The Electric Discharge Interface
The Electric Discharge (edis) interface (), found under the Electric Discharge branch (), is used to simulate electric discharges and predict electrical breakdown in gas, liquid, and solid dielectrics. It contains built-in charge transport models that solve the drift-diffusion equations of electrons, holes, as well as positive and negative ions fully coupled with Poisson’s equation. In addition, it can also model the surface charge accumulation and relaxation effect at dielectric interfaces. Typical modeling applications are streamer discharges, corona discharges, electrostatic discharges, and dielectric barriers discharges. The effect of a background magnetic field or a flow field can be easily considered by coupling to another physics interface such as the Magnetic Fields or Laminar Flow.
The interface supports simulation of electric discharges in 1D, 2D, and 3D as well as for axisymmetric components in 1D and 2D. Stationary; time dependent; and frequency dependent, perturbation study types are available for the interface.
Theory for the Electric Discharge Interface
Settings
The Label is the default physics interface name.
The Name is used primarily as a scope prefix for variables defined by the physics interface. Refer to such physics interface variables in expressions using the pattern <name>.<variable_name>. In order to distinguish between variables belonging to different physics interfaces, the name string must be unique. Only letters, numbers, and underscores (_) are permitted in the Name field. The first character must be a letter.
The default Name (for the first physics interface in the model) is edis.
Domain Selection
If any part of the model geometry should not partake in the transport model, remove that part from the selection list.
Physical Model
Dielectric Medium Selection
Use the checkboxes available to add dielectric medium to be modeled. See Overview of Physical Models for more details. There are three types of mechanisms that can be freely combined:
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Gas: which is selected by default for modeling gas discharges.
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Liquid: select this box when the system has liquid dielectric such as transformer oil.
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Solid: select this box when the system has solid dielectrics such as insulators, good and poor conductors, rubber, plastic, and so on.
Out-of-Plane Thickness
For 2D component and 1D axisymmetric components, the Out-of-plane thickness dz (default value: 1 cm) defines a parameter for the thickness of the geometry perpendicular to the two-dimensional cross section. Only constant thickness is supported. The value of this parameter is used, among other things, to automatically calculate the electric current flowing across the boundary.
Cross-Sectional Area
For 1D components, enter a Cross-sectional area Ac to define a parameter for the area of the geometry perpendicular to the 1D component. Only constant thickness is supported. The value of this parameter is used, among other things, to automatically calculate the electric current flowing across the boundary. The default is 1 cm2.
Consistent Stabilization
To display this section, click the Show More Options button () and select Stabilization. By default, the Streamline diffusion checkbox is selected. The streamline diffusion stabilization does not change the original equation but adds the diffusion in the weak form and it vanishes once the original equation is converged. Use it when the transport equation is drift or convection-dominated. See more details in Numerical Stabilization in the COMSOL Multiphysics Reference Manual.
If the Streamline diffusion checkbox is selected, the Include time steps effect on stabilization time scale checkbox will become visible. Enabling this checkbox will account for the time steps’ effect on the stabilization time scale in time dependent studies.
Inconsistent Stabilization
To display this section, click the Show More Options button () and select Stabilization. By default, the Isotropic diffusion checkbox is not selected, because this type of stabilization adds artificial diffusion and affects the accuracy of the original problem. However, this option can be used to get a good initial guess for underresolved problems. To add isotropic diffusion, select the Isotropic diffusion checkbox. The field for the Tuning parameter δid then becomes available. The default value is 0.1; increase or decrease the value of δid to increase or decrease the amount of isotropic diffusion. See more details in Numerical Stabilization in the COMSOL Multiphysics Reference Manual.
Discretization
Use this section to change the discretization of the transport equations and Poisson’s equation. Two formulations — Finite element, log formulation (linear shape function) (the default) and Finite element, log formulation (quadratic shape function) — are available for the discretization of Charge carriers. Three formulations — Finite element (linear shape function) (the default), Finite element (quadratic shape function), and Finite element (cubic shape function) — are available for the discretization of Electric potential.
To display all settings available in this section, click the Show More Options button () and select Advanced Physics Options.
The Compute boundary fluxes checkbox is activated by default so that COMSOL Multiphysics computes predefined accurate boundary flux variables. When this option is selected, the solver computes variables storing accurate boundary fluxes from each boundary into the adjacent domain.
If the checkbox is cleared, the COMSOL Multiphysics software instead computes the flux variables from the dependent variables using extrapolation, which is less accurate in postprocessing results but does not create extra dependent variables on the boundaries for the fluxes.
The flux variable affected in the interface is ntflux_c (where c is the carrier name). This is the normal total flux and corresponds to all flux contributions (drift, convection, and diffusion).
Also the Apply smoothing to boundary fluxes checkbox is available if the previous checkbox is selected. The smoothing can provide a more well-behaved flux value close to singularities.
For details about the boundary fluxes settings, see Computing Accurate Fluxes in the COMSOL Multiphysics Reference Manual.
The Value types when using splitting of complex variables setting should in most pure mass transfer problems be set to Real, which is the default. It makes sure that the dependent variable does not get affected by small imaginary contributions, which can occur, for example, when combining a Time Dependent or Stationary study with a frequency-domain study. For more information, see Splitting Complex-Valued Variables in the COMSOL Multiphysics Reference Manual.
Dependent Variables
The dependent variables are named as Space charge density rho and Electric potential V by default. The names must be unique with respect to all other dependent variables in the component.
Note that all physics features might add additional dependent variables depending on feature settings. For example, the Gas feature adds the natural logarithm of the number density of electrons, positive ions, and negative ions if the Material model is set to Charge transport and Charge carriers is set to Electrons, positive and negative ions. Note that these dependent variables added by physics features are not shown in this section.
You can access the number density of a carrier c (e, h, p, n for electrons, holes, positive ions, and negative ions, respectively) through the physics scope variable name.n_c where name is the physics interface name, as described earlier. Note that for Finite element, log formulation, the actual dependent variable is the natural logarithm of the number density divided by one per cubic centimeter, which is named as name.logn_c and defined as log(n_c/(1 cm−3)).