A mass conserving boundary condition for the lattice Boltzmann method for tangentially moving walls

In the present discussion a no-slip boundary condition for walls with a tangential movement is derived. The resulting closure is local, conserves mass exactly and is second order accurate with respect to the grid spacing. In addition it avoids the numerical instabilities observed for other types of boundary conditions. Therefore the resulting boundary condition is stable for relaxation frequencies close to two. The present boundary condition is verified for Couette flow, half Poiseuille flow, the second problem of Stokes and flow in a lid-driven square cavity.