Numerical modeling of sloshing using the radial basis function collocation method

Abstract

A series of numerical models have been developed to study sloshing in 2D and 3D Rigid Tanks. The problem is approached with Potential Flow Theory and Laplace’s equation is solved with Neumann type lateral and bottom boundary conditions and with Dynamic and Kinematic free surface boundary conditions. For the numerical method to solve the initial-boundary value problem; Meshless Radial Basis Function Collocation Method is used and a predictor-corrector type time marching scheme is used with Adams- Bashworth predictors and Adams-Moulton correctors. The 2D models were verified by performing some numerical tests and comparing the results with available second or third order asymptotic analytical formulae from the literature, numerical experiments from the literature, and with lab experiments from the literature. For the 3D models, linear analytic formulae were used for verification. The results were supported with laboratory experiments, and by employing another numerical model developed using the Virtual Mass technique. Fully nonlinear boundary conditions with deformable boundaries have been used in the 2D sloshing models. The numerical tanks have been tested with linear standing wave, lateral excitation, vertical excitation and combined lateral and vertical excitation inputs. Fast convergence and excellent accuracy is obtained for the low amplitude test cases. For the high amplitude sloshing cases, some experimental techniques are used and a good accuracy is achieved. For the 3D sloshing studies, linearized mathematical formulation was used; and the RBFCM, Virtual Mass, and the Laboratory Experiment models were benchmarked by demonstrating their performances in estimating the sloshing mode shape frequencies. Finally, a sample tank from the industry was analyzed by applying real earthquake motions using the RBFCM and Virtual Mass models, and the calculated maximum wave amplitudes were compared. The numerical experiments show that the models created in this study may be utilized for the research on the optimum tank design; which may eventually lead to improvements on the design code.