Sharp Interface Level Set Method on a Co-located Grid for High Density Ratio Two-Fluid Flow

Abstract

Fundamental building block in any simulation is the underlying framework in which numerical methodology is developed. In general, these frameworks are of two types—staggered and co-located grid. Even though co-located grids are the easiest to implement, majority of the simulations in computational multi-fluid dynamics are performed on a staggered grid. Generation of spurious currents at high density ratio in co-located grids was the major obstacle. To tackle this issue, Francois et al. (Francois et al. in J Comput Phys 213:141–173, 2006) introduced a “Balanced Force Method” which projected the relevance of similarity in discretization between interfacial forcing term and pressure gradient. To achieve this similarity, interfacial forces were evaluated at the faces of control volume. This numerical procedure violates the physical principle that interfacial forces should be acting at the interface. Hence, in this study, a physically accurate sharp interface level set method (SI-LSM) is implemented in a co-located framework which treats interfacial forces at the interface. The capability of the SI-LSM to handle high density ratio is demonstrated on various benchmark problems.