Research
In research ... we investigate applied problems and application driven basic
problems using a plethora of theoretical and numerical tools. We also explore
the possibility of useful changes in various applied fields by developing new as
well as by making use of existing algorithms.
Research Interests
- Fluid dynamics (Newtonian, non-Newtonian and Geophysical),
Hydrodynamic stability and turbulence,
Singularity formation,
Interfacial flows,
Multiphase flows,
Porous media flows,
Chemical enhanced oil recovery,
Hele-Shaw flows,
Applied mathematics,
Conservation laws,
Nonlinear waves,
Numerical analysis and methods (FEM,FD,Spectral),
Analysis based fast algorithms for PDEs,
Computational mathematics,
Computational fluid dynamics,
Mathematical modeling,
Probabilistic methods,
Data Science,
Machine Learning,
Current Research
I am currently working broadly on problems in areas highlighted above under Research Interests, which are broadly related to Fluid Dynamics and Mathematics in general, and Numerical Methods/Analysis. Click below for projects in these areas some of which (the ones marked with an *) have been in collaboration with my recent graduate students, postdocs and collaborators. Please see the Publications tab in my homepage for my work on miscellaneous fluid dynamics problems and numerical methods not covered within the list of topics below.