Assessing moment-based boundary conditions for the lattice Boltzmann equation: A study of dipole-wall collisions

The accuracy of moment-based boundary conditions for no slip walls in lattice Boltzmann simulations is examined numerically by using the dipole-wall collision benchmark test for both normal and oblique cases. In the normal case the dipole hits the wall perpendicularly while in the oblique case the dipole hits the wall at an angle of 30° to the horizontal. Boundary conditions are specified precisely at grid points by imposing constraints upon hydrodynamic moments only. These constraints are then translated into conditions for the unknown lattice Boltzmann distribution functions at boundaries. The two relaxation time (TRT) model is used with a judiciously chosen product of the two relaxation times. Stable results are achieved for higher Reynolds number up to 10000 for the normal collision and up to 7500 for the oblique case. An excellent agreement with a benchmark data is observed and the local boundary condition implementation is shown to be second order accurate