A curved no-slip boundary condition for the lattice Boltzmann method

We present a generalization of the no-slip boundary condition by Lätt et al. [J. Lätt, B. Chopard, O. Malaspinas, M. Deville, A. Michler, Straight velocity boundaries in the lattice Boltzmann method, Physical Review E 77 (5) (2008) 056703] from straight to curved geometries for the lattice Boltzmann Bhatnager–Gross–Krook method (LBGK). The boundary condition is based on a reconstruction of the populations from the density, velocity and rate of strain. For curved boundaries, the reconstruction reduces the question of accuracy to a technical issue of interpolation. We present a method of interpolation allowing a very accurate representation of the curved boundary. The resulting boundary condition is verified for three different test cases: Taylor–Couette flow in-between rotating cylinders, laminar flow around a cylinder and flow past an impulsively started cylinder, demonstrating its second order accuracy and low error constant. The present boundary is stable for relaxation frequencies close to two.

Research Highlights
► Derivation of a curved boundary condition for the lattice Boltzmann method.
► Second order accurate in space and stable for a relaxation frequency close to two.
► Comparison between different approximation methods.