  The present study proposes a highly accurate lattice Boltzmann direct
coupling cell-vertex algorithm, well suited for industrial purposes, making it
highly valuable for aeroacoustic applications. It is indeed known that the
convection of vortical structures across a grid refinement interface, where
cell size is abruptly doubled, is likely to generate spurious noise that may
corrupt the solution over the whole computational domain. This issue becomes
critical in the case of aeroacoustic simulations, where accurate pressure
estimations are of paramount importance. Consequently, any interfering noise
that may pollute the acoustic predictions must be reduced.
  The proposed grid refinement algorithm differs from conventionally used ones,
in which an overlapping mesh layer is considered. Instead, it provides a direct
connection allowing a tighter link between fine and coarse grids, especially
with the use of a coherent equilibrium function shared by both grids. Moreover,
the direct coupling makes the algorithm more local and prevents the duplication
of points, which might be detrimental for massive parallelization. This work
follows our first study (Astoul~\textit{et al. 2020}) on the deleterious effect
of non-hydrodynamic modes crossing mesh transitions, which can be addressed
using an appropriate collision model. The Hybrid Recursive Regularized model is
then used for this study. The grid coupling algorithm is assessed and compared
to a widely-used cell-vertex algorithm on an acoustic pulse test case, a
convected vortex and a turbulent circular cylinder wake flow at high Reynolds
number.

Computational Physics;Fluid Dynamics