The system of potential equations in batteries is elliptic with Neumann boundary conditions ( constant current density condition ).
To solve this system, we must force each node of the grid to satisfy the compatibility equation.
x direction: i_ electrode+i_ electrolyte=i_ applied
To solve the equations in 2D, should we consider the compatibility equation in other direction too for each node of the grid?
y direction: i_ electrode+i_ electrolyte=0
Is it wrong to have little current in the perpendicular direction?
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