Fundamentals of Turbulent Flows

An overview of the three modern categories of methods for numerical prediction of turbulent flows is provided: direct numerical simulation (DNS), solution of the Reynolds-averaged Navier-Stokes (RANS) equations, and large-eddy simulation (LES). We describe zero-equation, one-equation, two-equation, and Reynolds stress transport models for the RANS equations. RANS computations require significantly fewer grid points and lower computational cost since the solutions are smooth and turbulent structures are not captured, but there is a need to tune model parameters for different flows to match experimental data. In LES, only the large-scale motions are resolved, whereas unresolved small scales are modeled. We introduce the notion of filtering, subgrid-scale parameterization, as well as the seminal dynamic Smagorinsky subgrid-scale model. Wall-resolved and wall-modeled LES are briefly discussed. With ever increasing computer power, as well as advances in numerical methods and subgrid-scale models, LES is rapidly becoming a viable tool for practical computations. In selecting a method, one should consider quantities to be predicted, accuracy of the predictions, and the computational cost.