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micheldup November 3, 2012 04:56

Incompressible Navier-Stokes / channel / BC

The Chorin's algorithm to solve the incompressible
Navier-Stokes equations has three steps:

1- velocity prediction: u_i
2- pressure computation: p
3- velocity correction: u .

Using a finite element method to solve the problem,
the weak formulation of equation 2- may be written as:

if p_n is the pressure computed at a previous step,
we seek for a pressure p that verifies

int_Omega grad(p).grad(phi) dx = int_Omega grad(p_n).grad(phi) dx
+ int_OmegaBoundary grad(p_n).normal phi ds
+ (1/Delta(t)) int_Omega div(u_i) phi dx

where phi is a test function.

I am wondering what are the right boundary conditions for
the pressure equation ?

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