Numerical methods for incompressible viscous flow

We present an overview of the most common numerical solution strategies for the incompressible Navier–Stokes equations, including fully implicit formulations, artificial compressibility methods, penalty formulations, and operator splitting methods (pressure/velocity correction, projection methods). A unified framework that explains popular operator splitting methods as special cases of a fully implicit approach is also presented and can be used for constructing new and improved solution strategies. The exposition is mostly neutral to the spatial discretization technique, but we cover the need for staggered grids or mixed finite elements and outline some alternative stabilization techniques that allow using standard grids. Emphasis is put on showing the close relationship between (seemingly) different and competing solution approaches for incompressible viscous flow.