How Can Surface Evolver Software Help in Solving PDEs?

  • Context: Graduate 
  • Thread starter Thread starter alokgautam
  • Start date Start date
  • Tags Tags
    Pde
Click For Summary

Discussion Overview

The discussion revolves around the use of Surface Evolver software in solving partial differential equations (PDEs) related to mean curvature and free surface configurations. Participants explore the mathematical formulation of the problem and seek assistance in deriving equations for a three-dimensional system.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Exploratory

Main Points Raised

  • One participant identifies the first term in the equation as the expression for mean curvature and suggests an axisymmetric solution, proposing a specific form of the equation.
  • Another participant confirms the identification of the mean curvature and mentions having solved the axisymmetric case, expressing interest in deriving the equation for a 3D system.
  • A participant notes the complexity of the problem, indicating that it is generally difficult to solve except for particular cases, and recommends the Surface Evolver software as a potential tool for this type of problem.

Areas of Agreement / Disagreement

Participants generally agree on the complexity of the problem and the relevance of mean curvature in the context of the equations discussed. However, there is no consensus on the specific methods or solutions to be employed, as different approaches are suggested.

Contextual Notes

The discussion highlights the need for boundary conditions and the distinction between closed and open surfaces, which may affect the problem's complexity and the applicability of solutions.

Who May Find This Useful

This discussion may be useful for individuals interested in computational methods for solving PDEs, particularly in the context of free surface problems and mean curvature applications.

alokgautam
Messages
8
Reaction score
0
Hello friends please attached file to see my problem
 
Last edited:
Physics news on Phys.org
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!
 
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




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


gato_ said:
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
 

Similar threads

Graduate Solving System of PDEs: Analytical Methods & Solutions
  • · Replies 9 ·
Replies
9
Views
4K
Undergrad Stuck on solving a non homogenous (linear) PDE
  • · Replies 36 ·
2
Replies
36
Views
6K
Graduate Generic Solution of a Coupled System of 2nd Order PDEs
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad 1D time dependent PDE - using orthogonal collocation
  • · Replies 2 ·
Replies
2
Views
4K
Undergrad Can FDM solve any type of PDE same as FEM?
  • · Replies 13 ·
Replies
13
Views
3K
MHB How Do You Write a PDE in Terms of x and y?
  • · Replies 3 ·
Replies
3
Views
2K
MHB Problem 13 from section 16.1 of Taylor's PDE textbook.
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Deep Learning the new key to nonlinear PDEs?
  • · Replies 2 ·
Replies
2
Views
2K
Graduate How to solve simple 2D space-time PDE numerically
  • · Replies 5 ·
Replies
5
Views
3K
Looking for resources to help me understand the basics of PDEs for physics
  • · Replies 5 ·
Replies
5
Views
2K