Although COMSOL Multiphysics typically solves models using the finite element method, the software accommodates other numerical methods as well. In transport problems in which convection or migration are large compared to diffusion, the finite volume method can provide superior stability while also ensuring conservation of flux between elements.  To take advantage of this, COMSOL offers finite volume formulations in the Plasma Module and Semiconductor Module, where strong electric fields can sometimes cause convergence difficulties when using the finite element method.  In such cases, setting the discretization to “Finite volume (constant shape function)” can help to avoid solver failure due to the development of instabilities during the solution process. See setting below.

It is also possible to implement a finite volume method for a user-defined equation using the PDE interfaces.  In this method, the flux rather than the dependent variable is continuous across element boundaries.  To set up a finite volume problem, the user can set the element type to Discontinuous Lagrange with a constant shape function.  The flux between elements can then be specified using the Weak Contribution on Mesh Boundaries feature.  Since the solution is computed for each element rather than at the element vertices, any Dirichlet boundary conditions must be implemented by applying suitable flux terms on the relevant boundaries. See setting below.

We thank Luke Gritter for this Tip & Trick. Luke is one of our Research Engineers, and has been instrumental in the development and application of multiphysics analysis to real world problems in the Medical Products, Consumer Products, Semiconductor Devices and Energy markets.

More to come...

Jeff & Kyle

Principals