Eulerian description of high-order bounce-back scheme for lattice Boltzmann equation with curved boundary

We propose an Eulerian description of the bounce-back boundary condition based on the high-order implicit time marching schemes to improve the accuracy of lattice Boltzmann simulation in the vicinity of curved boundary. The Eulerian description requires only one grid spacing between fluid nodes when the second-order accuracy in time and space is desired, although high-order accurate boundary conditions can be constructed on more grid-point support. The Eulerian description also provides an analytical framework for several different interpolation based boundary conditions. For instance, the semi-Lagrangian, linear interpolation boundary condition (Bouzidi et al. [Phys. Fluids 13, 3452 (2001)]) is found to be a first-order upwind discretization that changes the time marching schemes from implicit to explicit as the distance between the fluid boundary node and the solid boundary increases.