Investigation and Comparison of Different Methods for Solving Fluid Flow with Heat Transfer on Collocated and Staggered Grids in Natural Convection Problem

To solve governing equations in computational fluid dynamics, there are two kind of grids: collocated and staggered; the difference is where to store the velocity. There is much geometric complexity in staggered grid and implementing boundary conditions is more difficult than the collocated grid. When governing equations are solved on collocated grids, the problem of checkerboard prediction of pressure is encountered. Some interpolating methods are available to overcome this problem. Here, three basic methods including momentum interpolation, pressure gradient interpolation and smoothing pressure correction techniques are used and their results are compared with the results of staggered grid in the problem of natural convection in a square cavity. To solve fluid flow SIMPLE algorithm on the basis of finite volume method is used. Velocity, pressure and temperature profiles are showed and it is seen that the pressure gradient interpolation method has not totally removed the checkerboard pressure and just alleviated it. Momentum interpolation and smoothing pressure correction methods have not successed near the upper wall and velocity and pressure still have oscillations. On the other hand according to the results, convergance time and number of itrations required in the collocated grid is less than the staggered one. The staggered grid, in this problem, provided better result than the collocated and predict the pressure and velocity well. The Nusselt number in staggered grid is exactly the same as one of the standard solutions.