A PRESSURE CORRECTION METHOD FOR UNSTRUCTURED MESHES WITH ARBITRARY CONTROL VOLUMES

Abstract

SUMMARY A pressure correction procedure for general unstructured meshes is presented. It is a cell-centred, collocated finite volume method and the pressure-velocity coupling is treated using SIMPLEC. The cells can have an arbitrary number of grid points (cell vertices). In the present study the number of faces on the cells varies between three and six. The discretized equations are solved using either a symmetric Gauss-Seidel solver or a conjugate gradient solver with a preconditioner. The method is applied to three two-dimensional test cases in which the flow is incompressible and laminar. The extension to three dimensions as well as to turbulent flow using transport models is straightforward. It can also be extended to handle compressible flow. Computational fluid dynamics (CFD) is now used frequently in industry. When using structured methods, however, the grid generation for complex geometries remains a major task. The generation of grids for complex geometries usually requires considerably more time in terms of manpower than the actual flow field computations. In order to become a useful tool, CFD must be capable of handling complex flow in complex geometries. The lack of generality in treating complex geometries is one of the major reasons why CFD has not become a powerful tool in everyday engineering. The use of unstructured methods facilitates the grid generation enormously and there exist automatic methods for triangulation of arbitrary geometries.' For Navier-Stokes computations a structured mesh near the boundaries can be matched with an internal or external (automatically generated) triangulated region.2 Local mesh refinement, either adaptive or fixed, is another advantage of unstructured methods. Quadnlaterals are easily split into smaller quadrilaterals or into triangles, while triangles are readily split into smaller triangles. If, as in the present study, cell-centred methods are adopted, 'hanging' grid points cause no problems, as a cell can have an arbitrary number of grid points (cell vertices). There exist a number of papers using unstructured finite volume flow solvers for compressible aerodynamics2-10 in which algebraic and transport turbulence models have also been used. However, unstructured methods employing pressure correction techniques are not very common. There are a limited number of papers in the literature. Lonsdale and Webster used a staggered grid arrangement and presented three-dimensional, turbulent flow calculations. A number of papers were presented in the 1980s on CVFEMs (control-volume-based finite element