High-order numerical methods are an excellent candidate for high-performance computational fluid dynamics. These methods are highly accurate and have a low ratio between communication and computation. However, they are susceptible to numerical instabilities in the presence of under resolved turbulence or shocks. Robust entropy stable methods address this problem with stability proofs based on continuum entropy conservation turned discrete entropy stability. This dissertation experimentally tests this robustness in various situations, including benchmark problems in different flow conditions and a challenging engineering application: Large-eddy simulation (LES) of turbulence and pollutant dispersion in the Planetary Boundary Layer(PBL). The code framework used, denoted SSDC for entropy Stable Discontinuous Collocation, is applied here for the numerical solution of the compressible Navier–Stokes equations. It satisfies mass, momentum, and energy conservation, plus entropy stability. The benchmark tests compare one entropy stable discretization with alternative(non-entropy stable) discretizations. The results constitute evidence favoring the entropy stable discretization in accuracy, cost, and robustness at high order, compared with non-entropy stable alternatives. These benchmarks span a wide variety of flow conditions, including subsonic, supersonic, smooth flows, and turbulent transition. SSDC is then used in a challenging application: implicit LES of the PBL. This highly turbulent subsonic flow is simulated for a parametric study assessing the impact the PBL’s depth has on turbulence and pollutant dispersion. The PBL depths studied ranged from 1 km (typical in moderate latitudes) to 4 km (close to extreme depths ofdesert PBL). A methodology was developed to emulate the PBL’s thermal structure and turbulence. The accuracy of SSDC, and especially its robustness, were crucial for the simulation’s success. Considerable domain dimensions were required to develop turbulence from smooth boundary inflow with implications for nesting. A passive tracer emulating stack emissions was used for the dispersion process. The plume’s center and its height distribution were tracked. The results show the height of the tracer’s vertical mixing in the PBL growing nonlinearly with the depth of the PBL. This finding could pave the way to improving pollutant injection parametrization and subgrid mixing in mesoscale and global atmospheric models.
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|KAUST Research Repository