I'm working with the incompressible Navier-Stokes equations with a moving boundary (free-surface flows). I solve the 3D hydrodynamic field by Finite Volume Method with a fractional step procedure, where a Poisson equation must be solved in order to ensure the mass conservation. I've a problem about the outlet pressure boundary condition. When pressure and velocity are unknown at the outlet of the domain, in fact, the simmetry boundary condition is commonly employed for the velocity. In this case, what is the correspondent boundary condition for the pressure in the Poisson equation?

Thanks for your time and for your answers.

The NS equations deal with the pressure gradient, so the pressure value itself is not critical. Usually, an arbitrary value is placed at one point in the domain. For example, in a square driven cavity put the pressure equal to zero at the center of the bottom wall. Good Luck!

Steve Ciesla

Could you kindly tell me how to derive Poisson's equation for pressure for Non-Newtonian fluid? I am trying to derive a Poisson-like equation using a method similar to SIMPLE-algorithm, but it seems doesn't work for 3D using tetrahedron elements. Thanks.

Bao

Take the divergence of the momentum equation to get a Poisson equation. Then introduce the continuity equation into the time derivative terms.