Hello, friends, In 3D problems, the point at corner usually has several surface which should be applied boundary condition. This can increase error at this point, so this point usually is the source of error and the hardest point to treat. I am confused about this problems for a long time, who can give me some idea on how to cope with it? Best Regards, Hua Zhou Shenyang Institute of Aeronautical Engineering

There is no ambiguity in how to apply boundary conditions if you adopt a finite volume perspective, for then boundary conditions are applied at the midpoints of boundary faces, not at vertices. Even with a cell-vertex method there need not be a problem, because the boundary conditions can be applied to faces of the dual mesh. In my opinion this is the correct way to handle boundary conditions. If you must apply boundary conditions at vertices, I suppose you will have to come up with some sort of priority list saying which conditions take precedence when an ambiguity exists.

But still you need to applied the boundary conditions to three of six midpoints at boundary faces, the other faces can be determined by scheme, these three must be treated with some kind of boundary conditions which can,I think, introduce more errors into the domain.

Why do you think that applying a boundary condition on 3 faces of a volume introduces errors? This is the physical reality. The corner volume has three faces facing a boundary! Like the previous poster wrote, if you look at it from a finite volume perspective it is all natural.