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