Conduction equation
<ParameterList name="Closure Model">
<ParameterList name="model_id">
...
...
...
</ParameterList> <!--model_id-->
</ParameterList> <!--Closure Model-->
- Closure Factory Type
- Type:
string
- Value:
Conduction
- Usage:
Required
- Description:
Closure factory type to set source terms and material properties to solve the conduction equation.
1 </ParameterList> <!-- Initial Conditions -->
Material Properties
- Type
- Type:
string
- Value:
ConstantMaterialProperties
- Usage:
Required
- Description:
Material property type to set density, heat capacity and thermal conductivity.
- Density
- Type:
double
- Value:
\([0,\infty]\)
- Usage:
Required
- Description:
Constant density.
- Specific Heat Capacity Value
- Type:
double
- Value:
\([0,\infty]\)
- Usage:
Required
- Description:
Constant specific heat capacity.
- Thermal Conductivity Type
- Type:
string
- Value:
constant, inverse_proportional
- Usage:
Optional
- Default:
constant
- Description:
Model to use for the thermal conductivity.
- Thermal Conductivity Value
- Type:
double
- Value:
\([0,\infty]\)
- Usage:
Required if Thermal Conductivity Type is set to constant.
- Description:
Constant thermal conductivity value: \(k(T) = k_0\).
- Thermal Conductivity Coefficient
- Type:
double
- Value:
\([0,\infty]\)
- Usage:
Required if Thermal Conductivity Type is set to inverse_proportional.
- Description:
Coefficient \(k_0\) for the thermal conductivity \(k(T) = \frac{k_0}{T}\).
1 <Parameter name="X-value of the left boundary" type="double" value="0.0"/>
2 <Parameter name="X-value of the right boundary" type="double" value="1.0"/>
3 <Parameter name="Volumetric Heat Source Value" type="double" value="10.0"/>
4 </ParameterList> <!-- Constant heat source -->
5 <ParameterList name="Material Properties">
6 <Parameter name="Type" type="string" value="ConstantMaterialProperties"/>
7 <Parameter name="Density Value" type="double" value="1.0"/>
<Error Norm>
- Type
- Type:
string
- Value:
ConductionErrorNorms
- Usage:
Required if computing error norms against an exact solution.
- Description:
Computes the \(L_1\) and \(L_2\) error norms between the numerical solution and an exact solution.
1 <ParameterList name="Closure Models">
2 <ParameterList name="solid">
<Heat Source>
- Type
- Type:
string
- Value:
ConductionVolumetricSource
- Usagge:
Optional.
- Description:
Add a volumetric source term to the conduction equation.
- Heat Source Type
- Type:
string
- Value:
constant, xlinear
- Usage:
Optional
- Default:
constant
- Description:
Model to use for the volumetric source term.
- Volumetric Heat Source Value
- Type:
double
- Value:
\([-\infty,\infty]\)
- Usage:
Required.
- Description:
Constant volumetric heat source value \(q_0\).
- X-value of the left boundary
- Type:
double
- Value:
\([-\infty,\infty]\)
- Usage:
Required if Heat Source Type is set to xlinear.
- Description:
x-coordinate of the left boundary \(x_{left}\).
- X-value of the right boundary
- Type:
double
- Value:
\([-\infty,\infty]\)
- Usage:
Required if Heat Source Type is set to xlinear.
- Description:
x-coordinate of the left boundary \(x_{right}\).
Note
Volumetric heat source definition
A constant volumetric heat source is defined as \(S = q_0\). A xlinear volumeteric heat source is defined as \(S = q_0 \frac{x - x_{left}}{x_{right} - x_{left}}\). The later is used for a verification case.
1 <Parameter name="Volumetric Heat Source Value" type="double" value="10.0"/>
2 <Parameter name="Thermal Conductivity Coefficient" type="double" value="1.0"/>
3 <Parameter name="Right Temperature Boundary Value" type="double" value="330.0"/>
4 </ParameterList> <!-- Exact Solution -->
5 <ParameterList name="Constant heat source">
6 <Parameter name="Type" type="string" value="ConductionVolumetricSource"/>
7 <Parameter name="Heat Source Type" type="string" value="xlinear"/>
<Exact Solution>
- Type
- Type:
string
- Value:
ConductionExactSolution
- Usage:
Required if computing error norms for the verification case.
- Description:
Computes the \(L_1\) and \(L_2\) error norms between the numerical solution and an exact solution.
- Volumetric Heat Source Value
- Type:
double
- Value:
\([-\infty,\infty]\)
- Usage:
Required if Thermal Conductivity Type is set to inverse_proportional.
- Description:
Constant volumetric heat source value \(q_0\).
- Thermal Conductivity Coefficient
- Type:
double
- Value:
\([0,\infty]\)
- Usage:
Required if Thermal Conductivity Type is set to inverse_proportional.
- Description:
Coefficient \(k_0\) for the thermal conductivity \(k(T) = \frac{k_0}{T}\).
- Right Temperature Boundary Value
- Type:
double
- Value:
\([0,\infty]\)
- Usage:
Required if Thermal Conductivity Type is set to inverse_proportional.
- Description:
Value of the temperature at the right boundary.
1 <Parameter name="Closure Factory Type" type="string" value="Conduction"/>
2 <ParameterList name="Error Norm">
3 <Parameter name="Type" type="string" value="ConductionErrorNorms"/>
4 </ParameterList> <!-- Error Norm -->
5 <ParameterList name="Exact Solution">
6 <Parameter name="Type" type="string" value="ConductionExactSolution"/>