For a given computational domain, boundary conditions can be given that over-specify or under-specify the problem. This usually results in non-physical solutions or failure of the solution to converge. It is important, therefore, to understand the meaning of well-posed boundary conditions.

An example of an over-specified problem is a constant area duct, with a specified fluid velocity at the inlet, and a different velocity specified at the outlet. Clearly, both conditions cannot be physically satisfied in the absence of a mass source for an isochoric fluid.

An example of an under-specified problem is that of a closed box for which only heat flux boundary conditions were specified. In this case, the temperature level is not constrained and, while the solution may converge, the resultant temperature level would be unpredictable.

The best way to determine if the boundary conditions are well posed is to ask the question "Could the configuration I have set be physically recreated in a laboratory?" In the first example above, this is clearly not possible. In the second example, no matter how good the insulation of the boundary, there would eventually be some heat flow from or into the environment that would serve to set the temperature level.

For details, see Boundary Conditions in Multiphase Flow.