Many problems in nature can be modeled using partial differential equations. These equations are simplifications of nature. The more detailed they become, the closer they are to reality. For example, one of the most important phenomena in physics is turbulence. To describe the physics of turbulence, a system of partial differential equations must be solved. However, simulating turbulence at all scales is beyond the capabilities of the most powerful computers available today. Solving partial differential equations (PDEs) in a manageable computational time would be an extraordinary advance for science. The aim of this project is to investigate the potential of quantum computers for numerical simulations, by developing a quantum algorithm that can solve large-scale systems in fluid mechanics, such as turbulence.