Teko is a package for development and implementation of block preconditioners. This includes support for manipulation and setup of block operators. Furthermore tools exist to support decomposition of a fully coupled operator. Additionally, facilities that allow the construction of approximate inverse operators using the full complement of available preconditioners and solvers are available in Teko. Finally, a small number of generic block preconditioners has been implemented in Teko, including block Jacobi, and block Gauss-Seidel. For the Navier-Stokes equation, Teko has implementations of SIMPLE, PCD and LSC. For details on these methods see Stabilization and Scalable Block Preconditioning for the Navier-Stokes Equations and the references therein
P. Benner, and J. Heiland. Active Flow and Combustion Control 2014, volume 127 of Notes on Numerical Fluid Mechanics and Multidisciplinary Design, page 365--379. Cham, Springer, (2015)