How to compute rotation of rotation of V

ztdep · September 18, 2016, 02:00

Dear friends:
I am implementing the following pressure boundary condition for 2D incompressible flow problem accordind to the paper of KARNIADAKIS"High orer splitting methods for incompressible NS equations"

$\frac{\partial P}{\partial n}=n \cdot Nonelinear(U)-n \cdot \nu\nabla \times \nabla \times U$

Could you please give me some suggestions about the computation of term for 2D problems

$-n \cdot \nu\nabla \times \nabla \times U$

regards

FMDenaro · September 18, 2016, 03:58

Should be more simple if you consider that in 2D the curl of U is simply the vorticity that has only one component along the normal-to-plane direction.
So, you can first compute the vorticity field zeta and then you have to discretize curl (k zeta). The result is projected along the unit vector n.

The way in which the derivatives are discretized depends on the grid arrangement and accuracy requirement.

September 18, 2016, 02:00	How to compute rotation of rotation of V	#1
ztdep Senior Member p ding Join Date: Mar 2009 Posts: 427 Rep Power: 19	Dear friends: I am implementing the following pressure boundary condition for 2D incompressible flow problem accordind to the paper of KARNIADAKIS"High orer splitting methods for incompressible NS equations" $\frac{\partial P}{\partial n}=n \cdot Nonelinear(U)-n \cdot \nu\nabla \times \nabla \times U$ Could you please give me some suggestions about the computation of term for 2D problems $-n \cdot \nu\nabla \times \nabla \times U$ regards

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September 18, 2016, 03:58		#2
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,764 Rep Power: 71	Should be more simple if you consider that in 2D the curl of U is simply the vorticity that has only one component along the normal-to-plane direction. So, you can first compute the vorticity field zeta and then you have to discretize curl (k zeta). The result is projected along the unit vector n. The way in which the derivatives are discretized depends on the grid arrangement and accuracy requirement.