On CFL Evolution Strategies for Implicit Upwind Methods in Linearized Euler Equations∗

In implicit upwind methods for the solution of linearized Euler equations, one of the key issues is to balance large time steps, leading to a fast convergence behavior, and small time steps, needed to sufficiently resolve relevant flow features. A time step is determined by choosing a CourantFriedrichs-Levy (CFL) number in every iteration. A novel CFL evolution strategy is introduced and compared with two existing strategies. Numerical experiments using the adaptive multiscale finite volume solver QUADFLOW demonstrate that all three CFL evolution strategies have their advantages and disadvantages. A fourth strategy aiming at reducing the residual as much as possible in every time step is also examined. A truncation error-free sensitivity analysis investigating the influence of the CFL number on the residual is carried out confirming that, today, CFL control is still a highly intricate problem.