A Cascaded Lattice Boltzmann Model for Porous and Multi‐Layer Shallow Water Flows

ABSTRACT The work proposes the development of a Lattice Boltzmann (LB) Cascaded collision operator (CO) model with two unexplored main purposes: reproducing the dynamics of multilayer shallow water flows and modeling urban floods with a porosity approach. The Cascaded CO has been already proved to enhance accuracy and stability in low‐viscosity flows, like water, outperforming other mesoscopic models. Its adaptation to a multilayer model allows capturing vertical variations in hydrodynamic quantities of large‐scale geophysical flows. To simulate n‐layer flow dynamics, the model CaLB‐N solves n shallow water equations, one for each layer, with coupling terms representing the mutual interactions between layers. Capturing localized flow features in large scale flood events is still a challenge: in complex morphology like urban areas, the dimension of the city dominion is many orders of magnitude larger than buildings, thus they can hardly be taken into account. The introduction of a new sub grid porosity‐based LB model (CaLB‐P) allows facing this issue, considering in a specific source term the portion of a computational cell that is available for flow. The model is implemented in C and parallelized to achieve computational speeds suitable for large‐scale applications. This optimization allows for high‐resolution simulations while substantially reducing processing time. The applicability of the suggested model for hydraulic engineering is explored, paving the way for new approaches to realistically model complex water flows.