[Kyounghwa]

Hello. I need help.

I'm programing for Navier-Stokes eq. using Projection Method presented by Kim and Moin's paper.(Application of a Fractional-step Method to Incompressible Navier-Stokes equations)

I'm checking convergence order of exact solution.
My exact solution is different with Kim and Moin's example.
Kim and Moin's example has periodic Boundary condition but My example has non-periodic boundary condition.
There are two boundary conditions. One is u^=u(n+1), the other is u^=u(n+1)+dt(phi(n)_x).

For 1st B.C., there is no convergence order in Kim and Moin's paper.
But, it has 1st convergence order in my case.
Is it possible?
Do they tell us that all case doesn't exist convergence order?
I don't know well yet.

For 2nd B.C., I'm very confused.
I solve Poisson eq. for phi. There is Neumann Boundary Condition.
Especially, it equal to 0.
Which do I use 0 or approximate value?

Please, give me any advice.
Thanks.

[FMDenaro]

Originally Posted by Kyounghwa

Hello. I need help.

I'm programing for Navier-Stokes eq. using Projection Method presented by Kim and Moin's paper.(Application of a Fractional-step Method to Incompressible Navier-Stokes equations)

I'm checking convergence order of exact solution.
My exact solution is different with Kim and Moin's example.
Kim and Moin's example has periodic Boundary condition but My example has non-periodic boundary condition.
There are two boundary conditions. One is u^=u(n+1), the other is u^=u(n+1)+dt(phi(n)_x).

For 1st B.C., there is no convergence order in Kim and Moin's paper.
But, it has 1st convergence order in my case.
Is it possible?
Do they tell us that all case doesn't exist convergence order?
I don't know well yet.

For 2nd B.C., I'm very confused.
I solve Poisson eq. for phi. There is Neumann Boundary Condition.
Especially, it equal to 0.
Which do I use 0 or approximate value?

Please, give me any advice.
Thanks.

Hello, I studied this method in its aspects and the problem you are talking about concerns:

a) the assignment of intermediate boundary conditions V*
b) the boundary conditions for the prediction step.

If you prescribe V* = Vn+1 then you get a numerical boundary layer since it is an O(1) accurate condition. You see a first order slope in time, but you have to consider the division by the time-step for a single-step analysis.

The problem is quite complex, I suggest to read the literature appeared after the paper of Moin, there are many studies about ...