Preconditioning-squared methods for multidimensional aerodynamics

Several different preconditionings for the Euler and Navier-Stokes equations have been introduced to accelerate the convergence to a steady state and also to improve the accuracy of the approximate solution. In particular we consider three different preconditioners, one appropriate for low speed flow, a second appropriate for high frequencies and a third differential one that diagonalizes the system. We compare the properties of these various approaches and show how they can be combined to give the benefits of all the preconditionings.