Immersed Boundary Multi-scale Level-set Method for Immiscible Pore-scale Multiphase Flows at Low Capillary Numbers

Complex solid geometries are commonly observed in the study of multiphase flows in porous media. However, accurately capturing the interaction of the fluid-fluid interface with complex-shaped confinements at the pore-scale is challenging but critical for precise prediction of the flow evolutions inside porous media. In this work, for capturing complex solid boundaries, an immersed boundary method based on a direct forcing approach for fixed cartesian grids is coupled with a multiscale sharp-interface level-set method for immiscible two-phase flows at low capillary numbers. The incompressible Navier-Stokes equation is sequentially coupled with the level-set method and the immersed boundary approach to capture the dynamics and evolution of the fluid-fluid interface. Viscous bending of the advancing interface on the solid surface is captured by the level-set method and the Cox–Voinov theory. With this framework, multiphase flow at the pore-scale in the presence of irregular solid geometries is studied and compared with previous works.

Keywords: porous media, immersed boundary method, level-set method, multiphase flow