# Oscillations in Chorin's method due to the BC

I am pretty new to the CFD and I wanted to start with Chorin's projection. The starting problem is just a free jet flowing in the investigated area. I got terrible oscillations almost immediately and I think it is due to the wrong treated boundary conditions for intermediate velocity $u^*$. There is just a noob mistake somewhere in the process:

1. Calculation of the $u^*$ using:

$$u^* = u^{n}+\Delta t(u^n\cdot\nabla)u^n$$

1. Solving the Poisson equation with the source term $\frac{\Delta t}{\rho}\nabla \cdot u^*$ and then updating the velocity:

$$u^{n+1} = u^* + \frac{\Delta t}{\rho}\nabla p^{n+1}$$

• Where in the process should the BC for $u^*$ step in?
• How can I use a boundary condition $u^*=u^{n+1}$ if I don't have the $u^{n+1}$ yet?

I need zero Neumann BC for velocity and zero Dirichlet BC for pressure.

• The issue isn't the BCs, but the fact that pure Neumann BCs yield an ill-posed problem. See scicomp.stackexchange.com/questions/20166/… for a treatment. – Jesse Chan Jul 11 '16 at 15:30
• 1. Why you find $u_*$ and not $u_*-u^n$? 2. $u_*$ steps in in the calculation of the predictor term which, by the way, you wrote wrong. – Kbzon Jul 12 '16 at 10:15