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Problem on high density ratio in Level Set method 

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December 21, 2007, 08:37 
Problem on high density ratio in Level Set method

#1 
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Level Set method is not robust in the case of high density ratio. Many modified approaches for Level Set method have been proposed for this reason.
I want to know why Level Set method is not robust in the case of high density ratio. Would you help me? My understanding is that the problem can be solved if the values of density at faces of control volumes are as accurate as possible. I am not sure my understanding is right. Maybe there are some other causes on the issue. Would you give me a detailed statement for this issue? 

December 23, 2007, 17:19 
Re: Problem on high density ratio in Level Set met

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The pressure is sensitively influenced by the density. Thus, the small amount of density change may cause large pressure variation.
To avoid these errors, we would rather use a sharp interface method. How about the Ghost Fluid Method? It was good for chapturing gaswater compressible flows in my applications. 

December 24, 2007, 02:15 
Re: Problem on high density ratio in Level Set met

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Thanks for your response!
My research is mainly for incompressible fluid flow. Most of modified approaches for Level Set is to calculate face values of grids more accurately. Of course the influence of bulk density on pressure can not be ignored. For incompressible fluid flow, Would you give some more advice for the cause of high density ratio problem? 

December 24, 2007, 04:21 
Re: Problem on high density ratio in Level Set met

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kai,
>Level Set method is not robust in the case of high density ratio it's not correct, take care in ur speech, level set is an interface tracking method not fluid flow solution algorithm, so is not affected by high density ratio. u pass a known velosity and distance field to LS and its return its time evolution. The main known problem of LSM is mass loss which has its own treatment. but, (i guess) what u mean is related to variable density incompressible fluid flow solution which suffer from illposness due to high density ratio and has problem in the presence of high surface tension, without attention to method of interface tracking: VOF, ITM, LSM, ... main problem is related to solution of pressure equation > My understanding is that the problem can be solved if ... if u state ur problem in more details, maybe i could help. 

December 24, 2007, 07:56 
Re: Problem on high density ratio in Level Set met

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How about using the smoothed Heaviside function method with the LSM? In the book titled 'The immersed interface method' written by Zhilin Li, there is a part saying about it. Please see pp. 813.
I hope you enjoy with that method. 

December 24, 2007, 09:34 
Re: Problem on high density ratio in Level Set met

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Firstly thanks for responses of jinwon park and rt at Christmas eve.
To jinwon park: Thanks for recommend me the book section. But I can not access to the book. In fact, My attention is not the smoothed Heaviside function itself. The present approaches to modified Level Set Method seem to be not for the smoothed Heaviside function, but for improving the accuracy of values near interfaces. However, there seem to be no literatures having a clear and profound statement on the problem. To rt My research work has a relation, to some extent, to gas/liquid interface. I just very interested in the problem. What dose "main problem is related to solution of pressure equation" mean? Do you give me a more detailed explanation about it? Dose it mean that pressure is sensitive? 

December 24, 2007, 10:14 
Re: Problem on high density ratio in Level Set met

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> Firstly thanks for responses of jinwon park and rt at Christmas eve.
our native annual holiday and start of new year is start of Spring not "Christmas" (i do not know how is usefulness of holidays at the heart of winter!) > What dose "main problem is related to solution of pressure equation" mean? do u man that, u r begineer in this field and did not have any numerical experiment? i assume this. so do not distict between level set and other methods, and betterly talk about simulation of incompressible two phase flow with a sharp interface. there are some review paper which are useful to view E.G.: S. Zaleski (annual rev. fluid mech. 98, i have ecopy if u do not access), another due to G. Trywasson (front tracking, see: http://www.me.wpi.edu/Research/MFG/Papers/) or recent paper by Uzgoren et. al : Progress in Aerospace Sciences 43 (2007) 138โ"192 (it is very nice for implementation of advanced methods), ... in brief: one problem is due to large density ratio which leads to jump in coefficients of possion equation (solution of pressure). This leads to illposeness and so we needs rubost iterative solver or efficient direct solver. another problem is due to artifact ossilation in the vicinity of interface when surface tension be high. treatments: Ghost fluid method (see Fedkiw publications in JCP), sharp interface methods (e.g. Udaykumar JCP), discontinous fluid method (ACM TOG), ... another treatment for gas/liquid flow is to distinguish two phases based on physics and treat liquid as a incompressible phase drived by NS equation and gas phase as a compressible phase governed by ideal gas law eg. one of the beautiful work in this filed is: Hao and Prosperetti (JCP 2004). finally irecommed VOF method if u do not need high accuracy of surface tension computation. in this regard Gerris flow solver is a powerful opensource (adaptive, octree, cartesian with immersed bc for complex geomeries). hope this helps. 

