Hello,
In this Fenics solution scheme for Navier Stokes equations, one imposes a Neumann Boundary condition (BC)
\partial \phi / \partial n = 0
on the part of the boundary \partial \Omega_D where Dirichlet BCs are imposed for the velocity, and a Dirichlet BC
\phi = 0
on the part of the boundary \partial \Omega_N where Neumann BCs are imposed for the velocity.
If have the following question about this
- Why these BCs for \phi?
- What if one imposes \phi = 0 on all \partial \Omega?
- In this splitting scheme we are increasing the order of the PDE satisfied by \phi by manipulating the original NS equations and taking the derivative of both sides, resulting in a Poisson equation for \phi. This implies that we are increasing, with respect to the original problem, the number of BCs that needed to determine the solution. Are these additional BCs arbitrary? Do the physical observables depend on the choice of these BCs?
Thank you !