| Multi-scale flows in cross flow regimes are of great importance academically and practically.In the present work,the unified gas-kinetic scheme(UGKS)is further improved to increase its efficiency,and applied in the numerical studies in typical multi-scale flows.In order to improve the efficiency in large-scale parallel computations,based on blocking both in the physical and velocity space,together with the MPI Cartesian topology to group the inter-process communications and adjustment of the sequence in UGKS,the UGKS suitable for three-dimensional complex multi-block structured meshes is developed especially for large-scale computations.A large number of tests are conducted which validate its high efficiency both in small and large-scale computations.To simulate axisymmetric flows in all Knudsen number regimes with high efficiency,the analytical solution in the local three-dimensional Cartesian coordinates is utilized to construct the axisymmetric source term and thus the multi-scale UGKS-AS and the corresponding implicit scheme are developed.Its high efficiency is confirmed in typical axisymmetric flows.A simplification in UGKS is conducted in continuum regime of cross regime flows,without the discretization in velocity space which effectively improves the computational efficiency.Numerical studies by UGKS are carried out for small-scale statistics in typical compressible turbulent problems.It is found by the simulation of the acoustic wave/shock interaction that the rarefied effect in strong shock structure of Mach number 8 and highfrequency acoustic waves results in a significantly weaken amplification effect on the wave by the shock.Direct numerical simulations of two and three-dimensional compressible decaying homogeneous isotropic turbulence show the statistics of fluctuations with different scales.The rarefied effect of the small-scale fluctuations is studied and the applicability of the NS result is evaluated quantitatively. |
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