When the simulation first comes up does it show a charged conductor at equilibrium or a charged insulator with a uniform charge distribution?
A conductor has free electrons that can move around in response to an applied electric field. Consider a conductor with no net charge. With no external field the electrons and protons are uniformly distributed.
If an external electric field is applied the electrons shift in response to the field. The force comes from F = qE. The electrons move along the field line (opposite to the field, because the charge is negative) to the edge of the conductor. The number of electrons that move to the edge is just enough to reduce the field to zero inside the conductor.
When the electrons gets to the edge they still feel a force opposite to the field line. As long as the field is not large enough to create a spark, all the electrons can do is to move along the edge of the conductor. They keep moving until all the field lines hit the conductor perpendicular to the surface.