▪ Abstract An overview of preconditioning for the steady-state compressible inviscid fluid dynamic equations is presented. Extensions to the Navier-Stokes equations are also considered. These preconditioners are necessary for many algorithms in order to have the correct behavior at low speeds and to converge to the solution of the incompressible equations as the Mach number goes to zero. In addition, the preconditioning accelerates the convergence to a steady state for problems in which a significant portion of the flow is low speed. This low speed preconditioner can be combined with Jacobi and line preconditioners to damp high frequencies at all speeds. This is necessary for use with multigrid methods. Such combined methods are also better at accelerating problems with high aspect ratios. Details of the implementation are presented including several different variants for the preconditioning matrix.