P1-conservative solution interpolation on unstructured triangular meshes

Frédéric Alauzet 1, * Michel Mehrenberger 2, 3
* Corresponding author
2 CALVI - Scientific computation and visualization
IRMA - Institut de Recherche Mathématique Avancée, LSIIT - Laboratoire des Sciences de l'Image, de l'Informatique et de la Télédétection, Inria Nancy - Grand Est, IECL - Institut Élie Cartan de Lorraine
Abstract : 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.
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Frédéric Alauzet, Michel Mehrenberger. P1-conservative solution interpolation on unstructured triangular meshes. International Journal for Numerical Methods in Engineering, Wiley, 2010, pp.48. ⟨10.1002/nme.2951⟩. ⟨inria-00354509⟩

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