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
