Hello, I am trying to implement some boundary conditions in my model to simulate displacement currents "J" due to migration in an electric field.
According to the literature, I have to implement the following transport of charge carriers boundary conditions ( PLEASE SEE ATTACHED SCREENSHOT)
For example, for "p+", if the electric field multiplied by the normal vector is less than zero, the flux entering the solid should be zero. Otherwise, the flux should be nJ, where n is the outward normal vector from the liquid side, and J is the current flux given by upE, where u is the mobility, p is the charge density, and E is the electric field vector. I have been trying to implement this on the interface of the solid without success for at least 4 months. If anyone knows how to tackle this, it would be much appreciated
To implement this in a simulation (assuming you are using finite element analysis or another similar numerical method), you would generally need to :
-Define the interface between the solid and liquid
-Calculate the normal vector n at every point on the interface
-For each time step or iteration, calculate the electric field E at the interface
- Implement a conditional statement in your code that checks the sign of n.E at each point on the interface and applies the appropriate boundary condition for the flux. Danny Guana
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