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In this paper, we develop the THINC-scaling interface capturing scheme into cubic surface representation. As a lately proposed interface capturing method, the THINC-scaling scheme preserves the advantages of both VOF and level set methods, i.e. the mass/volume conservation of the VOF method and the geometrical faithfulness of the level set method. Compared to quadratic surface representation used in original THINC-scaling paper, the interface now is better defined as a 3^rd order polynomial surface of interface (PSI). The THINC reconstruction function is used to update the VOF field via a finite volume method, and the level set field via a semi-Lagrangian method.

Algorithms of both two and three dimension on unstructured meshes have been developed and verified. The numerical results reveal that the present scheme, with higher-order surface representation, can provide high-fidelity solution comparable to original THINC-scaling method and other most advanced methods.

Moving interface, Multiphase flow, VOF, Level set, THINC, High-order polynomial interface representation, Unstructured mesh