Lattice Boltzmann boundary conditions via singular forces: Irregular expansion analysis and numerical investigations

We present an investigation of a boundary condition algorithm for the lattice Boltzmann method, which introduces Dirichlet conditions on velocity using a singular force applied on the fluid solid interface (immersed boundary method). The algorithm has been proposed in the literature in different versions and mainly numerically tested, only in specific cases. An approach based on a generalized asymptotic expansion technique will be used to understand properties and point out problems of the scheme. As a result, we found that the algorithm achieves a first order accurate velocity in a strong sense, while accuracy for the pressure can be stated only considering a weak norm. Moreover, the analysis predicts a first order accuracy for the boundary force although the precision is affected by stability limitations. We benchmark the method on lattice Boltzmann flows past a rigid disk, comparing its numerical performances with standard boundary condition approaches.