Treatment of inflow boundary
 

Hi all

I am doing a gas computation. The inlet boundary is specified as pressure. I wonder how to extrapolate the velocity at this boundary.

Some papers extrapolate the boundary conditions based on the characteristic theory. (ie, Journal of Fluids and Structures (1997), 11, 947-963).

What is done in that paper is integrating the characteristic equation along the line dx/dt=u-c which is one of the wave speed with negative value.

According to Thompson (JCP 68,1-24), it seems to be an outgoing wave and I am confused between the outgoing wave and inlet flow.

Could anyone explain about it? I really appreciate it.

-W.M.

Re: Treatment of inflow boundary
 

Hi,

Basically, the transformation of the 3D compressible Euler equations using characteristics theory results in 5 local ODE similar to wave equations. Three of them propagate at the local speed u (two vortical waves and one entropy wave), the fourth and fifth ones being pressure waves of u+c and u-c velocity respectively (c is the local speed of sound).

Now, considering an inflow condition, u is simply the velocity in the incoming normal direction. Therefore if the flow is subsonic, u-c is negative. From a physical point of view, this simply states that a pressure wave can travel upstream in a subsonic flow. From a numerical point of view, this means that piece of information coming from inside the computationnal domain has to go out of it, even at an "inflow" BC.

Hope this helps,

Lionel

Re: Treatment of inflow boundary
 

Thanks, Lionel.