Advances in Computational Mathematics 4(1995)127-144 127 Analysis of preconditioning and multigrid for Euler flows with low-subsonic regions*

For subsonic flows and upwind-discretized, linearized 1-D Euler equations, the smoothing behavior of multigrid-accelerated point Gauss-Seidel relaxation is n lyzed. Error decay by convection across domain boundaries is lso discussed. A fix to poor convergence rates at low Mach numbers is sought in replacing the point relaxation applied to unconditioned Euler equations, by locally implicit "time"-stepping applied to preconditioned Euler equa-tions. The locally implicit iteration step is optimized for good damping of high-frequency errors. Numerical inaccuracy at low Mach numbers is also addressed