Elmer Multiphysics

Elmer is an open-source multiphysics FEM solver developed by CSC (the Finnish IT Center). It supports coupled analysis of heat, fluid, electromagnetic fields, structures, acoustics, etc. It is used via a combination of ElmerGUI and ElmerSolver.

Expressing this in mathematical form, it looks like this.

Thermal-electrical coupling:

The numerical solution methods for Elmer multiphysics are based on the Finite Volume Method (FVM) or the Finite Element Method (FEM). Being open-source, its greatest advantage is the ability to examine and modify algorithm details at the source code level. Discretization schemes and convergence criteria logic, which are black boxes in commercial solvers, can be directly verified, making it particularly suitable for academic research and method development. Continuous improvement and bug fixes by the community ensure its quality.

Depending on the type of open-source license (GPL, LGPL, Apache, BSD, etc.), obligations for publishing modified code and restrictions on commercial use differ. It is recommended to check the license terms before using it in a project and to consult with the company's legal department in advance. Also consider the handling of derivative works and the possibility of dual licensing.

Explains the theoretical foundation of numerical methods implemented in open-source CAE tools.

The principle of minimum potential energy, fundamental to structural analysis:

The displacement field $\mathbf{u}$ that makes $\Pi$ stationary is the equilibrium solution. CalculiX and Code_Aster implement the Galerkin method based on this variational principle.

The FVM adopted by OpenFOAM is based on the integral conservation law for a control volume:

Discrete equations are obtained by applying this integral form to each control volume and numerically evaluating the fluxes on the faces.

Because the source code of open-source CAE is public, algorithm verification by third parties is possible. On the other hand, there is no vendor support like with commercial tools, so information sharing within user communities and forums is important.

• Results from OSS tools should always be verified with known benchmark problems.
• Be aware of incompatibilities between versions (especially differences between forks of OpenFOAM).
• It is recommended to confirm the accuracy of OSS by comparing results with commercial tools.
• When documentation is lacking, direct reference to the source code may be necessary.

Understanding the dimensionless parameters governing the physical phenomenon being analyzed is the foundation for appropriate model selection and parameter setting.

• Peclet Number Pe: Relative importance of convection and diffusion. Pe >> 1 indicates convection dominance (stabilization methods are needed).
• Reynolds Number Re: Ratio of inertial forces to viscous forces. A fundamental parameter for fluid problems.
• Biot Number Bi: Ratio of internal conduction to surface convection. For Bi < 0.1, the lumped capacitance method is applicable.
• Courant Number CFL: Indicator of numerical stability. For explicit methods, CFL ≤ 1 is required.

For order-of-magnitude estimation of analysis results, dimensional analysis based on Buckingham's Π theorem is effective. Using characteristic length $L$, characteristic velocity $U$, and characteristic time $T = L/U$, estimate the order of each physical quantity beforehand to confirm the validity of the analysis results.

Choosing appropriate boundary conditions is directly linked to the uniqueness and physical validity of the solution. Insufficient boundary conditions lead to an ill-posed problem, while excessive boundary conditions cause contradictions.

Yeah, you're doing great! Actually getting hands-on is the best way to learn. If you don't understand something, feel free to ask anytime.

Explains the key points of numerical methods and implementation for Elmer multiphysics.

Building from source code uses CMake or dedicated build systems (like wmake for OpenFOAM). Proper version management of dependency libraries (MPI, PETSc, BLAS/LAPACK, etc.) is important. Linux environments are recommended, but using WSL2 or Docker containers makes it possible to build on Windows as well.