Harmonic Balance FV Transverse Magnetic Potential Model Reference

The Harmonic Balance FV Transverse Magnetic Potential model allows you to model transverse-magnetic modes (that is, magnetic fields that lie on a 2D domain) with single harmonic time dependence using the finite volume approach.

The model solves for the complex phasor representation of the transverse magnetic potential (see Eqn. (4320)). The magnetic flux $\hat{B}$ and the magnetic field $\hat{H}$ are calculated from Eqn. (4268). You can use the Harmonic Balance FV Transverse Magnetic Potential model in combination with the Excitation Coil model (see Excitation Coil Model Reference).

When using the Harmonic Balance FV Transverse Magnetic Potential model, you define most quantities (including boundary and region values) using complex profiles. For more information on defining complex profiles, see Complex Quantities.


Model Name	Harmonic Balance FV Transverse Magnetic Potential
Theory	See Harmonic Time Dependence and Transverse Magnetic Modes.
Provided By	[physics continuum] > Models > Electromagnetism
Example Node Path	Continua > Physics 1 > Models > Harmonic Balance FV Transverse Magnetic Potential
Requires	Space: one of Two Dimensional, Axisymmetric Time: one of Steady, Implicit Unsteady Material: one of Gas, Liquid, Solid Electromagnetism: Electromagnetism
Activates	Material Properties	Electrical Conductivity, Magnetic Permeability. See Material Properties.
	Reference Values	Excitation Frequency. See Reference Values.
	Initial Conditions	Magnetic Vector Potential Z. See Initial Conditions.
	Boundary Inputs	`Magnetic Vector Potential Specification`. See Boundary Settings.
	Region Inputs	`Electric Current Density Source Option`, `Current Conservation Option`. See Region Settings.
	Solvers	Harmonic Balance FV Transverse Magnetic Potential (uses the AMG Linear Solver.
	Monitors	Imaginary Transverse Magnetic Potential, Real Transverse Magnetic Potential.
	Field Functions	Magnetic Vector Potential-Z (Imag, Real, Phase, Magnitude), Magnetic Flux Density (Imag, Real, Phase, Magnitude), Magnetic Field (Imag, Real, Phase, Magnitude), Electric Current Density-Z (Imag, Real, Phase, Magnitude), Permeability, Electrical Conductivity (Imag, Real, Phase, Magnitude). See Field Functions.

Reference Values

Excitation Frequency: Allows you to specify the frequency $f_{0}$ in Eqn. (4245). Simcenter STAR-CCM+ requires the frequency to be the same across contact or baffle interfaces. When you associate different continua to contacting regions, make sure that you set the same frequency in both continua.

Material Properties

Magnetic Permeability: Allows you to define the magnetic permeability $μ$ in Eqn. (4320) using a constant or a scalar field function.
Electrical Conductivity: Defines $σ$ in Eqn. (4263) as a complex profile.

Initial Conditions

Magnetic Vector Potential Z: Allows you to initialize the transverse magnetic potential ${\hat{A}}_{z}$ (see Eqn. (4320)) to a specified complex profile.

Boundary Settings

Magnetic Vector Potential Specification

In transverse magnetic mode, the magnetic vector potential and electric current sheet are normal to the 2D domain. As only the normal component is non-zero, you specify the magnetic vector potential and the current sheet at a boundary using scalar profiles (see Boundary and Interface Conditions). For harmonic time dependence, these quantities are specified as complex profiles.

Method	Corresponding Physics Value Nodes
Electric Current Sheet Z Sets the electric current sheet at the boundary to: $J_{S} = {\hat{J}}_{S} n$ where $n$ is the boundary normal and ${\hat{J}}_{S}$ is a specified complex profile.	Electric Current Sheet Defines the complex profile, ${\hat{J}}_{S}$ .
Magnetic Vector Potential Z Sets the transverse magnetic vector potential at the boundary to: $A = \hat{A} n$ where $n$ is the boundary normal and $\hat{A}$ is a specified complex profile.	Magnetic Vector Potential Defines the complex profile, $\hat{A}$ .

Region Settings

Applies to fluid, porous, and solid regions.

Current Conservation Option

When activated, Simcenter STAR-CCM+ calculates the transverse magnetic potential while enforcing electric current conservation within the region. See Eqn. (4321). Deactivate this option when you explicitly specify the transverse magnetic potential at the outer boundaries of conducting regions (that is, when you use the Magnetic Vector Potential Z boundary condition). Only available when eddy currents are not suppressed.

Electric Current Density Source Option

Allows you to specify the electric current density for the region. This option is not available when you use the model in combination with the Excitation Coil model. In this case, the electric current density is supplied by the Excitation Coil model.

Method	Corresponding Physics Value Nodes
None No electric current density source is defined.	None
Specified Specifies a user-defined electric current density source ( $J_{u}$ in Eqn. (4311)).	Complex Electric Current Density Source Allows you to specify the electric current density as a complex profile.

Field Functions

Electrical Conductivity (Imag, Real, Phase, Magnitude): Represent the imaginary part, real part, phase, and magnitude of the complex electrical conductivity $σ$ in Eqn. (4320).
Electric Current Density-Z (Imag, Real, Phase, Magnitude): Represent the imaginary part, real part, phase, and magnitude of the complex electric current density ${\hat{J}}_{z}$ . The electric current density magnitude, $| {\hat{J}}_{z} |$ , is also referred to as the peak value.
Magnetic Field (Imag, Real, Phase, Magnitude): Represent the imaginary part, real part, phase, and magnitude of the complex magnetic field $\hat{H}$ (see Eqn. (4268)).
Magnetic Flux Density (Imag, Real, Phase, Magnitude): Represent the imaginary part, real part, phase, and magnitude of the complex magnetic flux density $\hat{B}$ (see Eqn. (4268)).
Magnetic Vector Potential-Z (Imag, Real, Phase, Magnitude): Represent the imaginary part, real part, phase, and magnitude of the complex magnetic vector potential ${\hat{A}}_{z}$ (see Eqn. (4252)).
Permeability: Represents the magnetic permeability $μ_{0}$ in Eqn. (4320).