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kei-tee April 23, 2003 10:54

limiter & entropy fix of Roe scheme

I use Roe scheme with MUSCL in low mach number, subsonic flow for high lift device analysis. I wonder Entropy fix technique & slope limiter of MUSCL is need or not in such case. Ofcourse, flow is shockfree. As far as my understanding, both methods are derivered from Riemann problem ,like shock wave. Are these are must or not? Please give me your opinion,

Best regards.


Mike April 23, 2003 10:59

Re: limiter & entropy fix of Roe scheme
Hi kei- tei

How low in Mach Number ? If you are very low in Mach like 0.1 (or below) you certainly need preconditioning.

Slope limiter is infact min-mod limiter that is modified to prevent instabilities and convergence problems.


kei-tee April 23, 2003 11:22

Re: limiter & entropy fix of Roe scheme
Thanks, Mike.

As for Mach number, my case is now about Mach 0.2. I don't need preconditioning ,so far from my results.

Slope limiter now I use is van albada deferentiable limiter. Also, I use this limiter in convection term of spalart-allmaras turbulence model.

I don't know modified min-mod for low mach number. Do you know available paper or something on it ?

Best regards. kei-tee.

Mike April 23, 2003 13:07

Re: limiter & entropy fix of Roe scheme

When I am available I will send you some info about modified min-mod limiter via email. Also I would like you to send me some info about Van albada limiter.


Praveen April 24, 2003 00:25

Re: limiter & entropy fix of Roe scheme
I have found that both limiter and entropy fix are not required when you are solving subsonic flows. I think you should first try solving without them.

frank April 24, 2003 02:59

Re: limiter & entropy fix of Roe scheme
The entropy fix is usually employed for the acoustic wave speeds, u+a, u-a. Even for subsonic high lift, if one has a slat the flow may accelerate to supersonic flow locally, but it should not be of much problem with the entropy fix.

Since the meshes are very fine it might be required to have the limiter at the early stages of the computation when the solution builds up. Even in subsonic, there may be strong discontinuities in the initial transient stage of the computation, which requires the use of limiters.

I actually prefer the HLLC scheme to the Roe. Roe is much more expensive and more difficult to extend for additional turbulence equations. For HLLC it is extremely easy to get more field equations (same for AUSM schemes). Easier to program, no dubious entropy fix, and much faster. Getting shocks and contact excellent. (HLLC by Batten and Leschziner).

When doing 2D high lift, it is very important to place the far field sufficiently far away. Without vortex correction, 20 chords are usually not enough for high angles (20 degrees). Vortex correction significantly improves the prediction of the drag. (the lift is not so much affected).


cfdeye April 24, 2003 04:09

Re: limiter & entropy fix of Roe scheme
I agree with you HLLC is much better than Roe. I still can't understand this entropy fix could you please explain it in general.

Mike April 24, 2003 09:09

Re: limiter & entropy fix of Roe scheme

Can you give me any reference, paper... for HLLC method?


cfdeye April 24, 2003 10:40

Re: limiter & entropy fix of Roe scheme
see the basic of HLLC

Toro E, Spruce M and Speares W

Restoration of the contact surface in the HLL-Riemann Solver

Shock Waves

1994; 4:25-34


Toro E. Riemann solvers and numerical methods for fluid dynamics.

Springer-Verlag. Berlin, 1999

I've derived HLLC for two-fluid model it was perfect for many test problems....

kei-tee April 24, 2003 10:53

Re: limiter & entropy fix of Roe scheme
Thanks, Mike,Praveen,frank & cfdeye for meaningfull opinions.

I will try without Entropy Fix but with limiter.

As for B.C., now I use non-reflective B.C. on inlet,outflow,& farfield & not use vortex correction method. Far field size is 20chords. My interests is mainly lift prediction & surface pressure distribution.

To cfdeye; Entropy fix is used to remove false expansion shock wave. My code adopts P.L. Roe's. i.e. where local expansion exists, lambda = lambda + 0.5(lambda_R - lambda_L) lambda means eigenvalues of systems. i.e. U,U+C,U-C. My code adopts on U. but, I don't know why. Because this part is programmed by others. May be dubious.

I don't know HLLC scheme. But I know AUSM. I will try it in the future.

Anyway, most difficult problem for me is that my code adopts overset method.

I think overset is not suite to high lift analysis. Its' fully dissipative & complex to handle with by nature compared with multi-block & unstructured.

Best regards. Kei-tee.

Mike April 24, 2003 11:12

Re: limiter & entropy fix of Roe scheme
Kei-tee, Previously I had done viscous flow computations around full aircraft config. using overset (chimera) grids and ROE scheme, k-e turb. model. As well as you avoid having orhan cells that lacks interpolation of flow info between fine and coarse grids, you will get very good results. I think it is not dissipative:)) but difficult to handle sometimes!!!

kei-tee April 24, 2003 12:14

Re: limiter & entropy fix of Roe scheme
Hi, Mike. 'full aircraft config'! You have great experience! Have you read the paper, listed below? If you are interested in these & not yet read, I will send you by e-mail.



