Streamf unction-Vorticity Boundary conditions

[mhtflexpde]

To dear moderator:

What are the correct boundary conditions for stream function and vorticity applied for wall, free surface, inlet and outlet, during calculation of a 2D axisymmetric incompressible fluid flow using FlexPDE?

[moderator]

1) contours of the stream function delineate flow paths, so a boundary with constant value of the stream function will be an impenetrable wall. A Natural(.)=0 will cause the contours to meet the wall at right angles, so this BC describes a penetrable opening.
2) from the definition of the stream function, you can see that a coordinate-dependent Value BC will specify the velocity flowing through the boundary, e.g. Psi=y means a uniform velocity crossing a vertical wall.
3) Boundary conditions for the vorticity are more difficult to define, but there are some notes on this issue in our version 6 example "Samples|Applications|Fluids|Buoyant.pde" ("Samples|Steady_state|fluids|buoyant.pde" in version 5).