**My general
area of research is ***Computational Fluid Dynamics (CFD) and Numerical Methods for
Partial Differential Equations***. More specifically my research encompasses
developing efficient Higher Order Compact (HOC) schemes to numerically
simulate incompressible viscous flows governed by the Navier-Stokes (N-S)
equations. **

**We have developed numerous
differential equation based HOC schemes for the two-dimensional (2D)
steady-state and transient Convection-Diffusion equations which has been
successfully implemented on the N-S equations both in the primitive variable
and the streamfunction-vorticity formulations. These schemes are well-equipped
to handle problems in rectangular as well as curvilinear coordinates, again
both in uniform as well as nonuniform grids. We have also applied them to flows
in porous media involving both heat and mass transfer. Recently we have
developed a super-compact HOC scheme for the three-dimensional (3D)
Convection-Diffusion equation which has been implemented to resolve flows
governed by the 3D N-S equations as well. Here
are some cool pictures of the simulations for the 3D lid-driven cavity flow at
Re=100 computed on a 65x33x65 grid.**

**Projection of the
stream-function on x-z plane at y=0.11, 0.5 and 0.8.**

**Projection of pressure on x-z
plane at y=0.11, 0.5 and 0.8.**

**Vector plots on x-z plane at
y=0.11, 0.5 and 0.8.**

**In addition
to this, we have also developed a ψ-v formulation for the 2D N-S
equations that uses an infinite series based HOC scheme. Recently we have
successfully extended this approach to curvilinear coordinates ; we have also
extended the scheme on rectangular domains to transient flows. (see the
following simulations: two-sided lid-driven cavity problem at Re=800, the
motion past a circular cylinder problem at Re=80 and periodic flow for the
motion past a square cylinder at Re=200.) Currently we are working on the 3D
version of this approach. **

**The two-sided lid-driven cavity at Re=800 with aspect
ratio 1.96:
the streamlines: top: numerical, bottom: experimental**

**Streamline evolution for the flow past a
circular cylinder at Re=1000: (a) t=2.5, (b)t=2.75, (c) t=3.00, (d) t=3.25 (e)
t=3.75 and (f) t=4.00.**

**Motion
past a square cylinder at Re=200: the streamfunction contours depicting the
wake behind three successive instants of
time over one vortex shedding period.**

**Motion
past a square cylinder at Re=200: the vorticity contours depicting the wake
behind three successive instants of
time over one vortex shedding period.**

**Recently, we have had some tremendous success with the
biharmonic formulation of the N-S equations on irregular geometries. Here is a
cool simulation of the streaklines for the laminar flow past an impulsively
started circular cylinder at Re=200. **

For an animated version of the von Kármán vortex street behind a circular cylinder at Re=50 click here and Re=200, click here. With this formulation we have also successfully simulated the flow past an impulsively started NACA 0012 airfoil in the laminar range. Following are the simulation for Re=1000 and angle of attack 34 degrees.

** At
present, we are trying to club together the HOC methodology to other existing
CFD tools to develop even more efficient schemes. One of such efforts has been to
club our HOC approach to the immersed interface method in Cartesian grids to
capture discontinuities and to solve interface problems. We are also in
the process of extending the existing HOC methodology to adaptive grids
and local defect correction strategy. More recently, we are moving in the
direction of applying the HOC methodology to mathematical approaches in
financial and biological problems.**

** I am
also interested in the implementation of advanced iterative solvers like
Conjugate Gradient (CG), BiConjugate Gradient (BiCG), BiConjugate Gradient
Stabilised (BiCGStab), Hybrid BiConjugate Gradient Stabilised
(BiCGStab2) methods as well as Multigrid methods. All along, I have been using
them quite extensively in my computer codes. **

**To know more about my research, feel free to
look at some of my publications. All of my published papers are available on request; you
can write to me at the following e-mail addresses:** jiten** [*AT]** iitg.ernet.in
or jiten_kalita** [*AT]** yahoo.co.in