compressible channel flow..

R.D.Prabhu

Hi there ,

I am developing a code to study compressible - convection in channel-flow..

As a validation check I wanted to see if as a limiting case I can obtain the fully developed velocity profiles including the 'developing flow ' profiles at the entrance.

I am faced with the following problems:

1. for random initial conditions for the velocity (transverse component suppressed) the flow does evolve to a smooth profile ..but remains in the developing phase. I used a linear density profile to start with.

I had scaled my time with respect to the sound crossing

time. Thinking that I was not allowing sufficient time

for the flow to develop ( and length as well) I changed my time and length scaling ( L ..w.r.t channel length ..not width ..as done earlier; and time w.r.t the L/(peak velocity))

2. the flow does evolve this time ..but does not quite converge . ( I use the sum_{i,j}(v_{n} - v{n-1}) to check for convergence....any better way ..?)

Instead the convergence is destroyed by something like

a 'boundary - disturbance' emanating from the outlet.

My understanding :

since I did start without bothering about the intial flow being 'divergence less' or not...there might be the

possibility of 'incoming 'waves from the outlet..destroying the solution.

I must add that I had left the outlet boundary to evolve by itself.. ( is this wrong..?)

Now ..if I carefully choose a div.V = 0 intial state

and put the velocity - profile by hand at the outlet

( fix it I mean ..) and start with a flat - profile

at the inlet (fixed) .....Can I expect to capture

what I intended to get ..viz..all the stages of a

developing flow..in a channel.?

Does the div.V =0 state eliminate the 'waves' ?

( how do I know if these are 'numerical' or 'real'

waves..?)

any suggestions..?

thanks

Prabhu