In this paper, a two-dimensional numerical model is developed to study liquid sloshing in containers considering liquid free surface deformation, liquid viscosity and surface tension. The model is validated by a comparison between the computational and theoretical/experimental results for various sloshing scenarios with different time-dependent linear/angular accelerations. The governing equations for the 2D incompressible fluid flow are continuity and Navier–Stokes equations along with an equation for the free surface advection. The deformation of the liquid–gas interface is modeled using the volume-of-fluid (VOF) method. The fluid flow equations describing the fluid sloshing in the container and the dynamic equation which describes the movement of the container are solved separately in two coupled programs. In each time step of computations, the outputs of the fluid program (forces and torque) are obtained and used as inputs for the dynamic program. The forces and torque are applied to the body of the container resulting in translational and rotational accelerations which are then used as inputs to the fluid program in the next time step.The model is also used to simulate the movement of a liquid container in a general case where a complete interaction between the liquid and solid body of the container exists and the container has both linear and rotational accelerations.

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