A coupled multigrid solver with wall functions for three‐dimensional turbulent flows over urban‐like obstacles

One of the objectives for rapid operational tools for urban atmospheric events is fast calculation of the computational fluid dynamics (CFD) models for multiphase flows to respond to deliberate or accidental chemical, biological, and radiological (CBR) releases. This article addresses the implementation of a coupled multigrid (CMG) method in an in‐house pressure‐based low‐speed CFD solver called STREAM in detail, including its validation against several 2D/3D benchmark test problems pertinent to urban flows. It was identified that solving the advection–diffusion equation of concentration for the prediction of dispersion of CBR agents is computationally very efficient, provided that the input data of turbulence viscosity and flow fields can be supplied in a timely fashion. Since most pressure‐based solvers adopt the segregated SIMPLE algorithm, and the coupling among different (linearized) equations is established via outer iterations on a single grid, its convergence rate is generally poor, particularly for turbulent flows in urban environments involving massive flow separation. The proposed approach and main contribution here is to adopt CMG to solve turbulent flows over urban‐like obstacles efficiently in 2D and particularly 3D, in which the standard Reynolds‐averaged Navier–Stokes k−ε$$ k-\varepsilon $$ turbulence model in conjunction with wall functions is employed. The results presented in this paper demonstrate a speedup ratio based on work unit (WU) for 3D laminar cavity flows of roughly 100, and 25 for 3D turbulent urban flow, depending on grid sizes. A coupled multigrid (CMG) methodology is developed to solve turbulent flow fields including a novel treatment of turbulent wall functions at multigrid levels. The CMG methodology is shown to provide a 100 times speedup for laminar flows and a 25 times speedup for turbulent flows over traditional segregated multigrid solvers.