[Simbelmynë]

Hey,

Many textbooks suggest a mix of boundary conditions to be prescribed at the boundaries. For instance at solid walls, usually a zero velocity condition is prescribed and a pressure condition is calculated with the use of the continuity equation and whatever discretization method is used for the momentum equations (dp/dn=0 is a common outcome of this).

My question is - why prescribe a pressure boundary condition at all? Is it not possible to solve the (interior) equation for pressure at the walls where the velocity is specified?

Likewise for velocity when the pressure is specified at a boundary etc.

[FMDenaro]

Originally Posted by Simbelmynë

Hey,

Many textbooks suggest a mix of boundary conditions to be prescribed at the boundaries. For instance at solid walls, usually a zero velocity condition is prescribed and a pressure condition is calculated with the use of the continuity equation and whatever discretization method is used for the momentum equations (dp/dn=0 is a common outcome of this).

My question is - why prescribe a pressure boundary condition at all? Is it not possible to solve the (interior) equation for pressure at the walls where the velocity is specified?

Likewise for velocity when the pressure is specified at a boundary etc.

Each problem requires the proper set of BC.s to be well posed...
the pressure problem is elliptic and requires only one boundary condition. Generally, the physics of the problem allows us to express the knowledge of the normal velocity component, for example on a wall.
This is the only condition we set to close correctly the pressure equation.
The value dp/dn is not fixed but it is a consequence of the velocity BC.s according to the Hodge decomposition Grad p = v* - v
Of course, you can work by fixing dp/dn but then you can fix also n.v.
Note that dp/dn = 0 on a wall is a low-order approximation when the Reynolds number is not sufficiently high since would imply n.v*=0

[Simbelmynë]

Originally Posted by FMDenaro

Each problem requires the proper set of BC.s to be well posed...
the pressure problem is elliptic and requires only one boundary condition. Generally, the physics of the problem allows us to express the knowledge of the normal velocity component, for example on a wall.
This is the only condition we set to close correctly the pressure equation.
The value dp/dn is not fixed but it is a consequence of the velocity BC.s according to the Hodge decomposition Grad p = v* - v
Of course, you can work by fixing dp/dn but then you can fix also n.v.
Note that dp/dn = 0 on a wall is a low-order approximation when the Reynolds number is not sufficiently high since would imply n.v*=0

Why do we have to specify pressure boundaries at cells where we have specified velocity boundaries? It seems to me that we can close the pressure equation with just the knowledge of a pressure boundary condition in 1 cell (Dirichlet in this case). Neumann conditions for pressure can arise from assumptions that the continuity equation is satisfied at the boundary, but this is also part of the pressure Poisson equation.

[FMDenaro]

Originally Posted by Simbelmynë

Why do we have to specify pressure boundaries at cells where we have specified velocity boundaries? It seems to me that we can close the pressure equation with just the knowledge of a pressure boundary condition in 1 cell (Dirichlet in this case). Neumann conditions for pressure can arise from assumptions that the continuity equation is satisfied at the boundary, but this is also part of the pressure Poisson equation.

We do not specify both pressure and velocity boundary conditions!
The first thing is using the physical BC.s: if you know the velocity use that, if you know pressure use that....

The pressure problem cannot be closed by fixing a value in a cell!
It is an elliptic problem that requires mathematically the BC.s to be posed on all boundaries.

Sorry to say that I see some confusion in your idea about the pressure problem..

[Simbelmynë]

Originally Posted by FMDenaro

We do not specify both pressure and velocity boundary conditions!
The first thing is using the physical BC.s: if you know the velocity use that, if you know pressure use that....

For an incompressible flow I am uncertain that we actually have the physical pressure boundary condition for walls etc.

Originally Posted by FMDenaro

The pressure problem cannot be closed by fixing a value in a cell!
It is an elliptic problem that requires mathematically the BC.s to be posed on all boundaries.

You are probably correct here, what I am perhaps confused about is that to me it seems that we have already imposed the boundary conditions to some extent in the creation of the pressure Poisson equation. The source term in the Poisson equation is dependent on the boundary condition imposed for velocity, is this not correct?

Originally Posted by FMDenaro

Sorry to say that I see some confusion in your idea about the pressure problem..

Yeah, this is why cfd-online is so great!

[FMDenaro]

very often the velocity is an available data for BC.s, few cases are suitable to be afforded with pressure...however, we do not need to know the pressure on a wall but only the relation for the normal derivative.

The continuity equation drives us to write the Poisson equation (in the interior) but to set a mathematically well-posed problem, the Poisson equation must be supplied by proper BC.s on the boundaries.
When the BC.s are prescribed, you can modify both the matrix line and the source term.
I remember a previous post on cfd-online with many details about

[FMDenaro]

this is one of the posts

http://www.cfd-online.com/Forums/mai...ep-method.html

[msm6166]

Can any please tell me how to define boundary condition for a solar collector as i m having lots of problem with it as the residual lines get converged but the message error keeps on repeating that 300 cells have temperature of 5000 k. Please help