Electrodynamic Potential Model Reference

This model calculates the electric potential according to Eqn. (4277). From the electric potential, Simcenter STAR-CCM+ calculates the electric field Eqn. (4232) and the electric current density Eqn. (4228). This model can be coupled together with the magnetic vector potential models, which include the magnetic vector potential term in Eqn. (4277).

Material Properties

Electrical Conductivity

Specifies the electrical conductivity $\sigma$ (see Electrical Conductivity: Generalized Ohm's Law).

The available methods for defining the electrical conductivity depend on the physics models that you activate in the physics continuum.

For heat transfer analysis, Simcenter STAR-CCM+ provides specific methods for defining $\sigma$ as a function of temperature.

Method	Corresponding Physics Value Nodes
Constant, Field Function Available for fluids and solids.	Electrical Conductivity > Constant, Field Function Specify $\sigma$ as a scalar profile.
Anisotropic, Orthotropic, Transverse Isotropic Suitable for non-isotropic materials (solid only).	Electrical Conductivity > Anisotropic, Orthotropic, Transverse Isotropic Specify $\sigma$ as a second-order tensor. For information on how to define second-order tensors, see Tensor Quantities. [Region] > Physics Values > Electrical Conductivity Orientation Specifies the local orientation for the definition of the electrical conductivity tensor. For more information, see Orientation Manager and Local Orientations.
Mass-Weighted Mixture Available for multi-component gases. Calculates $\sigma$ by mass-weighting the electrical conductivity of each gas component. See Using the Mass-Weighted Mixture.	None
Polynomial in T Available for fluids and solids, when you activate an energy model in the physics continuum. This method can produce non-positive values for electrical conductivity.	Electrical Conductivity > Polynomial in T Specifies $\sigma$ as a polynomial function of temperature, for heat transfer analysis. See Using Polynomial in T.
Resistivity Polynomial(T) Available for fluids and solids, when you activate an energy model in the physics continuum. Use this method for materials where the resistivity $\rho$ (see Eqn. (4229)) has a polynomial dependency with temperature. This method can produce non-positive values for resistivity.	Electrical Conductivity > Resistivity Polynomial in T Specifies $\rho$ as a polynomial function of temperature.
Table (T) Available for fluids and solids, when you activate an energy model in the physics continuum. This method does not extrapolate outside of the bounds you define in the table. If the table contains non-positive values for the electrical conductivity a warning message is displayed and the simulation does not proceed until all non-positive conductivities are fixed.	Electrical Conductivity > Table (T) Allows you to define $\sigma$ as a function of temperature by providing a table of $\sigma ,T$ values, from which Simcenter STAR-CCM+ determines the profile of $\sigma \left(T\right)$. See Using Table(T). The temperature range in the table must be consistent with the Minimum/Maximum Allowable Temperature settings that are specified under the Reference Values node for the physics continuum. This requirement is specific to electrical conductivity. Electrical Conductivity > Resistivity Interpolation Option When On, calculates the electrical conductivity of the material by interpolation of the resistivity values. The tabular conductivity values are converted to resistivity values to create an internal resistivity vs temperature table. Tabular resistivity values are first interpolated and then converted back to conductivity values.
Table (T,P) Available for compressible gases, when you activate an energy model in the physics continuum.	Electrical Conductivity > Table (T,P) Allows you to define $\sigma$ as a function of temperature and pressure by providing a table of $\sigma ,T,p$ values, from which Simcenter STAR-CCM+ determines the profile of $\sigma (T,p)$. See Using Table (T,P).
Tabular Available for fluids and solids, when you activate an energy model in the physics continuum.	Electrical Conductivity > Tabular Specifies $\sigma$ as a function of temperature using a table interpolation method. When using this method, specify the independent variables (including temperature) that are used to interpolate the electrical conductivity. See Using Tabular Data.
Table (T,c) Available for liquid materials from the Electrolyte Material Database, when you activate either the Li-Ion Electric Potential or Li-Ion Concentration model.	Electrical Conductivity > Table (T,c) Allows you to define the electrical conductivity of the electrolyte as a function of temperature and Li-ion/salt concentration by providing a table of $\sigma ,T,c$ values, from which Simcenter STAR-CCM+ determines the profile of $\sigma (T,c)$.
Electrochemical Species Available for fluids and multi-component fluids, when you activate the Electrochemical Species model, or for solids when the Solid Ion model is selected. Calculates the electrical conductivity using Eqn. (4078).	None
Ionic Conductivity Available for fluids when the Charged Species Effects model is activated. Calculates the electrical conductivity using Eqn. (4078).	None

