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tikes July 26, 2001 10:47

Arbitrary Lagrangian-Eulerian (ALE) Method
Hi guys, I am hoping to wtite a CFD code for oscillating solid-liquid interface problem. Well, probably I could use an existing software, like FLOTRAN, but I prefer to write the code myself. Going through the literature I found that people usually use the ALE method for this type of problems. Unfortunately the published papers do not have enough information so that one could write the code himself.

If any of you are aware of where I can get more detail information regarding the ALE method for incompressible viscous flows please let me know. Any information regarding this will be highly appreciated. T (

Eddy July 26, 2001 21:50

Re: Arbitrary Lagrangian-Eulerian (ALE) Method
I am also intersted in this method, but I have not found time to try. Which method will you use for solving fluid? Finite volume or finite element? For finite volume method, Shyy's papers should be good references. For finite element, there are a lot of papers can be found.

ALE is nothing but solving NS equations in moving coordinate system. This will yields additional grid velocities in convective iterms. These equations can be derived by performing time transform on normal NS equations. However, do not forget GCL.

Good luck.

Apurva Shukla July 27, 2001 07:54

Re: Arbitrary Lagrangian-Eulerian (ALE) Method

Here are some references, hope they may be of some use.




Hirt,C.W.,Amsden,A.A.,Cook J.L.,"An Arbitrary Lagrangian Eulerian Computing method for all Flow speeds",JCP,Vol 14,227-253.(1974) --> A Landmark Paper --------------------------------------------------------------------------

R.K.-C.Chan,"A Generalized Arbitrary Langrangian Eulerian method for incompressible flows with sharp interfaces", JCP, Vol 17, pp 311-331. (1975) --------------------------------------------------------------------------

Pracht,W.E.,"Calculating Three Dimensional Fluid flows at all speeds with an Eulerian Langrarian Computing Mesh", JCP, Vol 17, pp 132-159. (1975) --------------------------------------------------------------------------

Donea.J.,"Arbitrary Lagrangian Eulerian Finite Element methods", in T.B.Belytschk and T.J.R.Hughes(eds), Computational Methods for Transient Analysis, 1983, pp 474-516. --------------------------------------------------------------------------

Ramaswamy B., Kawhara,M.,Nakayam,T.,"Lagrangian Finite Element Method for the analysis of two dimensional sloshing problems",IJNMF, Vol 6, pp 659-670. (1986) --------------------------------------------------------------------------

Ramaswamy B.,Kawhara,M.," Arbitrary Lagrangian-Eulerian Finite Element Method for unseady,convective,incompressible viscous free surface fluid flow", IJNMF, Vol 7, pp 1053-1075. (1987) --------------------------------------------------------------------------

Hughes T.J.R., Lin W.K., Zimmerman T.,"Lagrangian-Eulerian Finite Element formulation for incompressible viscous flow", Comput. Meth. Appl. Mech. Engg., Vol 29, 329-349. (1987) --------------------------------------------------------------------------

Lin W.K.,Chang H.,Chen J.S. and Belytschko.T,"Arbitrary Lagrangian Eulerian Petrov-Galerkin Finite Elements for Nonlinear continua", Comput. Meth. Appl. Mech. Engg., Vol 68, pp 259-310. (1988). --------------------------------------------------------------------------

Okamoto,T.,"Two Dimensional Sloshing analysis by Lagrangian Finite Element Method",IJNMF,Vol 11,453-477. (1990) --------------------------------------------------------------------------

Ramaswamy,B.,"Numerical Simulation of unsteady viscous free surfaceflow", JCP, Vol 90,pp 396-430. (1990) --------------------------------------------------------------------------

Ushijima,S.,"Arbitrary Lagrangian Eulerian numerical prediction for local scour caused by turbulent flows",JCP, Vol 125,pp 71-82. (1996) --------------------------------------------------------------------------

Ushijima,S.,"Three Dimensional Arbitrary Lagrangian Eulerian Numerical Prediction for Non Linear Free surface Oscillation",IJNMF,Vol 26, 605-623. (1998) -------------------------------------------------------------------------

tikes July 27, 2001 17:35

Re: Arbitrary Lagrangian-Eulerian (ALE) Method
Hi Eddy, I was thinking of using the Finite Element method just because there are more published papers on it. But I am also open to Finite Difference or Volume method if I can find a good reference for incompressible NS.

btw, could you please list a few of Shyy's papers that deal w/ ALE and FV method. And, what is GCL?

