In this chapter we give an overview of various lifting strategies for lattice Boltzmann
models (LBMs). A lifting operator finds for a given macroscopic variable the corresponding
distribution functions, mesoscopic variables of the lattice Boltzmann model. This
is, for example, useful in coupled LBM and partial differential equation (PDE) models,
where one part of the domain is described by a macroscopic PDE while another part is
modeled by a LBM. Such a hybrid coupling results in missing data at the interfaces between
the different models. The lifting operator provides the correct boundary conditions
for the LBM domain at the interfaces. We discuss the accuracy, computational cost and
convergence rate of some analytical and numerical lifting procedures.
Keywords: Chapman-Enskog expansion, computational cost, Constrained Runs, hybrid models, initialization,
lattice Boltzmann models, lifting operator, macroscopic partial differential equations, numerical
Chapman-Enskog expansion, spatial coupling.