Initial Conditions

Electric Potential

Allows you to initialize the electric potential $\varphi$ to a specified scalar profile.

Boundary Settings

Applies to all boundary types other than Overset Mesh and Symmetry Plane.

Electric Potential Specification

At the domain boundaries, allows you to prescribe either the electric potential, the electric current, or the electric current density. See Boundary and Interface Conditions.

Method	Corresponding Physics Value Nodes
Specific Electric Current Allows you to define the electric current density normal to the boundary.	Specific Electric Current Sets the specific electric current $J_n$ to a specified scalar profile. See Eqn. (4283). For stabilization, you can optionally specify the derivative of $J_n$ with respect to the electric potential $\varphi$ using the Specific Electric Current Derivative Option. See Specific Electric Current Derivative Option.
Electric Potential Allows you to define the electric potential at the boundary according to Eqn. (4279).	Electric Potential Defines the potential $\overline{\varphi }$ in Eqn. (4279) as a scalar profile. When leaving the Electrical Resistance to the default value of zero, the potential at the boundary is simply $\varphi =\overline{\varphi }$. Electrical Resistance Potential Derivative For stabilization, allows you to specify the dependence of $R^{ex}$ on $\varphi$ by defining $d{R}^{ex}/d\varphi$.
Electric Current Allows you to define the total electric current through the boundary.	Electric Current Sets the total electric current $I_{\mathrm{\Gamma }}$ to a specified scalar profile. See Eqn. (4282). When using this option, specify the spatial distribution of electric current using the Electric Current Distribution condition. See Electric Current Distribution.
Electric Current Density Allows you to define the electric current density at the boundary.	Electric Current Density Sets $J$ to a specified vector profile. See Eqn. (4228).
Insulator Sets the Specific Electric Current $J_n$ (Eqn. (4283)) at the boundary to zero.	None
Current Voltage Characteristic Allows you to define the I-V curve at the boundary.	Current Voltage Characteristic Defines the relationship between the electric current flowing through the boundary and the electric potential at the boundary. In electrochemistry applications, you typically define this relationship using the Butler-Volmer method (see Butler-Volmer Current-Potential Characteristic). Alternatively, you can specify the I-V curve by providing tabular data. For more information, see Setting the Electric Current Potential Characteristic and Current-Voltage Characteristic Reference. Electric Potential Defines the potential ${\varphi }_1$ in Eqn. (4295) as a scalar profile.
Specific Electric Power Allows you to define the electric power normal to the boundary.	Specific Electric Power Sets the specific electric power $P$ to a specified scalar profile. Simcenter STAR-CCM+ uses $P=J_{n}V$ to compute the specific electric current $J_n$ at the boundary, where $V$ is the electric potential (voltage). See Eqn. (4283).

Electrical Resistance Option

Only available when Electric Potential Specification is not set to Insulator.

Defines the method for applying an additional source of electrical resistance ( $R^{ex}$ in Eqn. (4279)).

