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A Computational Study of the Spreading of Oil Underneath a Sheet of Ice Abstract: The spreading of oil underneath a sheet of ice is computed using an adaptive level set method for incompressible two-fluid flow. Factors such as viscosity, surface tension, and wall adhesion are taken into account in the computations. The results of the computations agree well with previous experiments and theory. In this work, we also present a very efficient and accurate computational method for determining the final steady profile of a body of oil under ice in water. The computational models are used to make further observations regarding the dependency of the oil spreading radius on the surface energies between the oil, ice, and water.