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 High Order Compact Scheme
And Driven Cavity Flow

 

High Order Compact (HOC) formulations are becoming more popular in Computational Fluid Dynamics (CFD) field of study. Compact formulations provide more accurate solutions in a compact stencil. High order compact schemes provide fourth order spatial accuracy in a 3×3 stencil. Even though, a high order compact (HOC) formulation have advantages in many ways, one disadvantage may be that there is not many different iterative schemes available for this type of formulation. When a HOC formulation is used the resulting equations are either solved directly or with a point or sometimes with a line iterative solver. A direct solver requires a lot of computer resources (ie. RAM, CPU time) especially when large number of grids are used. Point or line iterations are more preferred.

In the literature, it is possible to find numerous different type of iterative numerical methods for the Navier-Stokes equations. These numerical methods could not be easily used in HOC schemes because of the final form of the HOC formulations found in the literature. It would be very useful if any iterative numerical methods described in books and papers for Navier-Stokes equations could be applied to high order compact (HOC) formulations.

In this study, you will find 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, we have solved the steady 2-D incompressible driven cavity flow at very high Reynolds numbers using a very fine grid mesh to demonstrate the efficiency of this new formulation.

In the following web pages, you will find detailed information about the fourth order compact formulation Erturk and Gokcol have presented and its application to driven cavity flow, tabulated datas and figures and more.

 

 
 

www.cavityflow.com