New benchmark problems for validation and verification of incompressible multi-fluid flows based on the improved Volume-Of-Fluid (VOF) method

The present work describes the application of the improved Volume-Of-Fluid (VOF) method for the accurate capturing of phase interfaces in the problems of three-fluid bubble rising, water/oil droplets impacting onto wetted beds, three-fluid Rayleigh-Taylor Instability and merging of two rising bubbles, aiming to establish powerful benchmarking tools for validation of existing numerical models and code verification problems. To this end, an enhance version of the VOF model is exploited where a novel third-order TVD convection scheme is utilized for the discretization of convection terms in the Navier-Stokes and transport equations while the combination of the implicit non-iterative PISO and classical SIMPLER algorithms (PISOR) is applied for the treatment of the pressure-velocity coupling and acceleration of the iteration process in the Poisson equation. A series of canonical test cases including dam break over a dry bed, single and double rising bubbles, two-phase Rayleigh-Taylor Instability are considered to verify the performance and accuracy of the numerical method. The obtained results vividly demonstrate the superiority and versatility of the improved VOF model over the classical Eulerian and Lagrangian methods in handling multiphase flows with relevant breaking and fragmentation. Moreover, it is found that, the standard version of Lagrangian SPH models can not accurately address the problem of interface smearing, and thereby characterizing by noisy pressure distribution.