Electrical Resistance Option	Corresponding Physics Value Nodes
Specific Resistivity	Specific Resistivity Allows you to define $R^{ex}$ (m2Ω) directly for the boundary.
Resistance	Resistance Allows you to define a resistance value (Ω) for the boundary. Simcenter STAR-CCM+ then computes $R^{ex}$ based on how you specify the resistance value: By Surface Subgroup: $R^{ex}$ is the sum of the specified resistance values multiplied by the areas of the respective part surfaces. See Eqn. (4292). Per Boundary: $R^{ex}$ is equal to the specified resistance value multiplied by the area of the whole boundary surface. See Eqn. (4288). For disconnected parts assigned to a single boundary, you must use per-surface sub-grouping. For more information see Applying Quantities by Subgroup.

Correction Factor

When On, Simcenter STAR-CCM+ ensures the specific resistivity distribution over the boundary surface generates an ohmic heat equivalent to $I^{2}R$ . When using this option the current must flow in the same direction.

For most cases, On is appropriate. For cases involving recirculating currents, set this condition to Off. In general, if you observe counter-intuitive results, set this condition to Off

Electric Current Distribution

When defining the electric current at the boundary, this setting specifies the electric current spatial distribution. The available options are:

• Uniform Electric Potential—calculates the specific electric current spatial distribution so that the electric potential is constant along the boundary. When you use this method, it is recommended you set the Under-Relaxation Factor to 1.0. If you experience convergence issues it is recommended you modify the Convergence Tolerance and Max Cycles under the Solvers > Electric Potential > AMG Linear Solver node.
• Uniform Specific Electric Current—prescribes a constant specific electric current spatial distribution.

Only available when the method for the Electric Potential Specification boundary condition is Electric Current.

Specific Electric Current Derivative Option

When defining the specific electric current at the boundary, this option allows you to specify the derivative of the specific electric current with respect to the electric potential, $d{J}_n/d\varphi$. You typically define $d{J}_n/d\varphi$ to improve stability, by linearizing the relationship between $J_n$ and $\varphi$.

Method	Corresponding Physics Value Nodes
None Sets $d{J}_n/d\varphi$ to zero.	None
Specified Allows you to specify $d{J}_n/d\varphi$ at the boundary.	Specific Electric Current Derivative Defines $d{J}_n/d\varphi$ as a scalar profile. By default, this value is set to zero (that is, $J_n$ is independent of $\varphi$).

Only available when the method for the Electric Potential Specification boundary condition is Specific Electric Current.

Electromotive Force Source Option

Allows you to specify a source of electromotive source at the boundary level, overriding the electromotive source that is specified for the region. This option is available when you do both of the following:

1. You activate the region condition Electromotive Force Source Option.
2. You activate the region property Allow Per-Part Values.

Region Settings

Fluid, Solid, and Porous Regions:

The following region settings allow you specify additional sources of electric current, that are not directly modeled in the simulation. When you do not need to account for unresolved physics, you typically leave these source terms to the default value of zero.

Electromotive Force Source Option

Specifies the external source ${\rho }_{ϵ}$ in Eqn. (4277). By default, ${\rho }_{ϵ}=0$.

Method	Corresponding Physics Value Nodes
Deactivated Sets ${\rho }_{ϵ}=0$.	None
Activated Allows you to define an electromotive force source term, ${\rho }_{ϵ}$.	Electromotive Force Source Sets ${\rho }_{ϵ}$ to a specified vector profile.

Transfer Current Density Source Option

Specifies the external source $S_{\varphi }$ in Eqn. (4277). By default, $S_{\varphi }=0$.

Method	Corresponding Physics Value Nodes
Deactivated Sets $S_{\varphi }=0$.	None
Activated Allows you to define a transfer current density source term, $S_{\varphi }$.	Transfer Current Density Source Sets $S_{\varphi }$ to a specified scalar profile. Transfer Current Density Source Potential Derivative For stabilization, allows you to specify $d{S}_{\varphi }/d\varphi$ as a scalar profile. By default, this value is set to zero.

Fluid and Porous Regions:

Electrical Conductivity Constraint Option

Available when you activate an energy model, allows you to specify a minimum electrical conductivity for the fluid region.