December 24, 2007, 22:38 
Re: Problem on high density ratio in Level Set met

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Is Spring Festival important to you? It is to me.
I can access to the 2 papers you have recommended. Interface is not my major work. I just choose a proper method for my research and employ it. I prefer conservative Level Set Method(see paper "A conservative level set method for two phase ๏ฌow", Olsson, 2005, Journal of Computational Physics). After all, conservation is very important for gasliquid twophase flow. Conservation is primary. Your brief explanation will help for me. I have explored the wellposeness of twofluid model. The NS equations in Level Set/VOF is a special form of twofluid model when velocities of two phases are equal. It seems that wellposeness has no relation to density ratio. And the addition of surface tension helps to avoid illposeness. This seems not to accord to your opinion. Would you explain me more about this? 

December 25, 2007, 04:05 
Re: Problem on high density ratio in Level Set met

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first, i do not exactly know what u look for !
> I prefer conservative Level Set Method why? LS+ mass conservation is difficult (is really intrinsic limitation of numerical treatment of LS), if u look at literature, none of formal level set methods could compete with a formal PLIC VOF methods in terms of mass conservation. Usually you need spacetime high order method (TVD RK + WENO) + high grid resolution to preserve mass conservation. Some new treatments are: addition of hybrid particle for reinit (particle level set Fedkiw JCP which is memory and cpu intensive), or tree based level set countoring of J. Strain (3paper in JCP for 2D and one paper in ACM TOG for 3D) which is difficult to implement. There are also some variational LS methods (has similarity with phasefiled method) that do not need reinitialization. Another attractive method which is climed to be conservative and very accurate and "time step free" (CFLfree) is CIP family methods by Yabe and Xiao. They are algebraic like level set (and so easy to implement unlike geometric nature of PLIC VOF). >It seems that wellposeness has no relation to density ratio really? what is ur defenition from illposeness? i mean illposeness of poisson equation, solution of pressure equation, which is known and was stated in most of related literuature (is not my opinion), large density ratio = jump in coefficient matrix of poisson eq. = increase condition number = illposeness (has completely mathematical side ). In sharp interface methods or other new gasliquid methods (rather than variable density method), peoples tried to impose decoupling at the interface, simply it can be said that pressure eq. of gas is decoupled (completely or weakly) from the liquid phase and so we do not have previous pressure jump and illposeness. >And the addition of surface tension helps to avoid illposeness. in this regard, i mean physical illposeness that leads to sporious ossilation in the vicinity of interface which is a known phenomena too. what u mean from illposeness, robustness of solver ... ? and what u like to disscuss about? 

December 25, 2007, 05:16 
Re: Problem on high density ratio in Level Set met

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In fact, I have posted this thread just for the reason why Level Set may not work well in the case of high density ratio.
However we have turned to some other issues during the discussion. About well poseness, I mean that there are no complex eigenvalues for a partial differential equation system, which may be different from yours. I guess you are in China and very familiar with this field. Would you send me your email for deeper discussion? There are some other questions on this issue. My email is yka8150@gmail.com. 

December 25, 2007, 06:12 
Re: Problem on high density ratio in Level Set met

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> I guess you are in China
no, i am in Iran, my id: rohtav@gmail.com u'r wellcome to disscosion around this concept! >I have posted this thread just for the reason why Level Set may not work well in the case of high density ratio what is sign of this problem in ur result? do u have experience or only guess? > I mean that there are no complex eigenvalues for a partial differential equation system, which may be different from yours. this may be interesting for me, but i do not understand what u say. There r several doubt in this complex eigenvalues : do u mean presence of complex eigenvalue is sign of wellposeness? (ur Refs. ?) (precence of samll real and positive eigenvalue for a linear system, Ax=b, is a sign for wellpseness), if, how do you analyse this and how to conclude if density ratio be high leads to illpseness? 

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