CFD Example 1

Lid driven cavity flow (Finite Element Method)

This page contains an example of a how CFD tools can solve the problem of determining the field (velocity and pressure) in a lid driven cavity. This test case is a typical case validation: an incompressible fluid is contained in a square vessel, whose lid is moved with a constant velocity. In this case, the lid is moved towards the right of the domain.

This example has been solved using a software that uses Finite Element Method. More precisely, this software implements the Characteristics Based Splitted (CBS) algorithm, explained in "The Finite Element Method Volume 3: Fluid Dynamics". O.C. Zienkiewicz, R.L. Taylor.

The results are compared with the reference Ghia, Ghia, and Shin (1982), "High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method", Journal of Computational Physics, Vol. 48, pp. 387-411.

The mesh used for solving this problem had been a structured tria mesh of (2x100) x (2x100) tria elements.

 

 

The following pictures shows the velocity profile inside the lid driven cavity for several Reynolds numbers. The obtained values have been compared with the reference Ghia.

Reynolds number 1000

Velocity field

 

 

Vx velocity along the vertical axis of symetry of the lid driven cavity

 

Vy velocity along the horizontal axis of symetry of the lid driven cavity


The obtained results are very close to the results of the reference (Ghia). The average error for the horizontal velocity along the vertical mid line is 0.66%, and the average error for the vertical velocity along the horizontal mid line is 0.74%

Reynolds number 2500

Vx velocity along the vertical axis of symetry of the lid driven cavity

Vy velocity along the horizontal axis of symetry of the lid driven cavity

As it can be seen, the results are very close to the results in the reference (Ghia).

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