Fluid dynamics inside a Hele-Shaw cell are simulated computationally. A Hele-Shaw cell is a rectangular chamber, filled with fluid, that consists of two closely placed parallel plates. It effectively turns a three-dimensional situation into a "quasi" two-dimensional situation. Whenever a denser fluid is above a less dense fluid, a potentially unstable situation is created. Rayleigh-Benard convection occurs in a layer of fluid in which the density difference (in a top-heavy arrangement) is large enough to cause the fluid to move. The incompressible Navier-Stokes equations are used to model and simulate the fluid motion. An energy equation is used to describe the evolution of the solute concentrations that are used to create the density differences in the fluid. The equations are addressed numerically using two different methods. A stability analysis is performed to evaluate the strength of the simulation.