Keep in mind that a simulation is not as theoretical as the pure math is. In the case of a diode, here is some leakage. You can roughly model that as a somewhat high value resistor just to get a feel for what might be happening. If we had a 1MegOhm resistor in parallel to the diode, then what would we see?
With DC voltages the 2v source would dominate Vout because the cap would look like an open circuit after all exponentials died down.
With an AC voltage for V1, Vout will be constantly changing and that 1Megohm resistor across the diode will not load the output too much.
For your diode choice though that parallel resistance could be as high as 500Megohms.

Think about these ideas.

Thank you very much for making the things really clear for me to understand, i understand the things a lot better now.

 

Thank you very much for making the things really clear for me to understand, i understand the things a lot better now.

Hello again,

Oh you are very welcome and lots of members here are always happy to help people with a genuine interest in electronic circuits and related.

I should mention one more thing regarding the theory of operation. The diode leakage could make the output look like it is permanently biased at 2vdc even with an AC input as then the output would look like a 2vdc with the AC superimposed on it (AC riding on DC). I would think this would show up in a simulation, but the diode leakage may have to be more than it is with a 1N4148 diode to see it. A Schottky diode would show this more clearly I think.
The DC bias builds up over time, and we have to know the value of the leakage current (or pseudo parallel resistance) to be able to calculate the output with any accuracy and how much time it takes to stabilize.