FEM EquationHeat/ro

Description

For information about the math of the equation, see the Elmer models manual, section Heat Equation.

Usage

1. Add an Elmer solver.
2. Select it in the Tree View.
3. There are several ways to invoke the command:
   • Press the Heat Equation button.
   • Select the Solve → Heat Equation option from the menu.
4. 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 heat equation provides these special settings:

• DateBubbles: There is also a residual-free-bubbles formulation of the stabilized finite-element method. It is more accurate and does not include any ad hoc terms. However, it may be computationally more expensive. If both DateBubbles and DateStabilize are false, no stabilization is used and then the results might easily be nonsensical.
  Note: If during the first solver iteration you get this error:
  ERROR:: IterSolve: Numerical Error: System diverged over maximum tolerance.
  The DateBubbles method failed. In this case set DateStabilize to true.

Equation:

• DateConvection: The type of convection to be used in the heat equation.
  Note: If this is not set to None, DateStabilize must be to true otherwise the convection term will not be considered for the heat equation.
• DatePhase Change Model: The model use for phase changes (ice to water etc.). The model Spatial 1 is the apparent-heat-capacity method, Spatial 2 and Temporal are effective-heat-capacity methods.
  For more info about the models, see this paper (section 2.5.2.2) (is in German). In the paper it was also shown that Spatial 1 has numerical problems on larger temperature gradients and that Spatial 2 was preferred for the phase change ice to water.

Analysis Feature Information

The heat equation takes the following analysis features into account if they are set:

• Body heat source
• Initial temperature condition
• Temperature boundary condition

Note

Except for calculations in 2D, for all the above analysis features it is important that they act on a face or a body. Features in 3D set to lines or vertices are not recognized by the Elmer solver.

Result

The result is the temperature in Kelvin.