Numerical Simulation of Sloshing Tanks with Shallow Water Model Using Low Numerical Diffusion Schemes and Its Application to Tuned Liquid Dampers

The initial part of this study fills a notable research gap by investigating the substantial impact of numerical diffusion errors from different schemes on sloshing tank models. Multiple numerical models were developed: first- and higher-order upwind schemes equipped with precise wall treatment using ghost nodes, MacCormack and central methods that are explicit second-order finite difference methods, and Preissmann and staggered methods employed in full-implicit and semi-implicit modes. Furthermore, the separation of variables technique was proposed for simulating sloshing tanks and deriving an analytical equation for the tank’s natural period. An analytical solution to the perturbation was employed to examine the numerical diffusion of the schemes. Subsequently, two sloshing tests, resonant and near-resonant excitations, were employed to determine the numerical diffusion and calibrate the physical diffusion coefficients, respectively. Finally, an efficient and accurate numerical scheme was applied to a linear shallow water model including physical diffusion and coupled with a single degree of freedom (SDOF), to simulate tuned liquid dampers (TLDs). It shows that the efficiency of TLD is associated with a compact domain around resonance excitation. Contrary to SDOF alone, when SDOF interacts with TLD the impact of structural damping on reducing the response is minimal in resonance excitation.