EOF-Library is open-source coupling library for Elmer FEM and OpenFOAM simulation packages. A combination of all three results in very capable multiphysics modelling software.

Main applications

Multiphysics modelling software EOF-Library - CFD coupled with electromagnetics
Any combination between OpenFOAM and Elmer FEM solvers is possible.


Most multiphysical problems on complex geometries are solved using the finite element method (FEM) and the finite volume method (FVM). The availability of high-quality FEM and FVM solvers combined with pre and postprocessing tools make them very popular.

Why EOF-Library exists?

The initial application for the EOF-Library was magnetohydrodynamics (MHD) with free surface modelling of various industrial applications. When we started development of EOF-Library in 2016, we were not able to find any other open-source tool that could solve such type of problems.


In principle, one could model multiphysics problems within a single framework by using either FEM or FVM.

In practice, FEM dominates in structural mechanics and electromagnetics, while FVM is preferred for computational fluid dynamics (CFD). FEM has the freedom to choose the order of basis functions, and for electromagnetics, FEM can make use of curl conforming edge elements allowing vector-potential continuity for tangential component and jumps for the normal component. On the other hand, FVM is easier to implement for CFD. In advection dominated transient fluid flows, especially highly turbulent ones, FVM is more robust and is therefore used more frequently than FEM.

Looking for alternative?

Here we will briefly discuss possible MHD modelling alternatives to our software, how it differs and when you should consider it.


  • OpenFOAM’s mhdFoam solver in our opinion has one major limitation – the user cannot set electric field or current density. This limits solver to applications with simple geometries and pre-defined magnetic field distributions such as Hartmann flow.
  • All other codes are developed mostly for academic and astrophysical applications in mind.


  • COMSOL Multiphysics® with AC/DC and CFD modules is a very capable alternative to EOF-Library. From our experience, it has convergence problems for high turbulence flows and is generally slower for transient (time-dependent) CFD than OpenFOAM.
  • ANSYS FLUENT Magnetohydrodynamics Module – very powerful CFD software with basic electromagnetics modelling capabilities. For example, there is no complex notation for time-harmonic fields therefore limited to low electromagnetic frequencies. Check documentation for a full explanation.
  • Tech-X USim – software for plasma MHD problems, not applicable to metallurgical applications.

Working principle

EOF-Library enables efficient internal field interpolation and communication between the finite element (FEM) and the finite volume frameworks (FVM). The coupling of the two packages is based on the Message Passing Interface (MPI), which results in low latency, high data bandwidth and parallel scalability.

Visit Research page to learn more about EOF-Library!