Method	Corresponding Physics Value Nodes
None Does not set a minimum electrical conductivity.	None
Minimum Allows you to set a minimum value for the fluid electrical conductivity.	Minimum Constraint Electrical Conductivity Defines the minimum electrical conductivity as a scalar profile.

Porous Regions:

Effective Porous Electrical Conductivity Option

Specifies the method for calculating the effective electrical conductivity of porous materials.

Method	Corresponding Physics Value Nodes
Volume fraction weighted Calculates the effective electrical conductivity in terms of the electrical conductivity of the fluid and solid components (see Eqn. (4230)). This method is suitable when: you want to use a specific value for the effective electrical conductivity the relationship for the effective electrical conductivity does not follow a Bruggeman relationship you have a mixed conductor, where both the solid and fluid phases conduct charge.	Solid Electrical Conductivity Specifies the electrical conductivity of the solid component ( ${\sigma }_{solid}$ in Eqn. (4230)) as a second-order tensor. For information on how to define second-order tensors, see Tensor Quantities. The electrical conductivity of the fluid component, ${\sigma }_{fluid}$, is specified within the material properties of the fluid physics continuum.
Bruggeman (solid) Calculates the effective electrical conductivity in terms of the electrical conductivity of the solid component (see Eqn. (4230)).	Solid Electrical Conductivity Specifies ${\sigma }_{solid}$ (see Eqn. (4230)) as a second-order tensor. Bruggeman Approximation Exponent Specifies the Bruggeman approximation exponent ($\beta$ in Eqn. (4230)) as a scalar profile. The default value is 1.5.
Bruggeman (fluid) Calculates the effective electrical conductivity in terms of the electrical conductivity of the fluid component (see Eqn. (4230)).	Bruggeman Approximation Exponent Specifies $\beta$ (see Eqn. (4230)) as a scalar profile. The electrical conductivity of the fluid component, ${\sigma }_{fluid}$, is specified within the material properties of the fluid physics continuum.

Interface Settings

Contact Electric Potential Specification

Available for fluid/solid and solid/solid contact interfaces, allows you to prescribe the electric potential at the interface.

Method	Associated Physics Value
None Calculates the electric potential at the two sides of the interface according to Eqn. (4281).	None
Specific Electric Current Prescribes the specific electric current at the two sides of the interface, $J_{n_0}$, $J_{n_1}$.	Specific Electric Current Sets the specific electric current $\left|J_{n_0}\right|=\left|J_{n_1}\right|$ to a specified scalar profile. See Eqn. (4283).
Electric Current Prescribes the total electric current through the interface	Electric Current Sets the total electric current $I_{\mathrm{\Gamma }}$ to a specified scalar profile. See Eqn. (4282).
Current Voltage Characteristic Allows you to define the I-V curve at the interface.	Current Voltage Characteristic Defines the relationship between the electric current flowing through the interface and the electric potential. In electrochemistry applications, you typically define this relationship using the Butler-Volmer method (see Butler-Volmer Current-Potential Characteristic). Alternatively, you can specify the I-V curve by providing tabular data. For more information, see Setting the Electric Current Potential Characteristic and Current-Voltage Characteristic Reference. Electrical Resistance Defines the electrical resistance $R$ in Eqn. (4295) as a scalar profile.

Electrical Resistance Option

Available for fluid/solid and solid/solid contact interfaces.

Defines the method for applying the additional source of electrical resistance ( $R^{ex}$ in Eqn. (4279)). There are two options for this:

Electrical Resistance Option	Corresponding Physics Value Nodes
Specific Resistivity	Specific Resistivity Allows you to define $R^{ex}$ (m2Ω) directly for the interface.
Resistance	Resistance Allows you to define a resistance value (Ω) for the interface. Simcenter STAR-CCM+ then computes $R^{ex}$ based on how you specify the resistance value: By Contact Subgroup: $R^{ex}$ is the sum of the specified resistance values multiplied by the areas of the respective part surfaces. See Eqn. (4292). Per Interface: $R^{ex}$ is equal to the specified resistance value multiplied by the whole contact area. See Eqn. (4288). For disconnected parts assigned to a single contact interface, you must use per-part sub-grouping. For more information see Applying Quantities by Subgroup.

