Convergence properties of high‐Reynolds‐number separated flow calculations

Abstract

AbstractThe convergence properties of an iterative solution technique for the Reduced Navier–Stokes equations are examined for two‐dimensional steady subsonic flow over bump and trough geometries. Techniques for decreasing the sensitivity to the initial pressure approximation, for fine meshes in particular, are investigated. They are shown to improve the robustness of the relaxation process and to decrease the computational work required to obtain a converged solution. A semi‐coarsening multigrid technique that has previously been found to be particularly advantageous for high‐Reynolds‐number (Re) flows with flow separation and with highly stretched surface‐normal grids is applied herein to further accelerate convergence. Solutions are obtained for the laminar flow over a trough that is more severe than has been considered to date. Sufficient axial grid refinement in this case leads to a shock‐like reattachment and, for sufficiently large Re, to a local ‘divergence’ of the numerical computations. This ‘laminar flow breakdown’ appears to be related to an instability associated with high‐frequency fine‐grid modes that are not resolvable with the present modelling. This behaviour may be indicative of dynamic stall or of incipient transition. The breakdown or instability is shown to be controllable by suitable introduction of transition turbulence models or by laminar flow control, i.e. small amounts of wall suction. This lends further support to the hypothesis that the instability is of a physical rather than numerical character and suggests that full three‐dimensional analysis is required to properly capture the flow behaviour. Another inference drawn from this investigation is that there is a need for careful grid refinement studies in high‐Re flow computations, since coarser grids may yield oscillation‐free solutions that cannot be obtained on finer grids.