Unfortunately i never used simulation program.
Operational amp. work as comparator if no negative feedback. When You connect a +voltage to -in (e.g.+5V while Vcc15V) as a reference, the output is low if +inV<-inV and suddenly go to high when +inV increase over -inV (open loop gain very high)In this case because for 555 need negative trigger - and for stability a hysteresis - the +refV(3.7V) coming from output divider to +in.If the switch is closed, -in=0V, out=15V,when the switch opened, the 100nF "slowly" charged via 10k, and when increase to +3.7V, the out go to about 0.5V (Uc-e sat from output transistor), +in near to 0V.