A vertical cross-section of the shape will be symmetrical with any other vertical slice. So suppose we took that slice (like a flattened letter "C") and drew it on a grid in a computer program. Let it initially have charge equally distributed among all cells that are part of the connected "C".

Since we know the exact distribution and location of charge, then at each cell in the grid, we can calculate the magnitude and direction of the E field by summing the contribution from each cell of charge from the amount and location of that charge, as per Coulomb's law.

Then, on the surface of the shape, wherever the E field is not normal to the surface, redistribute charge a slight amount in the direction that the charge would naturally flow due to the E field.

Then recalculate the E field over the entire grid again.

Continue iterating until the E field is normal to the shape and no more charge redistribution is needed.

Then this should model the real-life E field around such a shape.

Is there any problem with this approach?

My goal is to get a better understanding of how the field varies near the opening into the shape, for different sizes and shapes of openings.