Isogeometric boundary element analysis of liquid nonlinear sloshing in two dimensional rectangular tanks

This paper presents a numerical model based on the Isogeometric Analysis (IGA), Boundary Element Method (BEM) and the second order Runge–Kutta (RK2) method for solving the nonlinear sloshing problem in a two-dimensional (2D) tank. In this study, the IGABEM is employed to solve the Laplace equation for the velocity potentials of the liquid, and the singular integral is calculated by the Radial Integral Method (RIM). The Semi-Lagrange (SL) approach is adopted to capture the movement of the free surface, then the RK2 method is used to update the velocity potential and elevation of the free surface at each time step. The numerical results agree very well with the reference results in different situations including free sloshing and forced sloshing under different excitations, which illustrates the validity of the present method. Moreover, in comparison with the traditional element-based method with linear polynomial interpolation function, the present RK2-IGABEM can evaluate the velocity potential and elevation of the free surface more smoothly with only a few degrees of freedom added, leading to a high accuracy analysis of nonlinear sloshing problems.