A semi-Lagrangian meshless framework for numerical solutions of two-dimensional sloshing phenomenon

Abstract This paper presents a semi-Lagrangian meshless framework based on the localized radial basis function collocation method and the second-order explicit Runge–Kutta method (RK2-LRBFCM) for analyzing the sloshing phenomenon in a 2D tank. In the present method, the semi-Lagrangian approach is adopted to constrain the lateral movements of inner collocation nodes. And the LRBFCM is used to obtain the velocity potentials at each time instant governed by Laplace equation, then second-order explicit Runge–Kutta method is introduced to calculate the free-surface elevation and velocity potential at the next time instant. In comparison with the reference results, the efficiency and accuracy of the proposed RK2-LRBFCM are demonstrated in the solutions of several benchmark examples including horizontally excited tanks, vertically excited tanks, horizontally and vertically excited tanks. Moreover, the effect of the protrusion (shape and size) of the bottom wall on the sloshing phenomenon in horizontally excited tank is investigated.