Pressure Unit Conversion in Lattice Boltzmann Method*

The lattice Boltzmann method (LBM) is a class of computational fluid dynamics techniques that operates on mesoscale to simulate complex flows. It is a special discrete representation of the Boltzmann equation on lattice nodes/cells, solving the time evolution of particle distribution functions through a set of collision and propagation operations. The fluid particles propagate from one lattice node/cell to another and collide with each other at each time step, resulting in the redistribution of particle distribution functions according to local fluid properties. The macroscopic variables such as density and velocity are calculated through the zeroth and 1^st order moments of the particle distribution functions. One challenge in LBM is that pressure values are typically represented on the mesoscopic level, which may not directly correspond to macroscopic units like Pascals or atmospheres used in real-world flow systems. Therefore, it is crucial to establish an appropriate conversion between lattice units (mesoscale) and physical units (macroscale) to ensure the accuracy and relevance of computed pressure. In this study, we systematically explore pressure unit conversion in two specific scenarios: Stokes flow and laminar or turbulent pipe flow, considering viscous and inertial effects, respectively, to characterize the pressure field. The simulated pressure fields are rigorously validated against analytical solutions and experimental measurements. We also address pertinent issues concerning the influence of lattice models and LBM models on the accuracy of pressure quantification, providing practical recommendations to enhance the precision of pressure computations.