I don't see anything wrong with the circuit as an exercise in RCL circuit behaviour.
Assuming the upper switch is a SPDT (single pole double throw) switch, the operation would be as follows.
Throw the switch to the left to connect to the 12 VDC charging circuit.
Determine the charging current and capacitor voltage depending on which capacitor(s) is/are connected.
Throw the switch to the right to discharge the capacitor(s). Determine the capacitor(s) discharge current and voltage.
The two diodes in the circuit are irrelevant. Treat them as ideal rectifiers that conduct current in one direction with zero resistance.
As a first exercise, remove the inductor and replace it with a zero ohm resistor.