In this paper, a two-dimensional numerical model is developed to study liquid sloshing in containers in presence of liquid free surface deformation, liquid viscosity and surface tension. The model is validated by a comparison between the computational and theoretical/experimental results for time-dependent linear/angular acceleration sloshing scenarios. 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. The model is also used to simulate the movement of the liquid container in a general case where a complete interaction between liquid and solid body of the container exits and the container has both linear and rotational accelerations.

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