[gugum]

Hey everyone,

I am writing my own code to solve 2D navier-stokes equation with SIMPLE scheme in backward step simulation. Now, my supervisor asked me to add the static smagorinsky term in that model. However, I read in some references it need rate of strain tensor (0,5(dui/dxj+duj/dxi)). My question is how to calculate the rate of strain tensor from U,V velocity which I solved before ?

Thanks

[FMDenaro]

Originally Posted by gugum

Hey everyone,

I am writing my own code to solve 2D navier-stokes equation with SIMPLE scheme in backward step simulation. Now, my supervisor asked me to add the static smagorinsky term in that model. However, I read in some references it need rate of strain tensor (0,5(dui/dxj+duj/dxi)). My question is how to calculate the rate of strain tensor from U,V velocity which I solved before ?

Thanks

You use numerical derivatives applied on U and V, what is your problem?

[AliE]

Hello,

Basically you have to compute gradients (somethimg that you must have in your cfd code) assemble the tensor as you have defined it and calculate its module. Apply the formula for eddy viscosity and Smagorinsky ends here . In order to compute the gradient you can use the gauss formula gradPhi=(1/vol)×sum (phif×Sf) where phif is the face value of your velocity component, Sf in the surface normal vector while vol is the cell volume. Tje sum is extend to all cell faces.

[gugum]

Thank you professor. I already solve this problem

[ranjithdj]

Originally Posted by gugum

Thank you professor. I already solve this problem

How did you solve this?