ABSTRACT
Large Eddy Simulations are carried out in finite-size computational domains chosen by the user. For solving the governing differential equations, boundary conditions must be specified at all boundaries of this domain, as well as initial conditions for the dependant variables within the entire domain at the start of the time-marching simulation. The computational domain depends strongly on the geometry and flow conditions of the problem considered, and a variety of examples will be given in the Applications Chapter 9. The boundaries of the computational domain can be of various types, and those occurring in hydraulics problems are illustrated by way of the calculation domain being a stretch of a river in Figure 6.1. The bed consisting of a solid wall (which in exceptional cases may be permeable) and the free surface are physical boundaries. The wall boundary at the bed may be horizontal or inclined, but in channels with rectangular cross section and in the presence of man-made structures or idealized vegetation elements, vertical walls are also present as physical boundaries. In addition, artificial boundaries are usually introduced in order to limit the size of the calculation domain. Considering only a stretch of a river as shown in Figure 6.1, an inflow and an outflow boundary needs to be chosen by the user limiting the domain in the streamwise direction, but when the flow can be considered statistically homogenous in one of the other directions, the domain can be limited in this direction by introducing artificial periodic boundaries. Often the conditions at the boundaries cannot be formulated to represent exactly the real physical conditions prevailing at the boundaries, e.g. when details of a rough wall are unknown or velocity fluctuations at the inflow or at a free surface need to be approximated. Hence models are necessary for these approximations and these are named super-grid models. The uncertainties and possible errors introduced due to such super-grid modelling can be orders of magnitude larger than those due to subgrid-scale modelling and hence the quality of a LES is generally greatly affected by the treatment of each boundary in the numerical simulation.
