Design and analysis of ALE schemes with provable second-order time-accuracy for inviscid and viscous flow simulations

We consider the solution of inviscid as well as viscous unsteady flow problems with moving boundaries by the arbitrary Lagrangian–Eulerian (ALE) method. We present two computational approaches for achieving formal second-order time-accuracy on moving grids. The first approach is based on flux time-averaging, and the second one on mesh configuration time-averaging. In both cases, we prove that formally second-order time-accurate ALE schemes can be designed. We illustrate our theoretical findings and highlight their impact on practice with the solution of inviscid as well as viscous, unsteady, nonlinear flow problems associated with the AGARD Wing 445.6 and a complete F-16 configuration.