Hello everyone.
It's about the level set method. So, I have defined the value of phils as 0 and 1 as shown in the attached figure. The interface is at phils =0.5 (automatically).
I want to define the Heaviside function(Smooth function) in terms of interface thickness. My interface thickness is 0.013mm.
Values of phils (0 or 1) are domain-driven but 0.5 is at the interface. When phils is 0.5, it means its acted on the interface.
How can I define this Heaviside function using piecewise function or if there is any other way?
Probelm: Suppose if I use a piecewise function, what would be my "start" and "end" point. Please see the attached figure. Bec at phils= 0.5, its the whole domain, how can I define start and end point on this.
Looking forward to your replies.
In LSM, usually the distance function is adopted, but this may lead to area/volume conservation issues. Using the Heaviside function in its "rough" version is not suggested due to problems of numerical robustness. Instead, a smeared Heaviside function is adopted and its depends on the interface thickness, epsilon.
If we call Phi the level set function, then:
H(Phi)=[0, if Phi
Luigi Candido : Thank you for your reply. I got few basic questions:
1) In every paper where this formula is being used, phi is zero at the interface(it means, phi is 0 in condesed phase).
In my case phi is 0.5 at the inteface (it means, 1 in condensed phase and 0 in vopour as shown in my post). I am not sure if I can use the limits you have mentioned for my case. Please help me with it .
Well, at the interface the level set variable is equal to 0.5, see the image attached @Akash Meena
Luigi Candido :Thank you. Let me explain if I get this right. The picture you sent considers phi =0 and the lines of different colours represent episilon aka thickness of the interface.
In my case, phi is 0.5. So, what will be my limits for the following formula:
(1/2+Phi/2epsilon+1/2pi*sin(pi*Phi/epsilon), if -epsilon
Wolfgang Reichl
: Thank you for your comment. I wan to write Heaviside function as seen in the attached figure below but it is wrriten when level set variable(phils) is zero at the interface.In my case, phils is 0.5 at the interface. This part confuses me. How can I write the limits in my case. Limit is from -epsilon to epsilon for the "sin" formula. I am wondering what it could be in my case ?
Wolfgang Reichl
: Thanks Man. One last questions just to confirm::Can I use conditions based equations as in attached figure??
Akash Meena If you have to implement a level set method in COMSOL you can take advantage by using the interface Level Set
Wolfgang Reichl
: Thank you. I will try to impemement it.Luigi Candido : Yup/ I have used the level set physics itself. Yes, I am using the interface variable to define the heaviside function.
It's not clear to me what you want to do. In the LSM implemented in comsol the smeared heaviside function is already implemented, you just need to put the value of epsilon and the value of the reinitialization parameter. You give the location of the interface by selecting the corresponding boundary or surface
Luigi Candido : Oh. It applied automatically ? I read in few papers that they have to apply separately. I might be wrong though. Not sure.
Wolfgang Reichl
: Don't you think, the limits would be : Psi : [ 0.5-eps, eps + 0.5](not from> eps-0.5)
In the interface of the tree you have to simply put the value of epsilon (or you can allow comsol to use its default value calculated as half of the maximum of the mesh characteristic size near the interface) and to select the boundary or surface where to apply it.
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