Study of Simple Hydrodynamic Solutions with the Two-Relaxation-Times Lattice Boltzmann Scheme (Communications in Computational Physics, 2008)
For simple hydrodynamic solutions, where the pressure and the velocity arepolynomial functions of the coordinates, exact microscopic solutions are constructedfor the two-relaxation-time (TRT) Lattice Boltzmann model with variable forcing andsupported by exact boundary schemes. We show how simple numerical and analytical solutions can be interrelated for Dirichlet velocity, pressure and mixed (pressure/tangential velocity) multi-reflection (MR) type schemes. Special care is taken toadapt them for corners, to examine the uniqueness of the obtained steady solutions andstaggered invariants, to validate their exact parametrization by the non-dimensionalhydrodynamic and a "kinetic" (collision) number. We also present an inlet/outlet"constant mass flux" condition. We show, both analytically and numerically, that thekinetic boundary schemes may result in the appearance of Knudsen layers which arebeyond the methodology of the Chapman-Enskog analysis. Time dependent Dirichletboundary conditions are investigated for pulsatile flow driven by an oscillating pressure drop or forcing. Analytical approximations are constructed in order to extend thepulsatile solution for compressible regimes.