Compressible lattice Boltzmann model on standard lattices [M. H. Saadat, F. Bösch, and I. V. Karlin, Phys. Rev. E 99, 013306 (2019).] is extended to deal with complex flows on unstructured grid. Semi-Lagrangian propagation [A. Krämer et al., Phys. Rev. E 95, 023305 (2017).] is performed on an unstructured second-order accurate finite-element mesh and a consistent wall boundary condition is implemented which makes it possible to simulate compressible flows over complex geometries. The model is validated through simulation of Sod shock tube, subsonic and supersonic flow over NACA0012 airfoil and shock-vortex interaction in Schardin's problem. Numerical results demonstrate that the present model on standard lattices is able to simulate compressible flows involving shock waves on unstructured meshes with good accuracy and without using any artificial dissipation or limiter.

中文翻译：

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非结构网格上可压缩流的半拉格朗日格子Boltzmann模型

标准晶格上的可压缩晶格Boltzmann模型[M. H. Saadat，F。Bösch和I. V. Karlin，物理学 启ë 99，013306（2019）。]被扩展以处理上非结构化网格复杂流动。半拉格朗日传播[A. Krämer等。，物理 E 95版，023305（2017）。]是在非结构化二阶精确有限元网格上执行的，并且实现了一致的壁边界条件，这使得可以模拟复杂几何形状上的可压缩流。通过模拟Sod激波管，NACA0012机翼上的亚音速和超音速流以及Schardin问题中的激涡相互作用来验证该模型。数值结果表明，在标准格子上的当前模型能够在不使用任何人工耗散或限制器的情况下，以良好的精度模拟非结构化网格上涉及冲击波的可压缩流。