I appreciate your response. thanks -t

tikes July 27, 2001 17:49

Re: Arbitrary Lagrangian-Eulerian (ALE) Method
Hi Apurva, thank you very much for listing the references. I have some of these and gonna check the other ones.

Actually, I have quite a few references on the ALE technique. But unfortunately they tell little about the computational part. What I need is a more detail description on the numerical algorithm so that I can write the major part of the code mysef.

I appreciate your kind response. thanks -t

Dean July 28, 2001 13:41

Re: Arbitrary Lagrangian-Eulerian (ALE) Method
You might find information on the numerical methods, including code listings, in some reports written by Group T-3 at Los Alamos National Laboratory. These should be available on the Department of Energy Information Bridge (OSTI). You can search by code name, and the relevant ones are YAQUI, BAAL, SALE, CONCHAS, and KIVA. Some of the authors are A. A. Amsden, T. D. Butler, L. D. Cloutman, J. D. Ramshaw, P. J. O'Rourke, and H. M Ruppel. Sorry I don't have the report numbers or titles. Some of these may still be available in hard copy from T-3, and their Web site is

Hope this helps.

John C. Chien July 28, 2001 14:42

Re: Arbitrary Lagrangian-Eulerian (ALE) Method
(1). Assuming that he is rich and has plenty of time to do research in the "jurasic park". (2). I once had a copy of YAQUI report, and I thought it was bigger than a dinosaur. So, I decided to go my own way many years ago. (3). National labs like big dinosaurs, or big companies, are disappering. (not because of wen-ho lee case or outdoor wild fire, but because of its size and man-made complexity. )

Dean July 29, 2001 13:58

Re: Arbitrary Lagrangian-Eulerian (ALE) Method
John, why the hostility toward the national labs? The original question from tikes was for details about how to code the ALE method, and for better or worse the most detailed information I know about is in those ancient reports. That doesn't mean that those methods are the best (they do have some serious limitations), but for someone starting out in CFD, reading this old work can be useful if for no other reason than as examples of how relatively simple methods can be implemented. As for your comment about the disappearance of the national labs and big business, your are welcome to your opinion but it isn't relevant.

John C. Chien July 30, 2001 05:40

Re: Arbitrary Lagrangian-Eulerian (ALE) Method
(1). "You can search by code name, and the relevant ones are YAQUI, BAAL, SALE, CONCHAS, and KIVA. " (2). Beyond the name search, have you actually read and studied each one of the codes cited? (3). If so, what was your experience in reading these codes? (4). How long does it take to read the code from YAQUI to KIVA?

Dean July 30, 2001 12:16

Re: Arbitrary Lagrangian-Eulerian (ALE) Method
Actually, I have used and modified two of those codes, and you raise a valid point about how long it takes to get familiar with what the coding really does. I would guess that for tikes purposes, it would take only a few hours to read one of these reports, which contains all the difference equations, and then check the listing if there is any question about those equations, or to see if some "trick" was put in the code that was not mentioned in the text. I wouldn't recommend reading a listing as a way to understand a numerical method, although I have met a couple of individuals who seemed to be able to do that with ease. The reports I mentioned are just another resource that each person is free to use (or not) as they see fit.

I would recommend that anyone who chooses to read these reports also read some of the more recent literature as a lot of important improvements have been made to ALE methods since the "Jurassic Park" days when those reports were written. The engine research group at the University of Wisconsin has a nice web site on their latest version of KIVA:

tikes July 31, 2001 10:32

Re: Arbitrary Lagrangian-Eulerian (ALE) Method
Hi Guys, thanks for your inputs. I appreciate it.

Regards, tikes

cacootl October 1, 2013 05:05

Hello tikes,

I just wanted to know if you were sucessful in your attempt, since I am currently working on a similar project.


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