What seems to be the issue with this simple diode bridge rectifier with smooth capacitor?
You have grounded the wrong point in your circuit.

If you monitor the bottom of your load resistor in the simulator you will get another surprise.







simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. (a) In the positive half cycle D4 and D5 are in play. (b) In the negative half D6 and D7 are in play.

Ground at the bottom of C1 instead. Normally for a ground referenced DC supply like this we let the transformer "float" and ground the DC-.


  And the current at the LOAD is not smooth, despite the capacitor being there.


You can get a good approximation of the discharge time by the RC time-constant: \$ \tau = RC = 100 \times 100n = 10 \; \mu s \$. The capacitor will be discharged by 63% at this time. For 1 kHz (as in your schematic) you would need at least 100 times your C value. For 50/60 Hz you need 1,000 to 10,000 times that depending on your load.