This work investigates the applicability of lattice Boltzmann equations based on the Shakhov kinetic equation to modeling rarefied flows under significant external force. As a benchmark problem, a two-dimensional plane Poiseuille flow at different Knudsen numbers and different amplitudes of external force is considered, resulting in characteristic flow velocities corresponding to Mach numbers in the range of 0.4 to 0.6. It is shown that two-dimensional lattice models with 37 velocities can describe nonequilibrium effects beyond the applicability of the continuum medium approximation, in the slip flow regime. Profiles of longitudinal and transverse heat fluxes, as well as velocity and temperature profiles of the rarefied gas, are examined.
O. V Ilyin (Wed,) studied this question.