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Solving PDE on a curved surface
Posted May 5, 2016, 11:34 a.m. EDT Parameters, Variables, & Functions, Studies & Solvers Version 5.2 1 Reply
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Hello All,
I'm trying to figure out whether I can use COMSOL to solve PDE on a curved surface. For example, diffusion of species on a 2D curved domain described by:
dC/dt = \Delta_S (C)
Here \Delta_S is the surface Laplace or Laplace-Beltrami operator. For simple surface geometry like a sphere or cylinder I figure I can use coordinate transformation to solve the problem on 2D Cartesian grid. But I'm wondering if there's a way to define the surface operator for arbitrarily shaped surface mesh so that I can solve the equation without doing coordinate transformation. Any leads on this are appreciated. Thanks in advance.
Regards,
Ming
I'm trying to figure out whether I can use COMSOL to solve PDE on a curved surface. For example, diffusion of species on a 2D curved domain described by:
dC/dt = \Delta_S (C)
Here \Delta_S is the surface Laplace or Laplace-Beltrami operator. For simple surface geometry like a sphere or cylinder I figure I can use coordinate transformation to solve the problem on 2D Cartesian grid. But I'm wondering if there's a way to define the surface operator for arbitrarily shaped surface mesh so that I can solve the equation without doing coordinate transformation. Any leads on this are appreciated. Thanks in advance.
Regards,
Ming
1 Reply Last Post May 5, 2016, 11:49 a.m. EDT
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Posted:
9 years ago
Absolutely. As you start a new file, in the Model Wizard, after selecting 3D for the dimension, on the "Select Physics" page you can select Mathematics > PDE Interfaces > Lower Dimensions, and then select between one of the three boundary formulations.
See Chapter 16 in the COMSOL Multiphysics Reference Manual, version 5.2 for more information on equation-based modeling.
Best,
Jeff
PS: For some cases, there are pre-implemented physics interfaces that you can take advantage of so you don't even have to enter the equations yourself. For instance the Electric Current, Shell physics interface available in the AC/DC Module essentially implements the surface Laplace operator you mentioned.
See Chapter 16 in the COMSOL Multiphysics Reference Manual, version 5.2 for more information on equation-based modeling.
Best,
Jeff
PS: For some cases, there are pre-implemented physics interfaces that you can take advantage of so you don't even have to enter the equations yourself. For instance the Electric Current, Shell physics interface available in the AC/DC Module essentially implements the surface Laplace operator you mentioned.