Direct Numerical Simulations (DNS) and Large Eddy Simulations (LES) - Theory and Practice - Course Notes

Recently, there has been a surge of interest from the industry in unsteady turbulent flows computations. Most of the Computational Fluid Dynamics (CFD) methods employed so far proceed by solving the Reynolds-Averaged Navier-Stokes (RANS) equations that are based on semi-empirical turbulence models. It is well known, however, that the RANS-based computations of unsteady turbulent flows are not fully reliable. This results in a high demand for the time-consuming and costly experiments in order to verify these CFD predictions. In the future, accurate LES and DNS are expected to gradually take over those validating duties. By doing a DNS, one resolves all relevant spatial and temporal turbulent scales. Similarly, in a LES the complete range of the temporal scales and at least large and moderate spatial scales are resolved. For that reason, the DNS and LES are the most accurate and comprehensive tools for predicting all relevant turbulent processes and investigating the nature of turbulence. In this DNS/LES course we are going to follow the entire route from observing a physical phenomenon to performing DNS and LES, starting from developing physical models and making their governing equations dimensionless. We will discuss the ways of discretizing and developing higherorder schemes, and will learn how to arrange the mesh resolution requirements. After that, we will consider the numerical stability of both explicit and semi-implicit timestepping schemes, as well as the filtering techniques and reliability of the subgrid scale turbulence models needed for the LES. In the practical part of the course, the abovementioned topics will be explored with the help of a free and open source software package Open-FOAM. This will enable the participants to practise the DNS and LES techniques in various flow problems, as well as allowing a continued usage of the same software after finishing the course. In addition to that, some learning programs will be used in order to give the participants a detailed understanding of the effect that the discretization order, mesh resolution and numerical stability have on the quality of the results obtained in a DNS or a LES