Roe Scheme; Shock Boundary layer Interaction
 

Hi there:

I am trying to run a test case of shock boundary layer interaction with first order Roe scheme. But i really have hard time to capture the circulation zone over the plate.

The test case: The test case i am running is the standard case that many people have run. It is a Mach =2 with shock angle=32.6 deg and Re_L=2.96e5 (L being the shock impingement to the plate if the flow is assumed invisid).

My problem: I need very clustedred grids near the wall to capture the circulation zone and around 200 nodes in transverse direction. But this case has succesfully been performed by maccormack or Beam and warming in 70's with about 60 nodes in transverse direction. I don't know my problem is because my code is first order or what? Any one in this group has tried this test case with first order Roe before? Thanks for your help.

Re: Roe Scheme; Shock Boundary layer Interaction
 

(1). I have heard about Roe's method, but I don't know whether it as developed for the viscous shock boundary layer interaction problem. I didn't have a chance to use it. (2). When you say MacCormack or Beam and Warming in 70's was able to compute the problem successfully with 60 nodes, it is likely the computers they used were more accurate. (3). You mentioned the Reynolds number, but you did not say whether it is laminar or turbulent. And more important of all, what is the boundary layer thickness at the inlet of your computational domain? zero? or finite? Are these consistent with MacCormack's condition? (4). Since the MacCormack's method is explicit and very easy to implement, it is a good idea to run a similar calculation using his method to verify that 60 node points are good enough.(by the way, I think, his method requires the use of 4th order artificial vicosity term )(5). It would be a valuable experience to repeat the same calculation using MacCormack method. (Did they publish the data on the mesh distribution? and what is your mesh distribution?)

Re: Roe Scheme; Shock Boundary layer Interaction
 

THanks for your reply. According to your numbering I reply as follows: (1)-Roe scheme is developed first for Inviscid flows. But because it is not diffusive at all for grid aligned flows, makes that very suitable for viscous flow computations as there is no means to augment the shear layer computation. (2)i don't know what you mean, when you say their computer were more accurate? (3)this is a laminar flow test case. and the computational domain is started some distance ahead of the plate where uniform free stream conditions are input for supersonic inflow of Mach=2. I am doing a time marching computation, and not a parabolic space marching along the plate. So I don't specifiy boundary layer thickness. (4)may be I will need to write a maccormack as well. But at this moment I will make my Roe code second order and see what is wrong with my computations. I don't think macccormack's need fourth order differencing for viscous terms. But the viscous terms must be in the opposite direction of either predictor or corrector, i.e. if the predictor is forward, then the viscous derivatives, e.g. u_x, in this step must be backward, to make the viscous terms with net of second order in space. (5)I tried to make my mesh as similar as theirs. But I got what I has said in my original message.

Regards.

Re: Roe Scheme; Shock Boundary layer Interaction
 

(1). your answers are consistent with my comments. There is no surprise. (2). I don't have further comments. Good luck in your CFD research.

Re: Roe Scheme; Shock Boundary layer Interaction
 

Fourth order artificial viscosity isn't the same thing as fourth order differencing.

Re: Roe Scheme; Shock Boundary layer Interaction
 

>Fourth order artificial viscosity isn't the same thing as fourth order differencing.

There is no A.V. in in the original Maccormack 1969 and it works for high speed flows well.

MAy be you are talking about Jameson's 1981?