Numerical simulation of multiphase flows using an enhanced Volume-of-Fluid (VOF) method

The main objective of the present work is to enhance the stability and accuracy of Volume-of-Fluid (VOF) method for simulating multiphase flow problems with large density ratios and moving interfaces. In order to accomplish this, a novel high-order TVD flux-limiter scheme is developed and applied to approximate the convective fluxes in the momentum, energy and volume fraction equations. Moreover, the classical implicit non-iterative PISO algorithm is modified according to SIMPLER algorithm and the combined model (PISOR) is then employed to handle the pressure-velocity coupling. Furthermore, the piecewise linear interface calculation (PLIC) based on the Efficient Least Squares Volume-of-Fluid Interface Reconstruction Algorithm (ELVIRA) is adopted for the treatment of the interface and curvature estimation. The robustness and consistency of the proposed modifications in handling violent free-surface flows involving interface rupture and coalescence are verified via simulation of several canonical test cases including: dam break over the dry and wet beds, rotating square patch of fluid and Rayleigh-Taylor Instability (RTI). The results show that, the proposed flux-limiter scheme can significantly suppress false-diffusion errors and maintain interface sharpness while preserving the boundedness and positivity of the volume fraction field. Moreover, it is found that the proposed PISOR model has robust convergence behavior in strongly coupled multiphysics problems and provides more stable and consistent results than the standard PISO and SIMPLER algorithms. The performance and efficiency of proposed models are further verified, for single phase flow, through analysis of transient entropy generation due to natural convection heat transfer in differentially heated cavity.