A Reproducible D3Q19 Multiple-Relaxation-Time Lattice Boltzmann Benchmark and Quantum-Operator Audit for Forced Wall-Bounded Flow Simulations

Journal article, 2026

Quantum algorithms for flow simulation are advancing rapidly, but reproducible wall-bounded benchmarks with classical reference data are still needed to evaluate future quantum and hybrid quantum-classical solvers. This work presents a forced D3Q19 multiple-relaxation-time (MRT) lattice-Boltzmann method (LBM) benchmark for body-force-driven Poiseuille flow in a three-dimensional channel. The solver combines periodic streamwise and spanwise boundaries, halfway bounce-back walls, moment-space relaxation, and body-force forcing with the half-force velocity correction. The solution is verified against the analytical parabolic profile using relative 𝐿2 and maximum profile errors, mass conservation, extrapolated wall slip, and wall-normal leakage. A verification study over grid resolution, relaxation time, forcing strength, and initialization demonstrates second-order grid convergence and robust conservation behavior. The verified timestep is then decomposed into quantum-relevant primitives, including streaming, wall reflection, moment transformation, MRT relaxation, equilibrium evaluation, forcing, macroscopic recovery, and measurement. The resulting benchmark connects flow-solver accuracy metrics with operator-level requirements for quantum implementation, providing a compact reference problem for future quantum processing unit (QPU)-assisted, hybrid quantum-classical, and quantum-linear-solver-based computational fluid dynamics (CFD) studies. Performance gains over classical LBM execution are not assessed here.