Multiscale semi-Lagrangian lattice Boltzmann method

We present a multi-scale lattice Boltzmann scheme, which adaptively refines particles' velocity space. Different sets of lower and higher order are consistently efficiently coupled, allowing us to use the higher-order model only when where needed. This includes regions high Mach or Knudsen numbers. The coupling procedure discrete consists either projection populations onto lower-order lifting Both local operations, enable flexible adaptive set. proposed scheme is formulated for both static an optimal, co-moving reference frame, in spirit recently introduced Particles on Demand method. validated with advection athermal vortex jet flow setup. performance further investigated shock structure problem high-Knudsen-number Couette flow, typical examples highly non-equilibrium flows set plays decisive role. results demonstrate that can operate accurately, flexibility terms underlying models reduced computational requirements.