# FEM EquationFlux

Other languages:  Flow equation Heat equation FEM  FEM EquationFlux

Solve → Flux equation
Workbenches
FEM
Default shortcut
None
Introduced in version
0.17
None

This equation is used to calculate the fluxes resulting usually from Poisson kind of equations. These include the Heat equation and the Electrostatic equation.

For info about the math of the equation, see the Elmer models manual, section Flux Computation.

## Usage

1. After adding an Elmer solver as described here, select it in the tree view.
2. Either use the toolbar button or the menu Solve → Flux equation.
3. Now either add a heat equation (toolbar button or menu Solve → Heat equation) or an electrostatic equation (toolbar button or menu Solve → Electrostatic equation). This is important because the flux equation needs the constraints set for these equastions.
4. When using the electrostatic equation, change the property DataFlux Coefficient to None. and the property DataFlux Variable to Potential.
5. Change the equation's solver settings or the general solver settings if necessary.

## Solver Settings

For the general solver settings, see the Elmer solver settings.

The flux equation provides these special settings:

• DataAverage Within Materials: If true, continuity is enforced within the same material in the discontinuous Galerkin discretization using the penalty terms of the discontinuous Galerkin formulation.
• DataCalculate Flux: Calculates the flux vector.
• DataCalculate Flux Abs: Calculates the absolute of the flux vector. Requires that DataCalculate Flux is true.
• DataCalculate Flux Magnitude: Computes the magnitude of the vector field. Requires that DataCalculate Flux is true.
Basically it is the same as DataCalculate Flux Abs but this requires less memory because it solves the matrix equation only once. The downside is that negative values may be introduced.
• DataCalculate Grad Magnitude: Computes the magnitude of the vector field. Requires that DataCalculate Grad is true.
Basically it is the same as DataCalculate Grad Abs but this requires less memory because it solves the matrix equation only once. The downside is that negative values may be introduced.
• DataDiscontinuous Galerkin: For discontinuous fields the standard Galerkin approximation enforces continuity which may be unphysical. As a remedy for this, set this property to true. Then the result may be discontinuous and may even be visualized as such.
• DataEnforce Positive Magnitude: If true, the negative values of the computed magnitude fields are set to zero.
• DataFlux Coefficient: Name of the proportionality coefficient to compute the flux.
• DataFlux Variable: Name of the potential variable used to compute the gradient.

## Constraint Information

The flux equation does not have own constraints. It takes the constraints from the Heat equation or the Electrostatic equation.

## Results

The available results depend on the solver settings. If none of the DataCalculate * settings was set to true, nothing is calculated. Otherwise also the corresponding results will be available.

The resulting flux is either the heat flux ${\rm {W/m^{2}}}$ (misleadingly named "temperature flux") or the potential flux in ${\rm {W/m^{2}}}$ (${\rm {A\cdot V/m^{2}}}$ ).  Flow equation Heat equation FEM 