Shear stress boundary condition at free surface
 

Hello everyone,


I am simulating a free rising bubble in a viscoelastic fluid with a moving mesh solver. I implemented the viscoelastic stress term in the momentum equation aswell as the equations to calculate velocity and pressure boundary conditions at the bubble interface. Since the newtonian stress can be directly expressed with viscosities and velocities, this leaves the just a pressure and a velocity field in the original solver. With boundary conditions at the free surface as follows:

Inside
velocity: fixed value
pressure: fixed gradient


Outside
velocity: fixed gradient
pressure: fixed value


While the viscoelastic stress can't be calculated directly from the velocity a PDE is solved returning a tau field for which I now have to find boundary conditions for.


What would be boundary conditions for my tau field at free surface?

Why were those boundary conditions for velocity and pressure chosen?
Is it done similar to inlet and outlet boundary conditions of a pipe for numerical stability? v_inlet=fixedValue, p_inlet=zeroGrad and v_outlet=zeroGrad, p_outlet=fixedValue.

Would I chose the boundary conditions similar to the velocity boundary conditions since the stress is a function of the velocity?
The fixed gradient boundary condition for the velocity is applied as with being the normal vector on the free surface. If I would apply the same boundary condition for the shear stress this would be where I have to find the gradient of a tensorField, which is not defined in OpenFOAM. I was experimenting with snGrad() but im not sure, if it does what i request.


I am working with foam extend 4.0.



Many thanks for your help, I hope you understand my problem.


Paul