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

Abstract
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 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 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.