The present study is concerned with the liquid tank sloshing at low filling level conditions. The volume of fluid method implemented in a Navier-Stokes computational fluid dynamics code is employed to handle the free-surface flow of liquid sloshing. A geometric reconstruction scheme for the interface representation is employed to ensure sharpness at the free-surface. The governing equations are discretized by second order accurate schemes on unstructured grids. Several different computational approaches are verified and numerical uncertainties are assessed. The computational results are validated against existing experimental data, showing good agreement. The capability is demonstrated for a generic membrane type LNG carrier tank with a simplified pump tower inside. The validation results suggest that the present computational approach is both easy to apply and accurate enough for more realistic problems.

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