Two-dimensional nonlinear sloshing analysis using boundary element method

A boundary element method to nonlinear analysis of free-surface motion in a two-dimensional container is developed based on the Lagrangian particle description. By using the weighted residual formulation to the relation between the velocity of the fluid particle and the gradient of the potential on the surface, a unifying formulation is obtained for the relation between the kinematic conditions and the boundary values. A time integration scheme is constructed in accordance with the Newmark method. The proposed method with linear element provides second-order convergence in both space and time directions. Through numerical experiments, influence of the treatment of nonlinear equations on the accuracy is discussed.