Detailed Simulation of Complex Hydraulic Problems with Macroscopic and Mesoscopic Mathematical Methods

Abstract

The numerical simulation of fast-moving fronts originating from dam or levee breaches is a challenging task for small scale engineering projects. In this work, the use of fully three-dimensional Navier-Stokes (NS) equations and lattice Boltzmann method (LBM) is proposed for testing the validity of, respectively, macroscopic and mesoscopic mathematical models. Macroscopic simulations are performed employing an open-source computational fluid dynamics (CFD) code that solves the NS combined with the volume of fluid (VOF) multiphase method to represent free-surface flows. The mesoscopic model is a front-tracking experimental variant of the LBM. In the proposed LBM the air-gas interface is represented as a surface with zero thickness that handles the passage of the density field from the light to the dense phase and vice versa. A single set of LBM equations represents the liquid phase, while the free surface is characterized by an additional variable, the liquid volume fraction. Case studies show advantages and disadvantages of the proposed LBM and NS with specific regard to the computational efficiency and accuracy in dealing with the simulation of flows through complex geometries. In particular, the validation of the model application is developed by simulating the flow propagating through a synthetic urban setting and comparing results with analytical and experimental laboratory measurements.