Incremental projection method - Page 3 -- CFD Online Discussion Forums

January 15, 2018, 12:18	Incremental projection method	#1
moshe Member Moshe De Leon Join Date: Nov 2017 Location: Portugal Posts: 31 Rep Power: 8	I am curious about the practical implementation of an incremental projection method. For pressure we have 3 time levels, $P^{n+1}, \phi^{n+1}, P^{n}$ . In the prediction step we have $\frac{\mathbf{u}^{} - u^{n}}{\Delta t} = - \mathbf{u}^{n} \cdot \nabla \mathbf{u}^{n} - \frac{1}{\rho} \nabla P^{n} - \nu \nabla^{2} \mathbf{u}^{n}$ We solve for pressure $\phi^{n+1}$ $\nabla^{2} \phi^{n+1} = \frac{\rho}{\Delta t} \nabla \cdot \mathbf{u}^{}$ We then project onto $\frac{\mathbf{u}^{n+1} - \mathbf{u}^{n}}{\Delta t} = - \nabla \phi^{n+1}$ Finally we update pressure $P^{n+1} = P^{n} + \phi^{n+1}$ In literature $P^{n}$ is referred to as an approximate to $P^{n+1}$ . My question is in practice how do I initialize $P^{n}$ and then update pressure. In my code I have, after updating the velocities Code: Pnew(i,j) = P(i,j) + phi(i,j) phi(i,j) = P(i,j) I have tried setting P = Pnew, but my simulation blows up.

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