Abstract
A method for shock capturing by adaptive filtering for use with high-resolution, high-order schemes for Large Eddy Simulations (LES) is presented. The LES method used in all the examples here employs the Explicit Filtering approach and the spatial derivatives are obtained with sixth-order, compact, finite differences. The adaptation is to drop the order of the explicit filter to two at gridpoints where a shock is detected, and to then increase the order from 2 to 10 in steps at successive gridpoints away from the shock. The method is found to be effective in a series of tests of common inviscid 1D and 2D problems of shock propagation and propagation of waves through shocks. As a prelude to LES, the 3D Taylor–Green problem for the inviscid and a finite viscosity case were simulated. An assessment of the overall performance of the method for LES was carried out by simulating an underexpanded round jet at a Reynolds number of 6.09 million, based in centerline velocity and diameter at nozzle exit plane. Very close quantitative agreement was found for the development of centerline mean pressure when compared to experiment. Simulations on several increasingly finer grids showed a monotonic extension of the computed part of the inertial range, with little change to low frequency content. Amplitudes and locations of large changes in pressure through several cells were captured accurately. A similar performance was observed for LES of an impinging jet containing normal and curved shocks.
Highlights
Large eddy simulation (LES) has become a widely-used technique
That the performance of the proposed method has been evaluated carefully in canonical problems of isolated shocks, wave refraction by a shock, and the evolution of a turbulent flow at a moderate Reynolds number accessible to direct numerical simulation (DNS), we turn to simulations of high Reynolds number, turbulent, supersonic jets
Shock positions and strengths change little with refinement. This serves as strong support for the adaptive filtering method for shock capturing used in these simulations
Summary
Large eddy simulation (LES) has become a widely-used technique. The greater expense in computing resources and time is justified when it provides accurate solutions, especially when the more common RANS (Reynolds-averaged Navier–Stokes) methods yield qualitatively incorrect solutions. Test cases included 1D and 2D inviscid flows and shock reflection from a laminar boundary layer They found that their adaptive filter method provided a significant improvement—oscillation-free solution—over their baseline filter-stabilized compact scheme, but shocks were smeared over a few cells; the hybrid compact-Roe scheme gave sharper shocks. First, we discuss the basic numerical method (sixth-order, Hixon–Turkel split compact scheme for spatial derivatives, and fourth-order Runge–Kutta for time-stepping) and the proposal for filter adaptation. The Taylor–Green problem is included to record the correctness of the code for viscous flows that develop a wide range of scales, as well as the effectiveness as LES for the inviscid case With these elements of flows completed, we turned to LES of supersonic jets at Reynolds numbers of O(106 ) (based on jet diameter and jet velocity at the nozzle exit). The second LES of an impinging jet provides further support for the method as a suitable approach for applications
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