[tas38]

Hello all. I have a question related to the well-posedness of the incompressible Navier-Stokes equations. Specifcally, I am looking for a clear explanantion (or reference to a clear explanation) as to the requirements on velocity and pressure at the domain boundaries for a problem involving solution of the incompressible Navier-Stokes equations to be well-posed.

For the steady flow through a pipe, an example of well-posed boundary conditions would be fixed total pressure at the inlet (Fluent's 'pressure inlet') and a fixed static pressure (Fluent's 'pressure outlet') at the outlet. Such boundary conditions could be used when no details of the velocity/mass flow are known. However, why are these boundary conditions well-posed but specifing a static pressure at the inlet and outlet is ill-posed?

[FMDenaro]

Originally Posted by tas38

Hello all. I have a question related to the well-posedness of the incompressible Navier-Stokes equations. Specifcally, I am looking for a clear explanantion (or reference to a clear explanation) as to the requirements on velocity and pressure at the domain boundaries for a problem involving solution of the incompressible Navier-Stokes equations to be well-posed.

For the steady flow through a pipe, an example of well-posed boundary conditions would be fixed total pressure at the inlet (Fluent's 'pressure inlet') and a fixed static pressure (Fluent's 'pressure outlet') at the outlet. Such boundary conditions could be used when no details of the velocity/mass flow are known. However, why are these boundary conditions well-posed but specifing a static pressure at the inlet and outlet is ill-posed?

I think that the first issue to be highlighted is that pressure in the incompressible model is ... not pressure.
Therefore, talking about static or total pressure is somehow not correct in term of mathematical condition for this problem.
Many old studies can be found, for example see

http://link.springer.com/article/10.1007%2FBF01061454