The Lid Driven Cavity Flow is most probably one of the most studied fluid problem in computational fluid dynamics field. Due to the simplicity of the cavity geometry, applying a numerical method on this flow problem in terms of coding is quite easy and straight forward. Despite its simple geometry, the driven cavity flow retains a rich fluid flow physics manifested by multiple counter rotating recirculating regions on the corners of the cavity depending on the Reynolds number.
In this study, Erturk et. al. have have presented a new, efficient and stable numerical method for the solution of streamfunction and vorticity equations. They also have presented steady solutions of driven cavity flow at very high Reynolds numbers using very fine grid mesh.
In the following web pages, you will find detailed information about the numerical method Erturk et. al. have presented and its application to driven cavity flow, tabulated datas and figures and more.
In the following study, E. Erturk have analysed the nature of the cavity flow at high Reynolds numbers. In the literature, while some studies claims that the flow in a driven cavity is not steady at a Reynolds number and present unsteady solutions, some other studies present steady solutions at even higher Reynolds numbers. There is a controversy on whether the flow in a cavity is steady or not at high Reynolds numbers. E. Erturk have analysed the cavity flow problem in terms of physical, mathematical and also numerical aspects with a brief literature survey on experimental, analytical and also numerical studies on cavity flow and then presented very fine grid numerical solutions of driven cavity flow at high Reynolds numbers obtained by solving the governing equations simply with Successive Over Relaxation (SOR) method.
In the following study, Erturk and Gokcol have presented a new fourth order compact (HOC) formulation. The main difference of this formulation from the ones found in the literature is the way that the final form of the equations are written. The main advantage of this formulation is that, any iterative numerical method used for Navier-Stokes equations, can be applied to this HOC formulation. Moreover if someone already have a second order accurate (O Dx2) code for the solution of steady 2-D incompressible Navier-Stokes equations, they can easily convert their existing code to fourth order accuracy (O Dx4) by just adding some coefficients into their existing code. Using this new compact formulation, the steady 2-D incompressible driven cavity flow is solved up to Reynolds number of 20,000 with using a very fine grid mesh.
In the following study, Erturk and Gokcol have analysed the steady 2-D steady incompressible flow inside a lid driven triangular cavity. The triangular cavity flow is solved using Successive Over Relaxation (SOR) method using a fine grid mesh at high Reynolds numbers and accurate solutions are presented.
In the literature, there are not much benchmark problems with non-orthogonal grids for numerical methods to compare solutions with each other. The skewed cavity problem can be a perfect test case for body fitted non-orthogonal grids and yet it is as simple as the cavity flow in terms of programming point of view. The test case is similar to driven cavity flow but the geometry is a parallelogram rather than a square. In this test case, the skewness of the geometry can be easily changed by changing the skew angle (a). In the following study Erturk and Dursun have presented thenumerical solutions of the driven skewed cavity flow problem for skew angles 15° £ a £ 165°, with body fitted non-orthogonal skewed grid mesh of (513×513). By changing the skew angle to extreme values it is possible to test numerical methods for grid skewness in terms of stability, efficiency and accuracy. The numerical solutions of the flow in a skewed cavity will be presented for Reynolds number of 100 and 1000 for a wide variety of skew angles ranging between a=15° and a=165° with Da=15° increments.