Coupled THINC and level set method: a conservative interface capturing scheme with arbitrary-order surface representations

TL;DR

This paper introduces a novel numerical scheme that combines THINC and Level Set methods to accurately and conservatively capture moving interfaces with arbitrary-order surface representations on fixed grids.

Contribution

The proposed THINC/LS method uniquely integrates polynomial interface representation with mass conservation and ease of implementation, advancing interface capturing techniques.

Findings

Achieves arbitrary-order accuracy in interface reconstruction

Provides more accurate results than classical VOF methods

Ensures rigorous mass conservation

Abstract

In this paper, we propose a simple and accurate numerical method for capturing moving interfaces on fixed Eulerian grids by coupling the Tangent of Hyperbola Interface Capturing (THINC) method and Level Set (LS) method. The innovative and practically-significant aspects of the proposed method, so-called THINC/LS method, lie in (1) representing the interface with polynomial of arbitrary-order rather than the plane representation commonly used in the Piecewise Linear Interface Calculation (PLIC) Volume of fluid (VOF) methods, (2) conserving rigorously the mass of the transported VOF field, and (3) providing a straightforward and easy-to-code algorithm for implementation. We verified the proposed scheme with the widely used benchmark tests. Numerical results show that this new method can obtain arbitrary-order accuracy for interface reconstruction and can produce more accurate results than the classical VOF methods.