"Eulerian Description of High-Order Bounce-Back Scheme for Lattice Boltzmann Equation with Curved Boundary"
T. Lee and G. K. Leaf
Preprint Version: [pdf]
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 °uid 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.