2IRMA, Universit´e Louis-Pasteur, UMR CNRS 7501, 7 rue Ren´e Descartes, 67084 Strasbourg, France.
SUMMARY
This document presents an interpolation operator on unstructured triangular meshes that verifies
the properties of mass conservation, P1
-exactness (order 2) and maximum principle. This operator is
important for the resolution of the conservation laws in CFD by means of mesh adaptation methods as
the conservation properties is not verified throughout the computation. Indeed, the mass preservation
can be crucial for the simulation accuracy. The conservation properties is achieved by local mesh
intersection and quadrature formulae. Derivatives reconstruction are used to obtain an order 2 method.
Algorithmically, our goal is to design a method which is robust and efficient. The robustness is
mandatory to apply the operator to highly anisotropic meshes. The efficiency will permit the extension
of the method to dimension three. Several numerical examples are presented to illustrate the efficiency
of the approach. Copyright c 2000 John Wiley & Sons, Ltd.
key words: Solution interpolation, conservative interpolation, localization algorithm, unstructured
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