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Analysis of the Non-Orthogonality Correction of Finite Volume Discretization on Unstructured Meshes

This paper is available in a repository.
This paper is available in a repository.

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Abstract

Computational fluid mechanics with finite volume method needs high-quality computational meshes that can be structured or not. When properly constructed, structured meshes provide several advantages over unstructured ones as, for instance, (i) higher metrics quality, (ii) a corresponding matrix of fixed bandwidth and (iii) a straightforward numerical implementation due to a simple and effective variable indexation. However, their lower adaptability to complex geometries can be considered as their main drawback. On the other hand, unstructured meshes are more flexible with respect to geometrical topology, at the expense of some loss regarding the advantages cited above. As a matter of fact, the non-collinearity between the center-to-center vector of adjacent cells and the normal vector of the face that connects these cells makes difficult the approximation of the gradient of a field at the face. A common procedure to overcome this problem uses a non-orthogonality correction. In this work, a methodology to compute to compute this correction taking account the mesh skewness was implemented and tested. It aims to obtain an iterative method that preserves second order of accuracy for the local approximation of the variables and their gradients on the mesh. Two test cases were addressed and the results compared to that obtained via the CFD softwares OpenFOAM R and ANSYS Fluent R .