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linhbao tran March 15, 1999 18:30

discontinuity detection

i am looking for literatures in this area with little luck. if you know any, please recommend. thank you very much.


Shigunov March 16, 1999 06:15

Re: discontinuity detection
Which discontinuities? Shock waves, contact discontinuities, or? And detection is in a numerical simulation or in a experiment? With best wishes

linhbao tran March 16, 1999 06:23

Re: discontinuity detection
both forms of discontinuities, shock and contact, in a numerical simulation. Regards.

Shigunov March 17, 1999 05:42

Re: discontinuity detection
There are two approaches, namely interface-tracking and interface-capturing, and a lot of variants. You can find almost all in J. Comput. Phys. and in Int. J. Numer. Methods in Fluids for the last four-five years. With best wishes

linhbao tran March 17, 1999 06:37

Re: discontinuity detection
maybe you misunderstood my post. given a flow field with a captured shock or contact surface, i'd like to know how to detect the location of these discontinuities, e.g. by fourier analysis, etc. thanks for responses and best regards.

John C. Chien March 17, 1999 10:24

Re: discontinuity detection
(1).pressure contour plot and velocity contour plot should give you the pressure jump or shear layer locations. By changing the contour levels, you can zoom in a particular location for detail picture. (2). If you use banded contour plot to paint area between two contour lines, you can get a bitmap representation of the flow field ( instead of line contour plot). (3). I think, you can use tools in pattern recognition to study the bitmap picture just like any digitized photo to remove the low gradient region. (4). Regardless of the approach used, the result can only be determined by your eyes and brain. I think the first method of using selective contour level plot of pressure and velocity is fun and easy to do . This is also an effective way to perform adaptive mesh refinement ( either based on the gradient or on the location).

linhbao tran March 18, 1999 05:11

Re: discontinuity detection
not visually but numerically.

Shigunov March 18, 1999 07:17

Re: discontinuity detection
The method for discontinuity capturing in Volume-of-Fluid (VOF) method will work in any case, but some expensively, especially for high-order representation. Best regards

Muhammad Akram March 20, 1999 14:41

Re: discontinuity detection
As I understand the problem is that of detecting shock and interface discontinuties during the computation. If you are solving in Lagragian (reference) description with shock fitting then no problem you always know where these discontinuties are. In Eulerian description they are a bit difficult to track. In this case for shock wave: look for the pressure as well as pressure gradient maxima. The shock is located where both coincide. For material interfaces you can look for maximum density gradients. A small routine can do it. But interfaces are always difficult to track in Eulerian description.

linhbao tran March 21, 1999 15:43

Re: discontinuity detection
at last...someone understood. you mentioned the shock is located where both presure and pressure gradient maxima coincide, yes, but in a computation, there's errors and it's not so easy...i think looking into maximum entropy is probably on way. i've read somewhere..have to go back and check.

Muhammad Akram March 22, 1999 13:49

Re: discontinuity detection
May be you are right. I told you my experience. Now I recall something more straight forward and easy. The shock front is located in your computational domain where the local acceleration a_i+1/2 = (p_i+1 - p_i)/((rho_i+1/2)(x_i+1 -x_i)) is maximum. Please look into the book "Numerical Simulation of reactive flow" by Oran and Boris, Elsevier, 1987.

Muhammad Akram March 23, 1999 13:59

Re: discontinuity detection
... and about material interface look for maximum density gradient in the domain where pressure gradient is zero (pressure is continous across interfaces).

K. Sundar March 23, 1999 21:15

Re: discontinuity detection

If you are looking at "entropy criterion" for designing schemes which are used for capturing shocks and contact discontinuities, you can refer to papers by Harten in Journal of Computational Physics on Total Variation Diminishing schemes.

The essential idea is at the discontinuity (shock), the entropy maximises. Some numerical schemes exploit this concept to design the numerical algorithm (TVD schemes).

The contact discontinuity, for such schemes would appear as an expansion shock, (which is obviously unphysical) and so the thermodynamic entorpy criterion is enforced to obtain the physical solution.

Several other papers notably by H. C. Yee have been published in J. Comp. Phy. Vols (58- 80 range)

You can also refer to Ch Hirsch (Text book) for a discussion on the entropy criterion.



ThoLi March 24, 1999 13:06

Re: discontinuity detection

the following paper describes a shock indicator:

U. Göhner, G. Warnecke: A Shock Indicator for Adaptive Transonic Flow Computations. Numer. Math. 66 (1994) 423-448.

the indicator is used to move nodes exactly on the shock-line to reduce blurring.

This article uses a potential flow (instead of velocity and pressure).

You can find more information about the second author at G. Warnecke's Curriculum vitae.



Dan Williams March 24, 1999 21:46

Re: discontinuity detection
>at last...someone understood. you mentioned the shock is >located where both presure and pressure gradient maxima >coincide, yes, but in
>a computation, there's errors and it's not so easy...i >think looking into maximum entropy is probably on way. i've >read somewhere..have
>to go back and check.

You can get very sophisticated and use things like VOF to get contact discontinuities, and shock tracking for shocks.

However, if you just have a regular old Euler code, gradient detection algorithms work fine. I used this approach in my own work, for tracking detonations, and had no real problems.

The main drawback is that checking for large gradients is a little crude, only works well for simple shock structures. More complex flow structures require a lot of tuning and fiddling around before the tracking works well. Deep down, I never really liked it all that much, but still, it worked fine for me at the time.

Dan W.

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