  A lattice Boltzmann method (LBM) with enhanced stability and accuracy is
presented for various Hermite tensor-based lattice structures. The collision
operator relies on a regularization step, which is here improved through a
recursive computation of non-equilibrium Hermite polynomial coefficients. In
addition to the reduced computational cost of this procedure with respect to
the standard one, the recursive step allows to considerably enhance the
stability and accuracy of the numerical scheme by properly filtering out second
(and higher) order non-hydrodynamic contributions in under-resolved conditions.
This is first shown in the isothermal case where the simulation of the doubly
periodic shear layer is performed with a Reynolds number ranging from $10^4$ to
$10^6$, and where a thorough analysis of the case at $Re=3\times 10^4$ is
conducted. In the latter, results obtained using both regularization steps are
compared against the BGK-LBM for standard (D2Q9) and high-order (D2V17 and
D2V37) lattice structures, confirming the tremendous increase of stability
range of the proposed approach. Further comparisons on thermal and fully
compressible flows, using the general extension of this procedure, are then
conducted through the numerical simulation of Sod shock tubes with the D2V37
lattice. They confirm the stability increase induced by the recursive approach
as compared with the standard one.
