Residual-based variational multiscale models for the large eddy simulation of compressible and incompressible turbulent flows.

摘要

In the large-eddy simulation (LES) for turbulent flows, the large scale unsteady turbulent motions which are affected by the flow geometry, are directly solved, while the effects of the small scale motions which have a universal character are modeled. Compared with direct numerical simulation (DNS), the huge computational cost for solving the small-scale motions in high Reynolds number flows is avoided in LES.;In the variational multiscale (VMS) formulation of LES, the starting point for deriving models is the weak or the variational statement of conservation laws, whereas in the traditional filter-based LES formulation it is the strong form of these equations. In the residual-based variational multiscale (RBVM) formulation, the basic idea is to split the solution and weighting function spaces into coarse and fine scale partitions. Splitting the weighting functions in this way yields two sets of coupled equations: one for the coarse, or the resolved, scales and another for the fine, or the unresolved, scales. The equations for the fine scales are observed to be driven by the residual of the coarse scale solution projected onto the fine scale space. These equations are solved approximately and the solution is substituted in the equations for the coarse scales. In this way the effect of the unresolved scales on the resolved scales is modeled.;In this thesis we develop and test several LES models that are based on the RBVM formulation. These include:;1. The RBVM model, which is extended to compressible flows for the first time. 2. A new mixed model for compressible flows comprised of the RBVM model and the traditional Smagorinsky-type eddy viscosity model. In this model the RBVM term is used to model the cross-stresses and the eddy viscosity is used to model the Reynolds stresses. 3. A new residual-based eddy viscosity (RBEV) model for incompressible and compressible flows that displays a "dynamic" behavior without the need to evaluate any dynamic parameters, thus making it easy to implement. 4. A purely residual-based mixed model comprised of the RBVM model for the cross-stresses and the RBEV model for the Reynolds stresses, that is relatively easy to implement.;All these models are tested in modeling the decay of compressible homogeneous isotropic turbulence using a Fourier-spectral basis. The RBVM, the RBEV and the purely residual based mixed model are also tested in predicting the statistics of an incompressible turbulent channel flow using the finite element method. It is found that in general, the new residual-based models outperform the traditional eddy viscosity models.