Modification of the LS-STAG Immersed Boundary Method for Simulating Turbulent Flows

We constructed the LS-STAG discretisation for 2D Reynolds-averaged Navier -- Stokes equations, filtered Navier -- Stokes equations (as used for large eddy simulation and detached eddy simulation) and equations employed in the Smagorinsky, Spalart -- Allmaras, k−ε, k−ω and k−ω Menter's Shear Stress Transport turbulence models. We added a fourth grid to the LS-STAG mesh consisting of three staggered grids. We computed the following parameters at the centres of the additional mesh cells: turbulent shear stress and, depending on the turbulence model used, turbulence kinetic energy, turbulent viscosity, and turbulent kinetic energy dissipation rate. We verified the developed numerical method by solving the problem of flow around a circular airfoil when the flow has a high Reynolds number (10²...10⁷). The obtained results are in good agreement with published experimental data and numerical results of other researchers. Our modification of the LS-STAG immersed boundary method made it possible to model the so-called "drag crisis" phenomenon for a circular airfoil when Re = 10⁵...10⁶

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