Lattice Boltzmann methods (LBM) recover the weakly compressible Navier-Stokes equations from local collisions and uniform streaming, which makes them a natural fit for modern parallel hardware. The same regularity is also their limitation. A uniform grid has to resolve the finest required scale everywhere, even in regions where the flow is quiescent and the resolution is wasted. Block-structured adaptive mesh refinement (AMR) is the standard response, but coupling it with LBM is not free: the acoustic time-step scaling ties sub-cycling to the lattice spacing, the non-equilibrium part of the populations has to be rescaled across refinement levels, and mass and momentum must be conserved at coarse-fine interfaces.
This thesis develops FLARE, a multi-GPU LBM solver built on top of the AMReX framework. The contribution is a parallel-algorithm and multi-GPU scaling result, not a new physical model. FLARE implements the Rohde-style explosion-coalescence coupling and the Berger-Oliger sub-cycled half-step pattern, exposes three dynamic refinement triggers (vorticity magnitude, Q-criterion, and a local Knudsen sensor), and supports both analytical and STL-driven embedded boundaries. The solver is validated against the Ghia lid-driven cavity across two decades of Reynolds number in close agreement with the reference data, against the published Strouhal sweep on a circular cylinder, and against the Kurtulus NACA0012 airfoil at Re=1000. For the airfoil, the lift coefficient lands within the spread of low-Reynolds NACA0012 literature, and the drag coefficient is flagged as an open item rather than as a validated result. The performance evaluation reports a single A100 PCIe baseline of roughly 1450 MLUPS in FP32 on the uniform-grid configuration, breaks down the cost of each algorithmic feature on top of that baseline, quantifies the cost savings of AMR at matched finest spacing, and characterises the multi-GPU scaling on up to four A100 PCIe cards placed one per node on the UniGE Baobab cluster, with host-staged MPI over InfiniBand. The chapter closes with an external-aerodynamics computation on the DrivAer car model that exercises STL embedded boundaries, multi-level AMR, sub-cycling, and the LES closure simultaneously.
The work bounds itself plainly. The conclusion lists five bounds: the NACA0012 drag discrepancy, the host-staged-communication ceiling on multi-GPU strong-scaling efficiency on the available hardware, the absence of a head-to-head benchmark against external LBM/AMR solvers, the framing of the Re=107 turbulent cylinder as a stability demonstration rather than a validation, and the extension to the transonic regime that the broader research direction targets. Each is left as a follow-up rather than as a result.
