How Can Surface Evolver Software Help in Solving PDEs?

[alokgautam]

Hello friends please attached file to see my problem

 

[gato_]

First term is actually the expression for mean curvature (H(z(x,y))) for a local patch. your equation reads:
H-z/c=0
(is that a bubble subject to gravity?) that said, I think you might better try an axysimmetric solution first, z(r), as your forcing (z/c) does not depend on x or y.
\frac{z_{,rr}}{(1+z_{r}^{2})^{3/2}}+\frac{z_{,r}}{r(1+z_{,r}^{2})^{1/2}}-z/c=0
this is an ODE (a though one). You should add your conditions, depending on wether the surface is closed (periodicity) or open (contact angle somewhere). Finding equilibrium configurations of free surfaces is not easy!

 

[alokgautam]

Hi,
Thanks for reply and help
Yes you are write this first term is mean curvature.
For axysimmetric this become Second order differential equation that is easy to solve. I already did that part now I am looking for 3D system. If u can help in the derivation of this equation that will be very helpful for me for me.
Is there any site in which the derivation of this equation is given.
Rest is fine
Take care
alok

First term is actually the expression for mean curvature (H(z(x,y))) for a local patch. your equation reads:
H-z/c=0
(is that a bubble subject to gravity?) that said, I think you might better try an axysimmetric solution first, z(r), as your forcing (z/c) does not depend on x or y.
\frac{z_{,rr}}{(1+z_{r}^{2})^{3/2}}+\frac{z_{,r}}{r(1+z_{,r}^{2})^{1/2}}-z/c=0
this is an ODE (a though one). You should add your conditions, depending on wether the surface is closed (periodicity) or open (contact angle somewhere). Finding equilibrium configurations of free surfaces is not easy!

 

[gato_]

Except for a few particular cases, this is a difficult kind of problem to solve. Try here, for a software specifically designed for it
http://www.susqu.edu/facstaff/b/brakke/evolver/evolver.html

 

[alokgautam]

Dear Friend,
Thank you very much.
I will try this surface evolver software.
rest is fine
take care
Alok

Except for a few particular cases, this is a difficult kind of problem to solve. Try here, for a software specifically designed for it
http://www.susqu.edu/facstaff/b/brakke/evolver/evolver.html