Enabling the cumulant lattice Boltzmann method for complex CFD engineering problems

Abstract

Computational Fluid Dynamics (CFD) uses numerical methods to solve problems involving fluid flows, e.g. in automotive engineering, energy, civil engineering, and aerospace. One of these methods is the lattice Boltzmann method (LBM). Beside giving accurate results for a wide range of complex flows, the LBM lends itself to efficient implementations on massively parallel systems such as the general-purpose computing on graphics processing units (GPGPU). This work considers the cumulant LBM, which overcomes some problems of classical LBMs, such as the violation of the Galilean invariance, the spurious coupling of the degrees of freedoms, and the hyper-viscosity. In order to enable the cumulant LBM for complex CFD engineering problems, this work focuses on the discretization of the computational domain and the analysis of turbulent flows in the near-wall region. The grid generation for LBM deals with several issues such as the second order boundary definition, the free shape grid refinement, and the level wise load balancing for parallel meshes. While discretizing complex geometries, these issues have to be handled simultaneously. Turbulent flows close to walls are characterized by high velocity gradients in a thin region called the boundary layer. In order to resolve numerically the boundary layer, a grid with a high resolution is required resulting in a high computational cost for the simulation. Empirical functions can be used for modelling the boundary layer, allowing to estimate the quantities at the wall even with coarse grids, and thus increasing the efficiency of the numerical simulation. In this work, a new grid generator that addresses the LBM discretization issues is implemented. It creates free shape multi-level three-dimensional meshes with second order accurate boundary definition for very complex geometries. It can be applied for generating grids of complex bodies, such as cars, porous media, and urban areas. Regarding the near-wall region treatment, a new wall function is introduced. It uses local information at the boundary nodes for recovering the quantities at the wall. For generating a proper turbulence for wall bounded flows, a new set of relaxation parameters is introduced, which eliminates the spurious dependence of the error on the bulk viscosity. In conclusion, this work addresses two important aspects for enabling the cumulant LBM for complex fluid flow problems: grid generation and boundary treatment for turbulent flows.