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SUMMARYIn this paper, a segregated finite element scheme for the solution of the incompressible Navier-Stokes equations is proposed which is simpler in form than previously reported formulations. A pressure correction equation is derived from the momentum and continuity equations, and equal-order interpolation is used for both the velocity components and pressure. Algorithms such as this have been known to lead to checkerboard pressure oscillations; however, the pressure correction equation of this scheme should not produce these oscillations. The method is applied to several laminar flow situations, and details of the methods used to achieve converged solutions are given.

IntroductionMost techniques for automatic mesh generation produce a mesh for the whole computational domain. This requires that a full description of the mesh boundaries is provided. In many engineering situations such a description may not be available. Also, in these cases, a change to the geometry in one area of the domain requires that a completely new mesh be built. If Boolean operations can be carried out on parts of a mesh, for example to join two meshes together or to impose an additional surface mesh on a volume mesh, then savings in mesh generation time should be achievable.In many areas of engineering, but especially in computational fluid dynamics (CFD) and three-dimensional structural analysis, finite element or similar methods are becoming widely used. Ideally, analysts must be able to use numerical methods quickly and easily to predict the performance of a device or component. For computational analyses to interact with the design process, the time taken from deciding to change the geometry of a design to the completion of the mesh and the addition of the associated analysis parameters must be about one day, or less if possible, for each analysis. Thus the preparation of the finite element mesh itself cannot be allowed to last more than a few hours. For many complex geometries, however, this turnaround time might be several months, as new computational models of the geometry and then the mesh have to be created. Recent work[1] using commercial solid modelling and finite element meshing capabilities[2] has shown that the creation of the necessary geometrical model and the generation of a mesh suitable for a fluid dynamics analysis of the port and cylinder of a piston engine, with an inlet valve, can still take between five and ten days. Hence all computer-based analysis techniques are restricted in their use by the time required to generate a suitable computational model [3].As model creation is such a time consuming process a large amount of research has been carried out in the area of the automation of mesh generation, as reviewed by George [4]. Starting at the lowest level meshes can be built