The application of large-eddy simulation(LES)to particle-laden turbulence raises such a fundamental ques-tion as whether the LES with a subgrid scale(SGS)model cancorrectly predict Lagrangian time correlations(LTCs).Mostof the currently existing SGS models are constructed basedon the energy budget equations.Therefore,they are able tocorrectly predict energy spectra,but they may not ensure thecorrect prediction on the LTCs.Previous researches investi-gated the effect of the SGS modeling on the Eulerian timecorrelations.This paper is devoted to study the LTCs in LES.A direct numerical simulation(DNS)and the LES with aspectral eddy viscosity model are performed for isotropicturbulence and the LTCs are calculated using the passivevector method.Both a priori and a posteriori tests are car-ried out.It is observed that the subgrid-scale contributions tothe LTCs cannot be simply ignored and the LES overpredictsthe LTCs than the DNS.It is concluded from the straininghypothesis that an accurate prediction of enstrophy spectrais most critical to the prediction of the LTCs.
A new shock-capturing method is proposed which is based on upwind schemes and flux-vector splittings. Firstly, original upwind schemes are projected along characteristic directions. Secondly, the amplitudes of the characteristic decompositions are carefully controlled by limiters to prevent non-physical oscillations. Lastly, the schemes are converted into conservative forms, and the oscillation-free shock-capturing schemes are acquired. Two explicit upwind schemes (2nd-order and 3rd-order) and three compact upwind schemes (3rd-order, 5th-order and 7th-order) are modified by the method for hyperbolic systems and the modified schemes are checked on several one-dimensional and two-dimensional test cases. Some numerical solutions of the schemes are compared with those of a WENO scheme and a MP scheme as well as a compact-WENO scheme. The results show that the method with high order accuracy and high resolutions can capture shock waves smoothly.
