This is a scientific web page about the two-dimensional steady incompressible flow in a driven cavity. The steady incompressible 2-D Navier-Stokes equations are solved numerically. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. This is a scientific web page about the two-dimensional steady incompressible flow in a driven cavity. The steady incompressible 2-D Navier-Stokes equations are solved numerically. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations. Driven cavity flow, numerical methods, steady incompressible flow, finite difference, Navier Stokes equations.

www.cavityflow.com Skewed Cavity Flow

 

In the literature, it is possible to find many numerical methods proposed for the solution of the steady incompressible N-S equations. These numerical schemes are often tested on several benchmark test cases in terms of their stability, accuracy as well as efficiency. Among several benchmark test cases for steady incompressible flow solvers, the driven cavity flow is a very well known and commonly used benchmark problem. The reasons why the driven cavity flow is so popular may be the simplicity of the geometry. Even though the geometry is simple and easy to apply in programming point of view, the cavity flow has all essential flow physics with counter rotating recirculating regions at the corners of the cavity. Because of its simple geometry, the cavity flow is best solved in Cartesian coordinates with Cartesian grid mesh. Most of the benchmark test cases found in the literature have orthogonal geometries therefore they are best solved in orthogonal grid mesh. Often times the real life flow problems have much more complex geometries than that of the driven cavity flow. In most cases, researchers have to deal with non-orthogonal geometries with non-orthogonal grid mesh. In a non-orthogonal grid mesh, when the governing equations are formulated in general curvilinear coordinates, cross derivative terms appear in the equations. Depending on the skewness of the grid mesh, these cross derivative terms can be very significant and can effect the numerical stability as well as the accuracy of the numerical method used for the solution. Even though, the driven cavity flow benchmark problem serve for comparison between numerical methods, the flow is far from simulating the real life fluid problems with complex geometries and non-orthogonal grid mesh. The numerical performances of numerical methods on orthogonal grids may or may not be the same on non-orthogonal grids.

Unfortunately, there are not much benchmark problems with non-orthogonal grids for numerical methods to compare solutions with each other. Demirdzic et al. have introduced the driven skewed cavity flow as a test case for non-orthogonal grids. 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). 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 main motivation of this study is then to reintroduce the skewed cavity flow problem with a wide range of skew angle (a) and present detailed tabulated results for future references. The skewed cavity flow problem will be solved for skew angles 15 a 165 using a fine grid mesh (513×513).

In this study, the numerical solutions of the driven skewed cavity flow problem, with body fitted non-orthogonal skewed grid mesh, will be presented. By changing the skew angle to extreme values we would be able to test the 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.

In the following web pages, you will find detailed information about the skewed cavity flow, figures and tabulated datas and more.

 

 

www.cavityflow.com