A mixed LES model based on the residual-based variational multiscale formulation

Recently the residual-based variational multiscale method (RBVM) has been used to model the subgrid stresses in the large eddy simulation of turbulent flows. The basic idea is to introduce decomposition of the solution into resolved or coarse scales and unresolved or fine scales. The fine scale equation is expressed in terms of the coarse scale residual analytically and is substituted into coarse scale equation which is solved numerically. The first part of this thesis analyzes the scale dependence of the RBVM model using fully resolved numerical solutions and conclude that the RBVM model accurately captures the scale dependence of the cross stress terms (uhu') but under-predicts the contribution from the Reynolds stress terms ( u'u'), which is well represented by an eddy viscosity model.;A mixed model then is introduced for large eddy simulation, wherein the cross stress term is modeled by the RBVM model, and the Reynolds stress term is represented by the Smagorinsky eddy viscosity. The mixed model is capable of accurately modeling all components of the subgrid stress. In the second part of this work, mixed model is implemented using a Fourier-spectral method to predict the decay of homogeneous isotropic turbulence. The unknown parameter is determined dynamically using the variational counterpart of the Germano identity. In the last part of this work, it is used to simulate the turbulent channel flow using a finite element method with Smagorinsky coefficient computed dynamically. We note that the mixed model yields better agreement with direct numerical simulation (DNS) than either of its components: the RBVM model and the dynamic Smagorinsky model.;The mixed model yields encouraging results for the large eddy simulation of homogeneous isotropic turbulence and turbulent channel flow. However, it needs further testing on more complex geometries, and for more complex flows, such as compressible flows and flows with magnetic field.