Stellar black holes are formed when a star of appropriate size reach the end of their life and no longer have the resources to keep it from collapsing in on itself. Due to the extreme gravitational pull from having a finite mass contained in an infinitely small volume, once light enters the event horizon of a black hole it will not come back out, hence their namesake. Inside the event horizon, time-space itself becomes twisted and there is no good way to model what lies inside, but the accretion disk around a black hole can be modeled using classical, Newtonian physics. In this study, I model the fluid dynamics of an accretion disk as it orbits and falls into a black hole. Understanding the accretion disk around a black hole lets us better model and understand the ways a black hole interacts with the universe around it.