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Flow equation

Heat equation

FEM

Description

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

Usage

1. Add an Elmer solver.
2. Select it in the Tree view.
3. There are several ways to invoke the command:
   • Press the Flux equation button.
   • Select the Solve → Flux equation option from the menu.
4. To include the required boundary conditions, do one of the following:
   • Invoke the FEM EquationHeat command.
   • Invoke the FEM EquationElectrostatic command.
5. When using an electrostatic equation, change the property ДанныеFlux Coefficient to None. and the property ДанныеFlux Variable to Potential.
6. 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:

• ДанныеAverage 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.
• ДанныеCalculate Flux: Calculates the flux vector.
• ДанныеCalculate Flux Abs: Calculates the absolute of the flux vector. Requires that ДанныеCalculate Flux is true.
• ДанныеCalculate Flux Magnitude: Computes the magnitude of the vector field. Requires that ДанныеCalculate Flux is true.
  Basically it is the same as ДанныеCalculate Flux Abs but this requires less memory because it solves the matrix equation only once. The downside is that negative values may be introduced.
• ДанныеCalculate Grad: Calculates the gradient of the flux.
• ДанныеCalculate Grad Abs: Calculates the absolute flux gradient. Requires that ДанныеCalculate Grad is true.
• ДанныеCalculate Grad Magnitude: Computes the magnitude of the vector field. Requires that ДанныеCalculate Grad is true.
  Basically it is the same as ДанныеCalculate Grad Abs but this requires less memory because it solves the matrix equation only once. The downside is that negative values may be introduced.
• ДанныеDiscontinuous 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.
• ДанныеEnforce Positive Magnitude: If true, the negative values of the computed magnitude fields are set to zero.
• ДанныеFlux Coefficient: Name of the proportionality coefficient to compute the flux.
• ДанныеFlux 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 ДанныеCalculate * 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 ${\displaystyle {\rm {W/m^{2}}}}$ (${\displaystyle {\rm {A\cdot V/m^{2}}}}$).

Flow equation

Heat equation

FEM