Predicting non-linear flow phenomena through different characteristics-based schemes

The present work investigates the bifurcation properties of the Navier–Stokes equations using characteristics-based schemes and Riemann solvers to test their suitability to predict non-linear flow phenomena encountered in aerospace applications. We make use of a single- and multi-directional characteristics-based scheme and Rusanov’s Riemann solver to treat the convective term through a Godunov-type method. We use the Artificial Compressibility (AC) method and a unified Fractional-Step, Artificial Compressibility with Pressure-Projection (FSAC-PP) method for all considered schemes in a channel with a sudden expansion which provides highly non-linear flow features at low Reynolds numbers that produces a non-symmetrical flow field. Using the AC method, our results show that the multi-directional characteristics-based scheme is capable of predicting these phenomena while the single-directional counterpart does not predict the correct flow field. Both schemes and also Riemann solver approaches produce accurate results when the FSAC-PP method is used, showing that the incompressible method plays a dominant role in determining the behaviour of the flow. This also means that it is not just the numerical interpolation scheme which is responsible for the overall accuracy. Furthermore, we show that the FSAC-PP method provides faster convergence and higher level of accuracy, making it a prime candidate for aerospace applications.