Implicit Large-Eddy Simulation: Theory and Application

Large-Eddy Simulation has been recognized as one of the major tools for the numerical simulation of complex turbulent flows, in events when more accessible alternative approaches, such as statistically averaged Navier-Stokes equations (Reynolds-averaged Navier-Stokes equations - RANS), fail. This is in particular the case, when complex flow phenomena (reaction, fluid-structure interaction, interfaces, shocks) introduce additional non-turbulent temporal or spatial scales. It is known since quite some time that the nonlinear truncation error of some classes of discretization schemes for the Navier-Stokes equations not only interferes with explicitly added subgrid-scale (SGS) models but also can provide some SGS closure when no model is added at all. More recent analyses of such schemes have outlined the way to a more systematic procedure for such no-model approaches, leading to what is called now implicit LES (ILES). With ILES no subgrid-scale model is added to the discretized Navier- Stokes equations, and SGS modeling is left solely to the numerical truncation error. In this contribution we will outline a theory of ILES which allows for physically motivated modeling of the nonlinear truncation error, called adaptive local deconvolution method (ALDM), and demonstrate its feasibility for reliable LES of a wide range of turbulent flow configurations.