Hi

I am solving the Navier-Stokes equation using TVD schemes. I tried using non-reflecting boundary conditions proposed by K.W.Thompson for the far field but the information is still being reflected back. Is there any other options

Cheers

Shuo

The Thompson derivation is essentially derived for plane waves normal to the boundary and deviations from this will give reflections. So to minimise reflections one should try to use a circular shaped boundary placed well into the far field with the acoustics sources at the origin.

If your grid does not allow the use of a circular shape a similar effect can be achieved by modifying the boundary conditions for a specified acoustic origin represenatative of the actual sources.

At higher computational cost one can introduce an absorbing layer consisting of rows cells beyond the boundary in which a modified form of the Navier-Stokes are solved with a view to absorbing the acoustic motion while presenting the smallest impedance mismatch at the boundary. This is probably the most common approach, particularly for exit boundary conditions, when solving for turbulent flow.

If you are ready to invest and modify the code you are using then you can treat the characteristics of the flow at the boundary and impose that the fast inflowing characteristics of the flow be zero there. There are plenty of methods, see e.g.

Givoli, D. 1991, Journal of Computational Physics,vol.94, page 1.

COuld you please provide with a reference for the absorbing layer. Thanks