Numerical solution of low-mach-number flows using the rational Runge-Kutta scheme

The rational Runge-Kutta scheme for the compressible Navier-Stokes equations is applied to the simulation of low-Mach-number flows. The residual averaging and multigrid techniques are incorporated into the scheme, so that the convergence rate to a steady-state solution is improved. As typical test flow problems, driven cavity flows and flows past a circular cylinder and the NACA 0012 airfoil are considered. The present scheme still gives converged solution even at Mach number 0.01, though the convergence rate becomes slower as the Mach number is reduced. Numerical solutions obtained at different Mach numbers from 0.01 to 0.2 agree well with one another and reliable solutions of the incompressible Navier-Stokes equations. The pressure distribution obtained around the NACA 0012 airfoil at Mach number 0.3 and Reynolds number 3.0 × 106 is in agreement with corresponding experimental data. The present scheme is confirmed to be reliable even for the analyses of low-Mach-number flows.