Research

I am interested in Applied Mathematics problems that include but not limited to fluid dynamics. I use advanced mathematical techniques to model fluid flow problems ranging several length and time scales. Both analytical and numerical techniques are used to solve the model. We often use simple toy problems to unfold effects of nonlinearities, which are inherent to applied mathematics problem.

My research past and ongoing research projects include:

1. Hydrodynamic instabilities: The aim of the research project, in collaboration with the research groups of Prof. Manoranjan Mishra (IIT Ropar), Prof. Anne De Wit (ULB), Prof. Ching-Yao Chen (NCTU), is to understanding various hydrodynamic instabilities, e.g. Saffman-Taylor (viscous fingering) and Rayleigh-Taylor (density fingering) instabilities in miscible fluids. I am mostly interested in the mathematical modeling of these instabilities using ordinary differential equations and partial differential equations, and their numerical solutions when analytical solutions are not available.

2. Premelting dynamics: In collaboration with Prof. John Wettlaufer, I focus on the understanding of the coupling between the fluid flow and deformation of a poroelastic medium. We use mathematical modeling and semi-analytical/numerical solution of the model to describe the observed physics.

3. Soft cells: With Prof. Chris MacMinn (Oxford), James Guan (UNC), I investigate to understand fluid-structure interaction in a soft-walled Hele-Shaw cell. A pivotal component of this project is to impose the volume conservation of the flow cell by restricting an indefinite inflation of the soft wall of the cell.

4. Homogenization : In this project, we are interested to understand the effects of pore geometry on the transport properties in flow through soft porous media. Collaborators in this projects involve researchers from University of Oxford, KTH, NORDITA, and OIST.