6. ELECTROMAGNETIC_BC Namelist

The ELECTROMAGNETIC_BC namelist is used to define boundary conditions for the electromagnetic (EM) models at external boundaries. Each instance of the namelist defines a particular condition to impose over a subset of the domain boundary. The boundary subset $\Gamma$ is specified using mesh face sets. The namelist variable face_set_ids takes a list of face set IDs, and the boundary condition is applied at all faces belonging to those face sets. Note that the mesh in view here is the one specified by the EM_MESH namelist. Also note that ExodusII mesh side sets are imported into Truchas as face sets with the same IDs.

Namelist Usage

Required/Optional:: Required
Single/Multiple Instances:: Multiple

6.1. Boundary Conditions

The following types of boundary conditions can be defined. The outward unit normal to the boundary $\Gamma$ is denoted $\hat{n}$.

Perfect electric conductor

A perfect electric conductor condition, $\hat{n}\times\vec{E}=0$ on $\Gamma$, is defined by setting type to “pec”.

Perfect magnetic conductor

A perfect magnetic conductor condition, $\hat{n}\times\vec{H}=0$ on $\Gamma$, is defined by setting type to “pmc”.

Magnetic induction source

A tangential H-field condition $\hat{n}\times\vec{H} = \hat{n}\times\vec{H}_\text{ext}$ on $\Gamma$, where $\vec{H}_\text{ext}$ is the external magnetic field defined by the INDUCTION_SOURCE_FIELD namelist, is defined by setting type to “ih-hfield”. This special purpose boundary condition is used in induction heating simulations.

Robin

A general Robin condition

\[\hat{n}\times\nabla\times\vec{E} + \alpha\,\hat{n}\times\vec{E}\times\hat{n} = \hat{n}\times\vec{g}\times\hat{n} \text{ on $\Gamma$},\]

is defined by setting type to “robin”. The complex constant $\alpha$ is specified by alpha, and the complex function $\vec{g}(x)\in\mathbb{C}^3$ is specified using either g for a constant, or g_func for a function. This is only applicable to the frequency domain EM model.

Impedance

This special form of a Robin condition approximates the effect of a well-conducting bounding material, by choosing $\alpha= \sqrt{-i\mu_0\omega\sigma}$ and $\vec{g}=0$. The conductivity of the bounding material $\sigma$ is specified by sigma, and the angular frequency $\omega$ is obtained from the configuration of the frequency domain model. Set type to “impedance” to select this condition.

Waveguide port feed

This special form of a Robin condition simulates an entry/exit port for the fundamental TE₁₀ mode at the boundary of a truncated rectangular waveguide. The shape and orientation of the waveguide cross-section, assumed rectangular, is specified by variables center, x_axis, y_axis, x_width, and y_width, and the power of the injected mode by power; see Figure 6.1.1. Set type to “wg-port” to select this condition.

Note

The ‘’wg-port’’ condition requires that the TE₁₀ mode is the only mode supported by the waveguide. The propagation of electromagnetic waves through a conducting rectangular waveguide with dimensions $a>b$ (see Figure 6.1.1) can only occur for frequencies $f\ge f_c = \tfrac{c}{2a}$. This constrains the frequency $f$ for the validity of the “wg-port” condition to $f_c \le f \le \min(2, a/b)f_c$.

../_images/wg-port.png — Figure 6.1.1 The shape and orientation of the of rectangular waveguide port boundary. The blue arrows depict the $\vec{y}$-direction and relative strength of the electric field’s linear polarization in the TE₁₀ mode within the rectangular waveguide.

6.2. Namelist Variables

name 

A unique name used to identify a particular instance of this namelist.

Type:: string
Default:: none

face_set_ids 

A list of face set IDs that define the portion of the boundary $\Gamma$ where the boundary condition will be imposed.

Type:: integer list (32 max)
Default:: none

type 

The type of boundary condition. Some types apply only to the frequency domain (FD) model as noted. The available options are:

Type:: string
Default:: none
Valid values:

Value	Description	Associated variables
“pec”	Perfect electric conductor
“pmc”	Perfect magnetic conductor
“ih-hfield”	Magnetic induction source	INDUCTION_SOURCE_FIELD namelist
“robin”	Robin (FD only)	alpha, g, g_func
“impedance”	Impedance (FD only)	sigma
“wg-port”	Waveguide port feed (FD only)	center, x_axis, y_axis, x_width, y_width, power, phase

alpha 

The constant value of the $\alpha$ parameter in the Robin boundary condition.

Type:: complex
Default:: none

g 

The constant value of the $\vec{g}$ parameter in the Robin boundary condition. To specify a function use g_func instead.

Type:: complex 3-vector
Default:: none

g_func 

The name of a COMPLEX_VFUNCTION namelist that defines the $\mathbb{C}^3$-valued function to use for the $\vec{g}$ parameter in the Robin boundary condition. The function is expected to be a function of $(x,y,z)$.

Type:: string
Default:: none

sigma 

The electric conductivity of the bounding material in the impedance boundary condition.

Type:: real
Default:: none

power 

The power of the injected TE₁₀ mode in the waveguide port feed boundary condition.

Type:: real
Default:: none
Notes:: No value needs to be specified for instances of the boundary condition that are managed by the MICROWAVE_HEATING namelist, and if a value is specified it is ignored.

center 

The coordinate of the center of the boundary of the truncated rectangular waveguide.

Type:: real 3-vector
Default:: none

x_axis 

The direction of the long edge of the rectangular boundary. Its length is not significant.

Type:: real 3-vector
Default:: none

y_axis 

The direction of the short edge of the rectangular boundary. Its length is not significant.

Type:: real 3-vector
Default:: none

x_width 

The length of the long edge of the rectangular boundary.

Type:: real
Default:: none

y_width 

The length of the short edge of the rectangular boundary.

Type:: real
Default:: none

phase 

The phase of the input TE₁₀ mode for the waveguide port feed boundary condition. This is only truly significant when there are multiple waveguides with differing phases.

Type:: real
Default:: 0.0