Investigation of Instabilities Arising with Non-Orthogonal Meshes Used in Cell Centred Elliptic Finite Volume Computations

Abstract

Transport processes in most engineering applications occur within complex geometries. In engineering practice, users rely heavily on commercial mesh generators, which can produce unacceptably skewed meshes. Convergence behaviour and absolute accuracy in finite volume CFD computations depend critically on mesh quality and in particular, mesh orthogonality. In this paper, the effects of non-orthogonality on the main component algorithms of pressure-correction type cell-centred finite volume codes are closely examined, systematically adjusted and tested. The modifications to the pressure correction method applied to cases using non-orthogonal grids are described. The SIMPLEC algorithm [1], with the aid of an inverse square distance interpolation, is used for overcoming instabilities arising in a few problematic cells. Solution instabilities which arise when using hexahedral or tetrahedral meshes are attenuated by bounding the maximum and minimum values of solved variables within a physically realistic range. The consistency and accuracy of the proposed method are compared with benchmark solutions [2] available in the literature. The usefulness of the present method is demonstrated by its application to illustrative problems for which comparison data are available.