My principle area of interest is Computational methods for Incompressible flows and turbulent flows.

Here is a brief review of the topics that I am currently working on

**1**. **Immersed boundary method** **:** Flows in complex geometries are difficult to solve. They bring in issues that
are otherwise nonexistent. Use of Cartesian mesh for all problems is not only an advantage, but perhaps it opens up opportunities to compute flows which are
otherwise prohibitively difficult. In particular applying this method in complex 3D flows or high-Re flows are challenges that lie ahead of us. Conventinal sharp interface immersed
boundary method suffers frrom sppuruss oscillation in aerodynamic force coefficients owing to velocity pressure discontinuity. The diffuse interface IBM, by treating the interface as fluid-fluid
one reduces the SFOs significantly. This greatly enhances its ability to handle complex FSI problems. Some simulated cases are shown here.

Instantaneous streakline visualization of the wake that forms behind a large-aspect ratio pitching plate at Re=1000

Instantaneous visualization of periodic side-by-side fluttering of a thin plate

Instantaous vortical structure behind an inclined cylinder at indicated Reynolds numbers

Swimming of a simplified insect at Re=500, two instances are shown

Turbulent flow past a wavy cylinder at Re=3900, spanwise vorticity surfaces

**2. Rayleigh-Benard Convection : ** Themo-convective instability in a bottom heated configuration is one of the fundamental topic in turbulent convection. Large-scale motion, Ra-number scaling and sustenance of turbulence via production due to buoyancy are especially a few attractive features. Currently we are aiming to see the effect of rotation on the turbulent convection in a cylindrical cell. Also work is in progress for turbulent structures and mean flow circulation in rectangular box both in 2D and 3D regimes.

Temperature visualization for stationary RBF for Ra=10