Numerical analysis of fully non-linear sloshing waves in an arbitrary shape tank by meshless method

Abstract

This paper is devoted to develop a truly meshless numerical procedure for the fully non-linear analysis of sloshing phenomenon in an arbitrary-shape tank. For this purpose, the potential theory is considered as a liquid sloshing model, and the Lagrangian form of kinematic and dynamic boundary conditions in a moving coordinate system fixed to the tank is used to accurately capture the free surface. The multi-quadric radial basis function (MQ-RBF) augmented with the polynomial terms is employed to determine RBF-FD weights on neighboring nodes surrounding the center point for the spatial derivatives. These weight coefficients are used to solve both boundary value problems for velocity and acceleration potential. Compared with mash-based methods, the present method has the advantage of being easy to construct and flexible in dealing with the moving boundary problems. The free surface elevations, hydrodynamic pressure, and first-order natural sloshing frequencies have been reported for various geometries tanks under horizontal excitations at resonance and non-resonance cases. Fairly satisfactory agreement is observed in the numerical results and exiting results, especially for free surface elevation and first-order natural sloshing frequency.