# Projection Methods for Incompressible Fluid Dynamics

Projection methods are the core mathematical and computational fluid methodology to accurately account for incompressibility in the Navier-Stokes equations. By continually projecting the evolving solution onto the subspace of divergence-free vectors fields through the Hodge decomposition, these methods provide a robust way to compute a wide host of pratical engineering problems. They are ubiquitous in computational fluid mechanics, and are at the core of current day aircraft simulations, combustion calculations, fluid/solid solvers, ocean and meteorological codes, and simulations of complex physiology such as the design of heart valves.