Hi, I am trying to find an alternative/similar dissipation term to the Jamesn's Scheme in order to remove the non-physical expansion shock at convergent part of the nozzle. Some terms were tried but wiggles in the tip of the Shock are still there!

Any suggestions/ references or Advice from your experience is appreciated.

Thanks for your time.

Hi!

Are you sure there is an expansion shock with Jameson scheme? I'm not quite sure this artificial dissipation scheme would give you answers just like that... Could you please give more detail of your code and of your numerical settings? =D

From our experience here, you removed wiggles near shock waves with upwind schemes, just like the upwind-biased CUSP scheme, or the Roe scheme (both second order). First-order Roe scheme gave us expansion shocks, but Jameson's explicitly-added AD not.

Looking forward for more details...

PS.: Are you from Bristol? I got a friend that graduated there... and I've been there once too!

Hi, Thanks for the reply.

>Are you sure there is an expansion shock with Jameson scheme

No, I am trying to experiment a different/new disspation term

More details about my work are as follows:

1- I am coding Maccormack's Scheme (Second order accurate...) for a Con-Di Nozzle using a conservative approach. The typical input values for the code cause a Shock wave at the divergent part.

> From our experience here, you removed wiggles near shock waves with upwind schemes,

My aim is to add an artificial viscosity to stabilise the solution.

Hope this helps.

Looking for you reply!

Meriem.A.

Hi, Meriem!

Ok! So there's no shock expansion, only shock wave, correct?

Maybe a shock-wave in the Div portion of your nozzle is correct, depending on your total pressure/exit static pressure ratio. A suggestion is that you should use the quasi-1-D relations to verify if you should really expect a shock wave in there or not. Other numerical schemes give you the same shock wave?

Which MacCormack scheme are you using? The 1969 one, based on predictor-corrector steps? MacCormack claims that this scheme does not require addition of artificial dissipation since it is a Lax-Wendroff-type scheme (which should be self-stabilising). However, I've never seen anyone who implemented it and did not have to use a little amount of artificial dissipation...

If there's any other information you would like to add...

Best regards, Biga