Systems and method for simulating liquid containment behavior. The system comprises a solid modeler and a nonlinear equation solver. The nonlinear equation solver takes as input the solid model representation of the containment vessel from the solid modeler, a desired orientation in space, dynamic conditions (e.g., lateral acceleration) and an amount of liquid. To find the level of liquid in the vessel, the system solver iteratively performs successive Boolean subtractions using an infinite horizontal half-space that represents the liquid level of the vessel. The resulting sliced solid model is used to compute the volume of the liquid at that level. The iterative system solver terminates when the computed volume of the sliced containment vessel matches the specified volume of liquid (e.g., fuel) within a given tolerance.