Research
My research work focuses on theoretical analysis and numerical simulations of Navier–Stokes and Cahn–Hilliard–Navier–Stokes equations. The following figures show some simulation results of my research.
Numerical analysis of discontinuous Galerkin method
Interior penalty discontinuous Galerkin methods form a popular class of accurate and robust numerical schemes for solving partial differential equations, which are known to be very flexible and have many positive features. I have strong interest in studying the numerical properties of discontinuous Galerkin methods. In my research, I rigorously study the discontinuous Galerkin method for Cahn–Hilliard/Cahn–Hilliard–Navier–Stokes systems, including unique solvability, stability analysis, and error analysis.
Single-phase flow in porous media
The complex fluid phenomena in nature and in industrial applications give rise to a large number of challenging mathematical problems. Incompressible Navier–Stokes equations describe the motion of viscous fluid substances which attract much attention in scientific and engineering fields.
Spinodal decomposition
Spinodal decomposition is a mechanism of phase transformation through which an initially homogeneous mixture decomposes into separate zones rich in either of the components.
Merging droplet
Cahn–Hilliard–Navier–Stokes model governed evolution of two merging droplets. As the system evolves, the two droplets merge to form one single drop in the stationary case as the most thermodynamically favorable configuration.
Capillary bridge
Contact angle is one of the common ways to measure the wettability of a surface or material. When the interface between two fluid media intersects the wall, the resulting surface tension on the contact line is balanced in all free movement directions at equilibrium state, which forms the contact angle between the interface and the wall. After the Cahn–Hilliard–Navier–Stokes system reaches equilibrium capillary bridge configuration, the enforced contact angles are accurately honored.
Snap-off phenomenon
Discontinuous Galerkin methods for numerical simulation of Cahn–Hilliard–Navier–Stokes system. Capillary forces cause droplets to snap off through the geometric constriction of the pore space.
Two-phase flow in porous media
Advances in pore-scale imaging, increasing availability of computational resources, and developments in numerical algorithms have started rendering direct pore-scale numerical simulations of multiphase flow on pore structures feasible. The flow fields computed at the pore-scale can be used to compute effective properties for two-phase flow such as relative permeability and capillary pressure for use at Darcy-scale flows as part of a truly multi-scale modeling system.
