P1‐conservative solution interpolation on unstructured triangular meshes

Abstract

AbstractThis paper 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 computational fluid dynamics by means of mesh adaptation methods as the conservation properties are not verified throughout the computation. Indeed, the mass preservation can be crucial for the simulation accuracy. The conservation properties are 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 that 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 3. Several numerical examples are presented to illustrate the efficiency of the approach. Copyright © 2010 John Wiley & Sons, Ltd.