[granzer]

I know implicit/explicit schemes but don't know what implicit/explicit boundary conditions mean. So what are implicit and explicit boundary conditions?

[sbaffini]

It's the exact same concept, but related to how you discretize the boundary conditions. Still, this distinction only makes sense in relation to a general implicit discretization: it doesn't make sense to discretize bc implicitly for an otherwise explicit code.

To make things clearer, imagine that, as bc, you are given the value on a boundary: T = Tb. Also, imagine a simple diffusion problem with a structured FV code and constant steps (dx,dy,dz), and that the boundary has entering normal along the positive y direction. Then, a possible discretization for the boundary flux Fb is:

Fb = q(x,y0,z) = - (dx*dz) * D * (T(i,1,k)-Tb)/(dy/2)

where D is a diffusion coefficient. Now, this flux actually enters in the equation for T(i,1,k) so, if you are solving the equations implicitly, it really makes sense to consider the implicit discretization for this bc as well. You can indeed rewrite it as:

Fb = a*T(i,1,k)+b

and, basically, add a to the implicit part. However, sometimes bc are in a form where this is difficult or can only be made approximately, or you simply don't want to. In that case you can simply use the bc flux explicitly and stop there.

[FMDenaro]

You have to consider "implicit", those BCs that require to change the structure of the matrix governing the system. Typically Neumann BCs produce that.
Have also a look here
Implicit boundary conditions


and here


https://www.sciencedirect.com/scienc...518?via%3Dihub