A geometric multigrid treatment of immersed boundaries for simulating atmospheric dispersion in complex urban environments

Quantification of the dispersion rate and extent of gaseous substances leaked into the atmosphere is important for public safety and risk management as industrial facilities are being situated ever closer to populated areas. The complex interaction between atmospheric conditions and built environments makes urban dispersion prediction challenging in nature. Computational fluid dynamics (CFD) has emerged as a credible tool for urban dispersion analysis over the past two decades as it provides greater detail and accuracy than traditional methods, albeit usually at greater cost in terms of time, computing power and expertise. This paper describes a multigrid acceleration method for three-dimensional CFD that ensures robustness when resolving the interaction between the atmospheric boundary layer and complex urban environments, including terrain, buildings and obstacles. The solver is segregated, pressure-based and is uniquely applied to structured grids with Cartesian anisotropic mesh refinement and an immersed boundary method (IBM). This work describes novel adaption of a geometric multigrid method (MGM) to an immersed boundary representation of the urban environment features of real cities. The innovative multigrid treatment selectively uses the immersed boundaries at coarse multigrid levels with the advantage of enhancing computational stability while maintaining efficient convergence rates. The novel CFD techniques are demonstrated at three flow scales (laboratory, model-urban and real-world scale), and comparisons of velocity, turbulence levels and gas concentrations are made to published numerical and experimental measurements. The unique combination of MGM, IBM and adaptive mesh refinement (AMR) has not previously been documented and shows a speed-up factor of seven in convergence, relative to single grid, at the laboratory scale. At the urban scale, the combination of numerical methods makes city-scale Reynolds-Averaged Navier-Stokes (RANS) turbulence CFD solutions possible in hours on a workstation computer and is shown to match experimental concentration measurements within acceptable statistical limits.