Research Projects

The process of upscaling during multi-phase flow is a pressing issue in fluid dynamics, particularly in non-equilibrium processes. This proposal aims to provide a thermodynamically-grounded, observationally-validated, and computationally efficient method for upscaling the effects of disorder on multiphase flows. India, with 4% of world water resources and 83.2 µg/cubic meter of pollutants, needs to address water reserve and air quality improvement. The project PI, doctoral student, and collaborators (Alex Hansen and Ran Holtzman) will work together to develop a novel approach to upscaling. They will create a framework based on analytic approaches and numerical techniques to bridge flow equations in different scales through an upscaling process. Coventry University and Porelab will provide computational support and participate in knowledge transfer through academic visits, conferences, and workshops. The study will study a 1+1 dimensional interface driven by external pressure, combining pore structure with scale effect to get a unified flow equation as a non-wetting fluid pushes a wetting fluid. The analytical approach will be based on the 'Enhanced Velocity Mixed Finite Element Method' and Euler homogeneity. An iterative method for energy minimization will be explored, such as the random field Ising model for inviscid fluids and a Range-Kutta algorithm in the presence of viscosity. This approach could help improve water reserves and air quality in countries like India.