A high-order flux reconstruction (FR) scheme on unstructured hexahedral grids is coupled with the localized artificial diffusivity (LAD) scheme for aiming at accurate simulation of shock-turbulence interactions. Suitable flux reconstruction procedure is derived for ensuring the global discrete conservation. We then propose a simple and efficient filter for obtaining smooth distribution of the artificial diffusivity on unstructured hexahedral meshes, which is one of the key issues for developing robust LAD method on unstructured meshes. The proposed scheme has favorable properties of sub-cell shock capturing with the length scale of O(h/p) and superior high-order-accuracy preservation for smooth flows. The proposed scheme is tested on typical shock-related problems, including 1D shock tube, 1D shock-entropy wave interaction, 2D steady shock flows, and 2D shock-vortex interaction. The comparisons between the proposed scheme, a conventional finite volume method and the FR scheme with a limiter illustrate the superior performance of the proposed FR-LAD scheme for the simulation of flows involving shocks, acoustic waves, turbulence, and their interaction.
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