The discovery of luminous red nova (LRN) V1309 Sco revealed a binary star system prior to its outburst in brightness, with an exponentially decaying orbital separation. This allowed, for the first time, theoretical models of contact stellar mergers to be verified by observations, although a direct comparison had not been made. In this thesis, we simulate the V1309 Sco light curve, thereby bridging the gap between theory and observation, and provide numerical tools that can be applied to other LRNe. I will first provide an overview of LRNe and their connection to stellar mergers, my method for simulating the mergers, and the fundamentals of the radiation physics that I applied to those simulations to obtain the light curves. Following this review, I will detail my process for simulating a V1309 Sco progenitor and show that ray tracing, a common method in SPH for reconstructing the radiation field, cannot give realistic brightness estimations where the simulated fluid transitions from optically thin to optically thick, such as near the surface of a star. I will address this limitation by implementing a new method called envelope fitting, which involves tabulating unique stellar profiles of known surface brightnesses and mapping the simulated mass elements to those profiles. Using envelope fitting, I will show that my simulated progenitor produces synthetic observations comparable to that of V1309 Sco prior to the outburst. Then, I will introduce a novel implementation of flux-limited radiative diffusion to my simulation method and evolve the progenitor dynamically beyond the merger. The resulting light curves will be compared to the V1309 Sco observations to reveal a match in the peak, plateau, and subsequent drop in luminosity. I explore the effects of various progenitor and simulation parameters on the light curves. Finally, I will summarize the main results of my work.