Semi-Implicit Projection Methods for Incompressible Flow based on Spectral Deferred Corrections

A semi-implicit form of spectral deferred corrections is used in a method of lines approach to create a projection method that is sixth-order accurate in both time and space for simple domains. The derivation of spectral deferred corrections is presented and compared to traditional deferred correction methods. An auxiliary variable form of the equations for Boussinesq flow is presented which facilitates a method of lines approach. A discussion of how these methods can be extended to complex spatial domains through the use of integral equation methods is also presented.