AN EFFECTIVE MULTIGRID METHOD FOR HIGH-SPEED FLOWS

We consider the use of a multigrid method with central differencing to solve the Navier Stokes equations for high-speed flows. The time-dependent form of the equations is integrated with a Runge-Kutta scheme accelerated by local time-stepping and variable-coefficient implicit residual smoothing. Of particular importance are the details of the numerical dissipation formulation, especially the switch between the second and fourth difference terms. Solutions are given for two-dimensional laminar flow over a circular cylinder and a 15-degree compression ramp.