  Turbulent compressible flows are traditionally simulated using explicit time
integrators applied to discretized versions of the Navier-Stokes equations.
However, the associated Courant-Friedrichs-Lewy condition severely restricts
the maximum time step size. Exploiting the Lagrangian nature of the Boltzmann
equation's material derivative, we now introduce a feasible three-dimensional
semi-Lagrangian lattice Boltzmann method (SLLBM), which circumvents this
restriction. While many lattice Boltzmann methods for compressible flows were
restricted to two dimensions due to the enormous number of discrete velocities
in three dimensions, the SLLBM uses only 45 discrete velocities. Based on
compressible Taylor-Green vortex simulations we show that the new method
accurately captures shocks or shocklets as well as turbulence in 3D without
utilizing additional filtering or stabilizing techniques, even when the time
step sizes are up to two orders of magnitude larger compared to simulations in
the literature. Our new method therefore enables researchers for the first time
to study compressible turbulent flows by a fully explicit scheme, whose range
of admissible time step sizes is only dictated by physics, while being
decoupled from the spatial discretization.
