Publications

The aerodynamic design of aircraft often involves evaluating flow conditions that span low subsonic to transonic, or even supersonic Mach numbers. Compressible flow solvers are a natural choice for such design problems, but these solvers encounter reduced accuracy and efficiency at low Mach numbers. In addition, simulations with supersonic conditions can be challenging to converge because of large gradients in the flow field. This paper presents three contributions to address these issues in the context of an approximate Newton–Krylov solver for the Reynolds-averaged Navier–Stokes equations. First, we propose a method for scaling artificial dissipation that improves accuracy at low Mach numbers while retaining the simplicity of the original scalar dissipation scheme. Second, we show that characteristic time-stepping combined with an approximate Newton method can accelerate convergence for low Mach number flows by reducing the stiffness in the linear system for each Newton iteration. Third, we introduce a dissipation-based continuation method for flows with shocks that improves robustness and accelerates convergence without sacrificing accuracy. These methods can be used to make compressible flow solvers more accurate and efficient across low and high Mach number regimes.