Cancellation problem of preconditioning method at low Mach numbers

The effects of cancellation errors on the convergence characteristics of preconditioned Navier–Stokes equations at low Mach numbers are analyzed. Laminar viscous flows around a circular cylinder are calculated at different Mach numbers. It is shown that the cancellation error in the energy equation grows faster than those in the other equations, as the Mach number decreases. It is also shown that the cancellation problem of the energy equation is due to the off-diagonal element that is related to a pressure change in the preconditioner.