Gagan Deep Prakash

• This thesis describes the implementation of the immersed boundary method with Cartesian grids for large eddy simulations in the lattice Boltzmann context. Wall modelling allows the use of the advantages of the lattice Boltzmann method for LES without the high computational costs caused by wall-resolved approaches. However, this presents challenges because the near-wall nodes lie in a wide range of y + values, and the adjacent nodes are not perpendicular, as in the body-fitted mesh used in traditional solvers. These problems are addressed by a reconstruction procedure for the distribution function, which consists of near-wall friction velocity interpolations for smooth and stable boundary behaviour with coarse grids. In addition, accurate explicit wall functions consistent with the turbulence model were implemented to reduce the computational effort while maintaining accuracy. Finally, near-wall turbulence modelling was enhanced using a hybrid RANS–LES model with a blending region. The implemented code was verified for the turbulent channel flow case for different frictional Reynolds numbers, showing reasonable results. A complete discussion of the required algorithms, common modelling errors, results, and possible future work is provided.