Now I will try to optimize donor & recipter cells like PEGASUS code. But It's too complex ! In my code, orphan you mentioned is not allowed, orphan not interpolated cell solved by itself anyway.

Nowadays I think sometimes, I wish I had the skill same as Stuart Rogers. or If I were American(I'm Japanese), I could use OVERFLOW code!

In my experience (2-4 elements), wider gap & overlap flap case agree with EXP. But for nallow case, separation is over-estimated. Now,I don't know whether this is due to S-A model or overset.

S-A also annoy me. I think S-A is over prediction eddy viscosity in wake region & in subonic, free transition depends on nu_infinity'value. But in their paper, they say nu_inifinity never affects results.

Anyway, Respectfully for your experience & opinions.


kei-tee April 24, 2003 12:22

Re: limiter & entropy fix of Roe scheme
Mike,Did you use preconditioning when you did computation around full aircraft config?


frank April 24, 2003 12:40

Re: limiter & entropy fix of Roe scheme
I posted some comments on the entropy fix. But it seems to got lost ?!

If the Roe is implemented it should work fine. But implementing an entropy fix is usually not difficult. One just has to correct the eigenvalues a bit.

For the lift 20 chord are often ok. Anyhow, the drag might be somewhat off at high angles, as also shown in some papars by Zingg. (and my recent findings on the AGARD AR303 L1/T2 high lift configuration in 2D).

Overset techniques should work ok. The problem is where to set the blocks and if the interpolation is done properly.

I also use the Spalart Allmaras for high lift. It seems to be ok so far. In the wakes, often the differences are more related to grid resolution than to the turbulence model. What I have seen in the literature. My wakes did not come out so well, compared with experiments. But lift and drag are fine up to stall.


frank April 24, 2003 12:52

Re: limiter & entropy fix of Roe scheme
I use the HLLC from Batten and Leschziner. Journal of computational physics, volume 137, pages 38-78, 1997

There are three wave speeds SL, SR and SM. SM is the contact, SL and SR are the left moving and right moving waves. SL and SR include Roe averaged states. Since they use square roots, these are more expensive to compute. I also replace them by a simplified approach proposed by Davis. The method is described by van der Vegt in Journal of Comp. Physics, volume 182(2), pages 546-585, 2002.

For inviscid hypersonics I still prefer the flux vector split by haenel and schwane, since it is more robust (for mach 8 flows or so).

One ends up with several schemes for all kind of situations. But in 90% HLLC is a good choice for me. One just has to see, that there are a couple of different HLLC schemes. It gets confusing which one is what. Batten, Leschziner and the one used by van der Vegt seem to be the newest ones. For implicit methods I just get the jacobian of the schemes by putting it in the ADIFOR (automatic differentiation) tool. Exact Jacobians in 5 minutes :) ...very nice.


Mike April 24, 2003 13:45

Kei-tee, I am not an American, I am a phd student from some other country:) But I am lucky that my supervisor is from NASA so that I had a great chance to learn a lot from him. I will be very happy if you send the above papers and please email me ( I hope we can share our experiences. Unfortunately, I am new to preconditioning. For the last 4-5 months I did a literature survey and I think 2-3 months later I can begin implementing it to my codes:)


Mike April 24, 2003 14:16

During my computations with overset grids, I didn't use preconditioning. Since Mach number was 0.4 . Mike

autofly April 26, 2003 12:00

Re: limiter & entropy fix of Roe scheme
I am lucky to learn so much from each opinions. now i have two problems. first, can overset grids work well in hypersonic with complex shocks interaction? second, FVS and FDS which is better in hypersonic. if FDS, which kind of scheme ia less dissipation? thanks in advance. if possible, you can send e-mail to me to discuss further.

cfdeye May 12, 2003 17:57

Re: HLLC with Automatic Differentiation
would you please explain this in details (I'm trying to use it but couldn't until now):-

<< For implicit methods I just get the jacobian of the schemes by putting it in the

ADIFOR (automatic differentiation)

tool. Exact Jacobians in 5 minutes. >>

is it (say 1-D) A(U) = \frac{\par F}{\par U}

what about the hyperbolicity matter with AD ???

Many thanks for your time.

Frank May 13, 2003 14:16

Re: HLLC with Automatic Differentiation
My jacobians are based on a first order method in space. Linearizing it second order in space also requires to linearize the limiters etc which is quite touch and probably not very robust.

What one needs is the Jacobian dF/dQ_Left and dF/dQ_Right.

F = convective flux, e.g. HLLC, Roe or whatever upwind scheme. Q = conservative vector.

Now one assembles the flux routine in such a way, that it computes one riemann problem, so one has a distinct input Q_L and Q_R and one output, F, for the flux routine.

Then ADIFOR can compute the jacobians of this routine, so one has a new code that besides F also contains the Jacobian with respect to Q_L and Q_R.

One has to note, that ADIFOR gives the transposed of the Jacobian, so I just copy the data into the arrays I need at the end.

Once having the right ADIFOR scripts, additional riemann solvers are done quite quick. I may provide my scripts, if required. They are just 4 small scripts or so, about 20 lines. They are all I know about using ADIFOR so far. So, one does not need to be an expert for this, if ADIFOR is installed on your machine.


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