So it is a legitimate question to discuss whether the simulator reflects this real word edit : world action, and if not, how to make it so.

Apologies for my bad spelling, I'm glad people seem to have picked up the correct meaning in post#17 anyway

 

Yes, I think BobTPH is correct on the initial operating conditions. It also works correctly if the power supply is started from 0 volts the time constant is set by ESR since the voltage source resistance is 0 in the simulation.. It does not account for leakage current or voltmeter load so that has to be accounted for somehow - same as real life.

There is a place in the capacitor models to plug in the parallel resistance.