I have 15W of power to feed in the capacitor. how do I calculate charging and discharging time?
If that 2100F is not a typo, so capacticance = 2.1kF, then you can do the sums as follows.

Stored energy at 2.8v = 0.5CV^2 = 8400J

However, you would not be able to charge/discharge efficiently over more than about a 2:1 voltage range, so let's put the minimum voltage at 1.4v. The available energy change by swinging between 1.4v and 2.8v is then 75% of the maximum stored energy, which is 6300J. 

If you read the Yunasko data you linked to, then you will see that the specific energy is computed according to note 1, which calls for a voltage swing between rated and 50% rated voltage.

At 15 watts (assuming 100% efficiency in a switchmode converter) that would take 420 seconds = 7 minutes to charge or discharge.

You can reduce the lower voltage further, but you are running into diminishing returns, and making the converter less efficient. If you swung between 2.8 and 1v for instance, then you would be able to use 87% rather than just 75% of the maximum stored energy.

Probably the best way to model a capacitor in SPICE is to use a capacitor, in simulink a current integral.