Revisit to the THINC scheme: A simple algebraic VOF algorithm

This short note presents an improved multi-dimensional algebraic VOF method to capture moving interfaces. The interface jump in the THINC (tangent of hyperbola for INterface capturing) scheme is adaptively scaled to a proper thickness according to the interface orientation. The numerical accuracy in computing multi-dimensional moving interfaces is significantly improved. Without any geometrical reconstruction, the proposed method is extremely simple and easy to use, and its numerical accuracy is superior to other existing methods of its kind and comparable to the conventional PLIC (piecewise linear interface calculation) type VOF schemes.

► We propose a simple algebraic VOF (volume of fluid) scheme which does not involve geometrical reconstruction.
► We use the THINC scheme as the one dimensional building block.
► The thickness of the jump transition is controlled to improve the shape faithfulness of the transported interface.
► Accuracy comparable to many existing VOF schemes is obtained.
► It provides a practical scheme of adequate numerical accuracy, without any complexity in other VOF schemes.