Assessment of an adaptive time integration strategy for a high-order discretization of the unsteady RANS equations

Many industrial applications, for example, aeronautics, aeroacoustics, and turbomachinery, are characterized by complex turbulent flow problems, whose numerical studies are mostly based on statistical models. These models rely on the Navier-Stokes equations averaged in time, namely the Reynolds-averaged Navier-Stokes (RANS) equations. RANS unsteady solutions require accurate and efficient time integration strategies, and the choice of the time-step can have a strong impact on the robustness and efficiency of the simulation. Adaptive time step algorithms can improve considerably the effectiveness of time integration, but in literature little information is available on their application to unsteady RANS equations for high-Reynolds number turbulent flows. This work aims at reducing this gap, presenting a numerical investigation of the performance of different adaptive temporal strategies applied to linearly implicit Rosenbrock-type schemes within a high-order discontinuous Galerkin framework. Several test cases of increasing stiffness and difficulty are considered for both compressible and incompressible turbulent flows.