Correction Factor

When On, Simcenter STAR-CCM+ ensures the specific resistivity distribution over the interface generates an ohmic heat equivalent to $I^{2}R$ . When using this option the current must flow in the same direction.

For most cases, On is appropriate. For cases involving recirculating currents, set this condition to Off. In general, if you observe counter-intuitive results, set this condition to Off

Electrodynamic Phase Contact Option

Allows you to electrically interface a solid region and one solid porous phase of a fluid region.

Available when both:

• the Electrodynamic Potential model is selected in the solid continuum
• the Electrodynamic Potential model is selected in the fluid continuum or in a solid porous phase within the fluid continuum

Method	Associated Physics Value
None The interface is impermeable between all phases.	none
Physics Continuum Available when the Electrodynamic Potential model is selected in the fluid continuum. Interfaces the fluid region with the solid region.	Electrical Resistance The electrical resistance at the interface between the solid region and the fluid region.
[Phase n] Available for each solid phase in which the Electrodynamic Potential model is selected. Interfaces the solid porous phase that you select with the solid region.	Electrical Resistance The electrical resistance at the interface between the solid region and the solid porous phase.

Electric Current Source Option

Available for fluid/fluid interfaces, allows you to prescribe the electric current at the interface.

Method	Associated Physics Value
Specific Electric Current Prescribes the specific electric current at the two sides of the interface, $J_{n_0}$, $J_{n_1}$.	Specific Electric Current Sets the specific electric current $\left|J_{n_0}\right|=\left|J_{n_1}\right|$ to a specified scalar profile. See Eqn. (4283).
Electric Current Prescribes the total electric current through the interface	Electric Current Sets the total electric current $I_{\mathrm{\Gamma }}$ to a specified scalar profile. See Eqn. (4282).

Baffle Electrical Option

Allows you to specify whether electric currents flow through the interface.

Available for baffle interfaces and porous baffle interfaces, except for those between porous phases when using the Electrodynamic Potential model. Baffle interfaces for phasic porous media, where the solid porous phases use the Electrodynamic Potential model, are non-conducting.

Method	Associated Physics Value
Non-Conducting No current flows through the baffle.	None
Conducting Current flows through the baffle.	Electrical Resistance Specifies the baffle electrical resistance.

Mapped Contact Interface

The Mapped Contact Interface is not supported by the Electrodynamic Potential model. However, if the simulation uses another model that supports the Mapped Contact Interface (for example, Segregated Solid Energy) on both interfacing regions, the Mapped Contact Interface becomes available but only when the Electrodynamic Potential model is selected in one of the interfacing regions, and not in both. For properties, see Mapped Contact Interface.

Field Functions

Boundary Specific Electric Current

Represents the specific electric current (Eqn. (4283)), with opposite sign.

Electric Current Density

Represents the electric current density $J$ in Eqn. (4228).

Electrical Conductivity

Represents the scalar electrical conductivity $\sigma$ of isotropic materials (see Eqn. (4228)).

Electrical Conductivity (Symmetric Tensor)

For porous regions and anisotropic solid regions, the electrical conductivity $\sigma$ in Eqn. (4228) is a symmetric tensor. For porous regions, this field function represents the effective electrical conductivity tensor ${\sigma }_{eff}$ (see Eqn. (4230)).

Previous versions of Simcenter STAR-CCM+ provided a scalar field functions for each component of the electrical conductivity tensor. When restoring simulations containing these field functions, you are provided with both the tensor field function and the component field functions.