Harmonic Balance FV Magnetic Vector Potential Model Reference

The Harmonic Balance FV Magnetic Vector Potential model allows you to model magnetic fields with harmonic time-dependance using the finite volume approach.

The corresponding solver solves for the complex magnetic vector potential according to Eqn. (4254). The magnetic flux $B$ and the magnetic field $H$ are calculated from Eqn. (4268). You can use the Harmonic Balance FV Magnetic Vector Potential model in combination with the Excitation Coil model.


Model Name	Harmonic Balance FV Magnetic Vector Potential
Theory	See Harmonic Time Dependence.
Provided By	[physics continuum] > Models > Electromagnetism
Example Node Path	Continua > Physics 1 > Models > Harmonic Balance Fv Magnetic Vector Potential
Requires	Space: one of Two Dimensional, Three Dimensional Time: one of Steady, Implicit Unsteady Material: one of Gas, Liquid, Solid Optional Models: Electromagnetism
Activates	Material Properties	Electrical Conductivity, Magnetic Permeability. See Material Properties.
	Reference Values	Excitation Frequency. See Reference Values.
	Initial Conditions	Magnetic Vector Potential. See Initial Conditions.
	Boundary Inputs	`Magnetic Vector Potential Specification`. See Boundary Settings.
	Region Inputs	`Electric Current Density Source Option`. See Region Settings.
	Solvers	Harmonic Balance Magnetic Vector Potential (uses the AMG Linear Solver.
	Monitors	Imaginary Magnetic X-Potential, Imaginary Magnetic Y-Potential, Imaginary Magnetic Z-Potential, Real Magnetic X-Potential, Real Magnetic Y-Potential, Real Magnetic Z-Potential.
	Field Functions	Magnetic Vector Potential (Imag, Real, Phase, Magnitude), Magnetic Flux Density (Imag, Real, Phase, Magnitude), Magnetic Field (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: Read-only. The current formulation assumes that the magnetic permeability is constant and equal to the vacuum permeability, $μ = μ_{0}$ .
Electrical Conductivity: $σ$ in Eqn. (4263). Set as a complex profile.

Initial Conditions

Magnetic Vector Potential: Allows you to specify the initial magnetic vector potential $\hat{A}$ (see Eqn. (4254)) as a complex profile.

Boundary Settings

Magnetic Vector Potential Specification

Simcenter STAR-CCM+ provides several methods to specify the magnetic vector potential and the electric current sheet at boundaries (see Boundary and Interface Conditions). For harmonic time dependence, these quantities are specified as complex profiles.

Method	Corresponding Physics Value Nodes
Electric Current Sheet Sets the electric current sheet ${\hat{J}}_{S}$ to the tangential component of a specified complex profile, ${\hat{\bar{J}}}_{S}$ : ${\hat{J}}_{S} = {\hat{\bar{J}}}_{S} \|_{t_{1}, t_{2}}$	Electric Current Sheet Allows you to specify a complex profile, ${\hat{\bar{J}}}_{S}$ . Simcenter STAR-CCM+ applies the components of ${\hat{\bar{J}}}_{S}$ tangential to the boundary and neglects the component normal to the boundary.
Magnetic Vector Potential Sets the magnetic vector potential at the boundary to a specified complex profile.	Magnetic Vector Potential Allows you to explicitly set the magnetic vector potential at the boundary as a complex profile, $\hat{A} = \hat{\bar{A}}$ .
Tangential Magnetic Field Sets the electric current sheet to the tangential component of a specified magnetic field $\hat{\bar{H}}$ : ${\hat{J}}_{S} = \hat{\bar{H}} \times n$ where $n$ is the unit vector normal to the boundary.	Specific Tangential Magnetic Field Allows you to specify the magnetic field as a complex profile, $\hat{\bar{H}}$ . Simcenter STAR-CCM+ sets $\hat{\bar{H}} \times n = J_{S}$ . The component of $\hat{\bar{H}}$ normal to the boundary is ignored.
Symmetry - Perfect Magnetic Conductor Sets the component of the magnetic vector potential normal to the boundary to zero, while leaving the tangential components free: $\begin{array}{l} {\hat{A}}_{t_{1, 2}} f r e e \\ {\hat{A}}_{n} = 0 \end{array}$	None
Anti-Symmetry - Perfect Electric Conductor Sets the tangential component of the magnetic vector potential $\hat{A}$ to zero, while leaving the normal component free: $\begin{array}{l} \hat{A} \|_{t_{1}, t_{2}} = 0 \\ {\hat{A}}_{n} f r e e \end{array}$ Most commonly, you specify $\hat{A} \|_{t_{1}, t_{2}} = 0$ at a boundary to prevent any magnetic flux from crossing the boundary.	None

Region Settings

Applies to fluid, porous, and solid regions.

Electric Current Density Source Option

Allows you to specify an electric current density for the region. This option is not available when you use the Harmonic Balance Fv Magnetic Vector Potential 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. (4263).
Electric Current Density (Imag, Real, Phase, Magnitude): Represent the imaginary part, real part, phase, and magnitude of the complex electric current density $\hat{J}$ in Eqn. (4269). The electric current density magnitude, $| \hat{J} |$ , 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 (Imag, Real, Phase, Magnitude): Represent the imaginary part, real part, phase, and magnitude of the complex magnetic vector potential $\hat{A}$ (see Eqn. (4252)).
Permeability: Represents the magnetic permeability $μ = μ_{0}$ .