These examples give a fairly representative view on the capabilities of Elmer. The most important physical models are also explained briefly. Many of the examples are simple in geometry but this does not reflect any shortcoming of ElmerSolver. You may also download a brochure (pdf) of the capabilities of Elmer.

## Examples in various fields of physics

### Heat Transfer

In heat transfer Elmer includes convective, diffusive and radiative heat transfer.

### Solid mechanics

In solid mechanics Elmer includes general elasticity and reduced dimensional models, i.e. plates and shells. Orthotropic materials, damping and other complications may be accounted for.

### Fluid mechanics

In fluid mechanics Elmer includes Navier-Stokes equations for compressible and incompressible (low Mach number) flows. Stabilization is achieved by SUPG or residual free bubbles. Turbulence models include Spalart-Almaras, k-epsilon, (SST) k-omega, and v^2-f. For FSI-problems an ALE formulation is available also many different kinds of free surface models (Lagrangian and Eulerian) may be used. There is also a dimensionally reduced flow model, i.e. the Reynolds equation.

- Flow in a driven cavity (2D)
- Flow in a driven cavity (3D)
- Flow past backward facing step (2D)
- Flow past backward facing step (3D)
- Compressible flow - Von Karman Vortices
- Kelvin-Helmholtz instability-A LES Model
- Free surface between two non-mixing liquids
- Thermocapillary convection
- Water heating example (axisymmetric)
- A transient coupled flow and heat simulation in 2D
- Transient gas flow due to moving boundary
- Free surface flow with flux
- Falling 2D drop resolved with the level-set method

### Earth Science

### Electromagnetics

Electromagnetics mainly includes special cases of the Maxwell's equations that may be expressed in terms of scalar or vector potentials.

- Magnetic field induced by a current driven magnet
- Induction heating of an axisymmetric crucible
- Computation of capacitance
- Electrostatic force in 3D

### Acoustics

Acoustics includes Helmholtz equation with the possibility of convection and damping. Also dissipative acoustics in terms of linearized time-harmonic Navier-Stokes equations have been modeled with Elmer.

### Quantum mechanics

Quantum mechanics includes an all-electron version of the Kohn-Sham equations.

- Electron structure of the hydrogen atom
- Electron structure of the carbon monoxide molecule
- Electron structure of the Fullerine C60 molecule

### Coupled problems

Generally, most physical models in Elmer may be coupled with one-another. Therefore there is no point of summarizing the capabilities in coupled problems.

- Vibroacoustics
- Sound waves in closed cavity
- A simple fluid-structure-interaction example
- Fluid-structure-interaction by artificial compressibility
- Fluid-structure-interaction in hemodynamics
- Electrostatic-thermal coupling
- Sedimentation of rigid bodies
- Electrokinetic flow in case of thick EDL

## Examples of industrial applications

### Czochralski crystal growth

The growth of mono-crystalline silicon by the Czochralski method was one of the initial applications of Elmer and it still provides plenty of challenges.

- Global Heat Transfer in Czochralski crystal growth
- Silicon melt flow in Czochralski crystal growth
- Adaptive mesh refinement in crystal growth
- Argon Gas Flow in Crystal Growth
- Magnetic Czochralski crystal growth

### Simulation of micro-electro-mechanical (MEM) components

MEMS provides a nice field of multiphysical simulation. Elmer has been used to solve most coupling types in steady state, transient and time-harmonic systems.

### Optical fiber manufacturing

Fiber manufacturing provides also many interesting cases, particularly in the area of free surface problems.

### Nozzle flow

This example has been provided by an Elmer user who use the simulations to optimize the nozzle geometries.

## Examples related to numerical methods

### Linear algebra

After the equations are discretized the problem is reduced to the solution of linear equations. The main iterative method are Krylow subspace methods and multilevel methods which show different scaling with problem size.