Self-affine surfaces are found in many physical systems, making it important to study flow over such surfaces. This project develops a code to simulate, through the coupled Lattice Boltzmann Method, gravity-stabilized flow, with lighter fluid flowing in an system initially filled with heavier fluid, over a self-affine surface of Hurst exponent, H = 0.8. Methods to qualitatively and quantitatively characterize the flow are introduced. Together with the expected stabilizing effect of gravity over long time scales, gravity is found to increase the initial flushing of the heavier fluid. Some explanations are given for this effect. The rate of dissipation is presented as a means of characterizing the magnitude of bouyancy in the system and of comparing simulations to possible experiments.