Adding a PDE Interface to a Component
To add a new Component and use one of the equation interfaces, start with the instructions in Creating a New Model. Then, when you are adding the physics, expand the Mathematics>PDE Interfaces node in the list of physics interfaces and select one of the PDE interfaces in the list. For PDEs on geometric entities other than domains, expand the Lower Dimensions node.
Specifying a System of Equations
COMSOL Multiphysics allows the creation of equations with more than one dependent variable. To do this, on the Add Physics page under Dependent variables, enter the Number of dependent variables in the field. The COMSOL software then automatically assigns variable names, typically u1, u2, u3, and so on. You can also edit the default variable name (as long as it is valid and unique) in the Dependent variables table. Several scalar PDEs can also be coupled using a multiphysics approach.
Modeling with PDEs on Boundaries, Edges, and Points
The Coefficient Form PDE, General Form PDE, and Weak Form PDE are also available on boundaries, edges, and at points in the geometry.
Extra weak equations can be added by adding auxiliary dependent variables to a Weak Contribution (PDEs and Physics) node. Use such weak form equations as a way to handle thin layers; COMSOL then solves the problem by modeling rather than meshing. This approach reduces the solution time.
See Transport and Adsorption (Application Library path COMSOL_Multiphysics/Chemical_Engineering/transport_and_adsorption) to learn how to use a General Form Boundary PDE interface to model a thin adsorption layer with diffusion as a PDE on the boundary of a convection-diffusion problem.
See Rock Fracture Flow (Application Library path COMSOL_Multiphysics/Geophysics/rock_fracture_flow) to learn how to use a Coefficient Form Boundary PDE interface to solve the Reynolds equation on a boundary in a 3D model.
See Shell Diffusion in a Tank (Application Library path COMSOL_Multiphysics/Equation_Based/shell_diffusion) for an example of tangential derivative variables.