FEM EquationFlux/ro

Description

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 boundary conditions set for these equations.
4. When using the electrostatic equation, change the property DateFlux Coefficient to None. and the property DateFlux 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:

• DateAverage 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.
• DateCalculate Flux: Calculates the flux vector.
• DateCalculate Flux Abs: Calculates the absolute of the flux vector. Requires that DateCalculate Flux is true.
• DateCalculate Flux Magnitude: Computes the magnitude of the vector field. Requires that DateCalculate Flux is true.
  Basically it is the same as DateCalculate Flux Abs but this requires less memory because it solves the matrix equation only once. The downside is that negative values may be introduced.
• DateCalculate Grad: Calculates the gradient of the flux.
• DateCalculate Grad Abs: Calculates the absolute flux gradient. Requires that DateCalculate Grad is true.
• DateCalculate Grad Magnitude: Computes the magnitude of the vector field. Requires that DateCalculate Grad is true.
  Basically it is the same as DateCalculate Grad Abs but this requires less memory because it solves the matrix equation only once. The downside is that negative values may be introduced.
• DateDiscontinuous 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.
• DateEnforce Positive Magnitude: If true, the negative values of the computed magnitude fields are set to zero.
• DateFlux Coefficient: Name of the proportionality coefficient to compute the flux.
• DateFlux Variable: Name of the potential variable used to compute the gradient.

Analysis Feature Information

The flux equation does not have its own boundary conditions. It takes the boundary conditions from the Heat equation or the Electrostatic equation.

Results

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

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