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rajeshkunwar February 4, 2011 06:00

Standard k-e model in Lid driven cavity

I have recently written code for solving 2-D Lid Driven Cavity using SIMPLE algorithm and Finite Volume Method discretisation for the Laminar case.

Now I want to solve the same problem for turbulence case. can somebody guide me and tell me the Governing equations in 2-d and how to model that using standard k-e many turbulent stress terms need to be modelled in RANS equation.

Thank You


DoHander February 5, 2011 19:03

For incompressible turbulent flows your equations will be basically the same, except for the viscosity which is composed by the sum of laminar and turbulent viscosity. Google for Reynolds Averaged Navier Stokes equation, or use this link:


rajeshkunwar February 10, 2011 06:07

Thank You. Mr. DoHander

In 2D RANS equations there are three unknown Reynolds Stress terms.Is it necessary to model each three terms or just model the rho*u'v' term.



DoHander February 10, 2011 08:34

Use the Boussinesq approximation (this will reduce the number of Reynolds stresses) and the ke turbulence model.

Check this book (second edition), you will find the equation you need:

Anderson DA Tannehill JC Pletcher RH. Computational Fluid Mechanics And Heat Transfer


rajeshkunwar February 11, 2011 03:18

After using Boussinesq approximationin x-momentum equation equation
changes are as given below
  1. meu_laminar is changes to (meu_laminar+meu_turbulent)
  2. u and v is relaced by U and V
  3. Extra term is generated -(2/3)*rho*k
How to model the extra model term -(2/3)*rho*k. Should I treat this term like the pressure difference term in momentum equation.

In the Pletcher book final equation after putting boussinesq equation is not given.


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