Simulation of Sloped-Bed Tuned Liquid Dampers Using a Nonlinear Shallow Water Model

Abstract

This research aims to develop an efficient and accurate model for simulating tuned liquid dampers (TLDs) with sloped beds. The model, based on nonlinear shallow water equations, is enhanced by introducing new terms tailored to each specific case. It employs the central upwind method and Minmod limiter functions for flux and interface variable assessment, ensuring both high accuracy and reasonable computational cost. While acceleration, slope, and dissipation are treated as explicit sources, an implicit scheme is utilized for dispersion discretization to enhance the model’s stability, resulting in matrix equations. Time discretization uses the fourth-order Runge–Kutta scheme for precision. The performance of the model has been evaluated using several test cases including dam-breaks on flat and inclined beds and run-up and run-down simulations over parabolic beds, which are relevant to sloshing in tanks with sloped beds. It accurately predicts phenomena such as asymmetric sloshing waves, especially in sloped beds, where pronounced waves occur. Dispersion and dissipation terms are crucial for capturing these effects and maintaining stable wave patterns. An initial perturbation method assesses the tank’s natural period and numerical diffusion. Furthermore, the model integrates with a single-degree-of-freedom (SDOF) system to create a TLD model, demonstrating enhanced damping effects with sloped beds.