Boundary conditions?

Tom

I am fairly new at CFD and want clear some personal misunderstandings on the implementation of boundary conditions. Any comments are most welcome indeed.

First of all, I am working with the Finite Volume Method (FVM) where boundaries are represented by cell faces on the "outside" of the mesh, i.e. faces not lying between two cells.

I gather from various literature sources that there are 4 posibilities when specifying boundary conditions:

(1) Fixed value (Dirichlet)

(2) Fixed gradient (von Neumann)

(3) Natural boundary condition (dependent on solution)

(4) Extrapolated boundary value

I also gather that each and every discretized equation to be solved requires either one or a combination of the above boundary conditions.

Number (1) and (2) is fairly understandable and the implementation is not too obscured.

Questions: [1] Am I right in saying that for (2) the boundary face value is calculated from the given gradient and the cell value lying along the boundary?

[2] In the discretized equation we require the value of the cell lying outside the boundary. But we assume that this cell has a zero volume so that its centroid coincides with the boundary face centroid? Therefore the value at the boundary can be used directly in the discretized equation?

[3] Another question on the fixed gradient boundary condition (2). Do we specify the FLUX at the boundary per unit area i.e.

q=-k d(phi)/d(n) = fixed value

where n is a outward pointing init vector on the boundary face,

or do we specify only the gradient of the dependent variable?

d(phi)/d(n)

[4] What is the difference between implicit and explicit treatment of boundary conditions and how does it effect the discretized equation? i.e. how is the diagonal influenced and and what about the explicit source term due to the boundary condition?

[5] What is the deal with conditions (3) and (4) and where are they typically used? How will (3) be implemented?

[6] Typically which conditions of (1) to (4) is used in which equations for example:

momentum equation pressure equation pressure correction equation

etc. etc.

Looking forward to your replies. Tom