FEM EquationHeat: Difference between revisions

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{{GuiCommand
{{GuiCommand
|Name=FEM EquationHeat
|Name=FEM EquationHeat
|MenuLocation= Solve → Heat equation
|MenuLocation=Solve → Heat equation
|Workbenches=[[FEM_Workbench|FEM]]
|Workbenches=[[FEM_Workbench|FEM]]
|Version=0.19
|Version=0.17
|SeeAlso=[[FEM_tutorial|FEM tutorial]]
|SeeAlso=[[FEM_tutorial|FEM tutorial]]
}}
}}
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This equation describes the heat transfer in rigid and fluid bodies.
This equation describes the heat transfer in rigid and fluid bodies.


<!--T:10-->
For info about the math of the equation, see the [http://www.elmerfem.org/blog/documentation/ Elmer models manual], section ''Heat Equation''.
For info about the math of the equation, see the [http://www.elmerfem.org/blog/documentation/ Elmer models manual], section ''Heat Equation''.


==Usage==
==Usage== <!--T:11-->


<!--T:12-->
# After adding an Elmer solver as described [[FEM_SolverElmer#Equations|here]], select it in the [[Tree_view|tree view]].
# After adding an Elmer solver as described [[FEM_SolverElmer#Equations|here]], select it in the [[Tree_view|tree view]].
# Now either use the toolbar button [[Image:FEM_EquationHeat.svg|24px]] or the menu {{MenuCommand|Solve → Heat equation}}.
# Now either use the toolbar button [[Image:FEM_EquationHeat.svg|24px]] or the menu {{MenuCommand|Solve → Heat equation}}.
# Change the [[#Solver_Settings|equation's solver settings]] or the [[FEM_SolverElmer_SolverSettings|general solver settings]] if necessary.
# Change the [[#Solver_Settings|equation's solver settings]] or the [[FEM_SolverElmer_SolverSettings|general solver settings]] if necessary.


==Solver Settings==
==Solver Settings== <!--T:13-->


<!--T:14-->
For the general solver settings, see the [[FEM_SolverElmer_SolverSettings|Elmer solver settings]].
For the general solver settings, see the [[FEM_SolverElmer_SolverSettings|Elmer solver settings]].


<!--T:15-->
The heat equation provides these special settings:
The heat equation provides these special settings:
* {{PropertyData|Bubbles}}: 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 {{PropertyData|Bubbles}} and {{PropertyData| [[FEM_SolverElmer_SolverSettings#Base|Stabilize]]}} are ''false'', no stabilization is used and then the results might easily be nonsensical.
* {{PropertyData|Bubbles}}: 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 {{PropertyData|Bubbles}} and {{PropertyData|[[FEM_SolverElmer_SolverSettings#Base|Stabilize]]}} are ''false'', no stabilization is used and then the results might easily be nonsensical.</br>'''Note''': If during the ''first solver iteration'' you get this error:</br> ERROR:: IterSolve: Numerical Error: System diverged over maximum tolerance.</br>The {{PropertyData|Bubbles}} method failed. In this case set {{PropertyData|[[FEM_SolverElmer_SolverSettings#Base|Stabilize]]}} to ''true''.


<!--T:16-->
Equation:
Equation:
* {{PropertyData|Convection}}: The type of convection to be used in the heat equation.
* {{PropertyData|Convection}}: The type of convection to be used in the heat equation.</br>'''Note''': If this is not set to ''None'', {{PropertyData|[[FEM_SolverElmer_SolverSettings#Base|Stabilize]]}} must be to ''true'' otherwise the convection term will not be considered for the heat equation.
* {{PropertyData|Phase 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.>/bar>For more info about the models, see [https://blog.rwth-aachen.de/gfd/files/2017/07/BT_2013_Schueller_elmer_icemole.pdf this paper] (section 2.5.2.2). 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.
* {{PropertyData|Phase 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.</br>For more info about the models, see [https://blog.rwth-aachen.de/gfd/files/2017/07/BT_2013_Schueller_elmer_icemole.pdf 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== <!--T:17-->

<!--T:18-->
The heat equation takes the following analysis features into account if they are set:

<!--T:19-->
* [[Image:FEM_ConstraintBodyHeatSource.svg|32px]] [[FEM_ConstraintBodyHeatSource|Body heat source]]
* [[Image:FEM_ConstraintInitialTemperature.svg|32px]] [[FEM_ConstraintInitialTemperature|Initial temperature condition]]
* [[Image:FEM_ConstraintTemperature.svg|32px]] [[FEM_ConstraintTemperature|Temperature boundary condition]]

===Note=== <!--T:20-->

<!--T:21-->
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== <!--T:22-->

<!--T:23-->
The result is the temperature in Kelvin.



<!--T:5-->
<!--T:5-->

Latest revision as of 14:08, 22 November 2023

Other languages:

FEM EquationHeat

Menu location
Solve → Heat equation
Workbenches
FEM
Default shortcut
None
Introduced in version
0.17
See also
FEM tutorial

Description

This equation describes the heat transfer in rigid and fluid bodies.

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

Usage

  1. After adding an Elmer solver as described here, select it in the tree view.
  2. Now either use the toolbar button or the menu Solve → Heat equation.
  3. 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:

  • DataBubbles: 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 DataBubbles and DataStabilize 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 DataBubbles method failed. In this case set DataStabilize to true.

Equation:

  • DataConvection: The type of convection to be used in the heat equation.
    Note: If this is not set to None, DataStabilize must be to true otherwise the convection term will not be considered for the heat equation.
  • DataPhase 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:

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.


FEM

Constraints

User documentation
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