An invariant-region-preserving (IRP) limiter for multi-dimensional hyperbolic conservation law systems is introduced, as long as the system admits a global invariant region which is a convex set in the phase space. It is shown that the order of approximation accuracy is not destroyed by the IRP limiter, provided the cell average is away from the boundary of the convex set. Moreover, this limiter is explicit, and easy for computer implementation. A generic algorithm incorporating the IRP limiter is presented for high order finite volume type schemes. For arbitrarily high order discontinuous Galerkin (DG) schemes to hyperbolic conservation law systems, sufficient conditions are obtained for cell averages to remain in the invariant region provided the projected one-dimensional system shares the same invariant region as the full multidimensional hyperbolic system does. The general results are then applied to both one and two dimensional compressible Euler equations so to obtain high order IRP DG schemes. Numerical experiments are provided to validate the proven properties of the IRP limiter and the performance of IRP DG schemes for compressible Euler equations.

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Numerical investigations of body-wake interactions were carried out by simulating the flow over a rod-airfoil configuration using high-order implicit large eddy simulation (HILES) for the incoming velocity U ∞ = 72 m s −1 and a Reynolds number based on the airfoil chord 4.8 × 10 5 . The flow over five different rod-airfoil configurations with different distances of L/d = 2, 4, 6, 8 and 10, respectively, were calculated for the analysis of body-wake interaction phenomena. Various fundamental mechanisms dictating the intricate flow phenomena including force varying regulation, flow structures and flow patterns in the interaction region, turbulent fluctuations and their suppression, noise radiation and fluid resonant oscillation, have been studied systematically. Due to the airfoil downstream, a relatively higher base pressure is exerted on the surface of the cylinder upstream, and the pressure fluctuation on the surface of the rod-airfoil configuration with L/d = 2 is significantly suppressed, resulting in a reduction of the fluctuating lift. Following the distance between the cylinder and airfoil strongly decreases, Kármán-street shedding is suppressed due to the blocking effect. The flow in this interaction region has two opposite tendencies: the influence of the airfoil on the steady flow is to accelerate it and the counter-rotating vortices connecting with the leading edge of the airfoil tend to slow the flow down. There may be two flow patterns associated with the interference region, i.e. the Kármán-street suppressing mode and the Kármán-street shedding mode. The primary vortex shedding behind the cylinder upstream, and the shedding wake impingement onto the airfoil downstream, play a dominant role in the production of turbulent fluctuations. When primary vortex shedding is suppressed, the intensity of impingement is weakened, resulting in a significant suppression of the turbulent fluctuations. Due to these factors, a special broadband noise without a manifestly distinguishable peak is radiated by the rod-airfoil configuration with L/d = 2. The fluid resonant oscillation within the flow interaction between the turbulent wake and the bodies was further investigated by adopting a feedback model, which confirmed that the effect of fluid resonant oscillation becomes stronger when L/d = 6 and 10.The results obtained in this study provide physical insight into the understanding of the mechanisms relevant to the body-wake interaction.

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