A comparative study of interface capturing methods with amr for incompressible two-phase flows

This paper presents a comparative study of interface capturing methods with adaptive mesh refinement for Direct Numerical Simulation (DNS) of incompressible two- phase flows. The numerical algorithms for fluid motion and interface capturing methods have been previously introduced in the context of the finite-volume approach for both mass conservative level-set methodology and coupled volume-of-fluid/level-set method for unstructured/structured fixed meshes. The Adaptive Mesh Refinement (AMR) method introduced in consist on a cell-based refinement technique to minimize the number of computational cells and provide the spatial resolution required for the interface capturing methods. The present AMR framework adapts the mesh according to a physics-based refinement criteria defined by the movement of the interface between the fluid-phases. Numerical experiments are presented to evaluate the methods described in this work. This includes a study of the hydrodynamics of single bubbles rising in a quiescent viscous liquid, including its shape, terminal velocity, and wake patterns. These results are validated against experimental and numerical data well established in the scientific literature, as well as a comparison of the different approaches used