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Commun. Comput. Phys., 35 (2024), pp. 395-426.
Published online: 2024-03
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In the numerical simulation of compressible turbulence involving shock waves, accurately capturing the intricate vortex structures and robustly computing the shock wave are imperative. Employing a high-order scheme with adaptive dissipation characteristics proves to be an efficient approach in distinguishing small-scale vortex structures with precision while capturing discontinuities. However, differentiating between small-scale vortex structures and discontinuities during calculations has been a key challenge. This paper introduces a high-order adaptive dissipation central-upwind weighted compact nonlinear scheme based on vortex recognition (named as WCNS-CU-Ω), that is capable of physically distinguishing shock waves and small-scale vortex structures in the high wave number region by identifying vortices within the flow field, thereby enabling adaptive control of numerical dissipation for interpolation schemes. A variety of cases involving Euler, N-S even RANS equations are tested to verify the performance of the WCNS-CU-Ω scheme. It was found that this new scheme exhibits excellent small-scale resolution and robustness in capturing shock waves. As a result, it can be applied more broadly to numerical simulations of compressible turbulence.
}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2023-0164}, url = {http://global-sci.org/intro/article_detail/cicp/22945.html} }In the numerical simulation of compressible turbulence involving shock waves, accurately capturing the intricate vortex structures and robustly computing the shock wave are imperative. Employing a high-order scheme with adaptive dissipation characteristics proves to be an efficient approach in distinguishing small-scale vortex structures with precision while capturing discontinuities. However, differentiating between small-scale vortex structures and discontinuities during calculations has been a key challenge. This paper introduces a high-order adaptive dissipation central-upwind weighted compact nonlinear scheme based on vortex recognition (named as WCNS-CU-Ω), that is capable of physically distinguishing shock waves and small-scale vortex structures in the high wave number region by identifying vortices within the flow field, thereby enabling adaptive control of numerical dissipation for interpolation schemes. A variety of cases involving Euler, N-S even RANS equations are tested to verify the performance of the WCNS-CU-Ω scheme. It was found that this new scheme exhibits excellent small-scale resolution and robustness in capturing shock waves. As a result, it can be applied more broadly to numerical simulations of compressible turbulence.