Modelling of two-phase incompressible flows in ducts

An improved level-set method for capturing interfaces combined with a second-order projection method for solving the time-dependent incompressible Navier–Stokes equations is implemented to compute two-phase viscous flows of Newtonian fluids on Cartesian staggered meshes. Various arrays of deformable droplets are suspended in an ambient fluid of different viscosity in ducts and the deformation and migration of droplets as they move along the duct are computed and discussed.In this study an efficient ‘hybrid’ iteration algorithm for the re-initialization of the level-set function with the property of keeping the thickness of the interface and to conserve mass is introduced. In addition, by implementing an adaptive mesh refinement, moving with the droplets, greater detail and accuracy of the contours of droplets and simultaneous higher speed-up of the calculations of the level-set algorithm are achieved.