A fast and improved mass-conservative approach for a sharp interface-level set method on co-located grid

Abstract

This study presents a novel sharp interface approach based on the level set method that achieves improved mass conservation and reduced computational time without introducing additional complexities in numerical implementation. The proposed approach is built upon recent formulations: the conservative phase field (CPF) method, the conservative diffuse interface (CDI) method, and the sharp interface level set method on co-located grid (SI − LSM col ). While the CPF and CDI methods advect the interface while preserving the boundedness criterion associated with the hyperbolic tangent-based interface advection function, the SI − LSM col ensures pressure-interfacial force balance on a co-located grid. Implementation in a three-dimensional coordinate system further demonstrates the robustness of enforcing jump conditions as interfacial boundary conditions for high density ratio simulations on co-located grids. Validation against several benchmark test cases—including the Young–Laplace law, rising bubble, falling droplet, and droplet coalescence—along with comparisons to the previous SI − LSM col method, shows improved mass conservation and reduced computational time, achieved without any loss in computational accuracy.