Preconditioned methods for solving the incompressible and low speed compressible equations

The introduction of artificial time derivatives which permit faster convergence to the steady state is used to precondition steady state incompressible equation-solving acceleration methods. An optimal value is obtained for beta, given constant alpha, where alpha and beta are arbitrary functions in the general preconditioning stage. A symmetric hyperbolic system is formed by the resulting incompressible equations. Compressible equations in conservation form with slow flow are also considered.