Boundary Conditions

The boundary conditions determine the solution of the PDEs. They correspond to the necessary and sufficient conditions for the well-posedness of solutions to the PDEs, i. e. to exist, be unique and depend continuously on the data. There are two types of boundary conditions traditionally associated with the above system, the tangency condition and the asymptotic condition in the far field.

The tangency condition expresses the fact that in an inviscid flow, the fluid is expected to slip along a solid, impermeable surface. This translates to

(V. n)obstade = Vn = 0 (2.4)

where Vn represents the normal relative velocity with respect to the solid surface.

Other conditions can be prescribed, for example in the case of a porous surface, the normal relative velocity can be given as

Vn = g (2.5)

where g is a given function along the surface.

The asymptotic condition states that, for a finite obstacle, the flow far away from the body, returns to the uniform, undisturbed flow V«,. In terms of u and w this reads

u, w ^ 0 as x2 + z2 (2.6)