Here are some notes and tutorials converted into web books
Teaching: In December 2025, I will be giving some lectures on finite volume method at the NBHM workshop to be held in IIT, Tirupati. From January 2026, I will be teaching a new elective on finite difference methods for evolutionary PDE.
Postdocs: There are some postdoc positions at TIFR-CAM, see here. If you are interested, write to me with your CV. There are limited positions at TIFR-CAM, and if you have your own funding, e.g., via NPDF, NBHM, etc., I encourage you to write to.
Projects/internships: If you are a student looking for internship, project assistant position or postdoc position in the topic of computational PDE, please read this and write to me if you are interested in doing some project.
I am a professor in the Center for Applicable Mathematics, Bangalore, which is part of the Tata Institute of Fundamental Research. This is my personal website while my official page is located here.
For the details of the numerical scheme, see here.
Latest News
- 05 Dec 2025: Postdoc positions at TIFR-CAM
- 01 Dec 2025: PhD in applied and computational mathematics
- 10 Nov 2025: Talk by Punit Yadav
- 01 Nov 2025: Talk by Devansh Sonigra
- 26 Sep 2025: Jalil Khan secures NPDF grant
Experience
- 3’rd Jan, 2005 to 14’th August 2006: Scientist, Computational and Theoretical Fluid Dynamics Division, National Aerospace Laboratories, Bangalore
- 1’st September 2006 to July 2008: Post-doc, Projet OPALE, INRIA, Sophia Antipolis
- 6 August 2008 to July 2011: Fellow (E), Tata Institute of Fundamental Research, Center for Applicable Mathematics, Bangalore.
- July 2011 to June 2018: Reader (F), Tata Institute of Fundamental Research, Center for Applicable Mathematics, Bangalore.
- July 2018 to December 2023: Associate Professor (G), Tata Institute of Fundamental Research, Center for Applicable Mathematics, Bangalore.
- January 2024 to present: Professor (H), Tata Institute of Fundamental Research, Center for Applicable Mathematics, Bangalore.
Education
- BE, Mechanical Engineering, KREC, Surathkal, 1994-1998
- ME, Aerospace Engineering, IISc, Bangalore, 1998-2000
- PhD, Aerospace Engineering, IISc, Bangalore, 2000-2004
Research
My primary research interest is CFD and its applications. I am also interested in numerical analysis and numerical solution of PDE in general.
- Computational Fluid Dynamics
- Kinetic schemes for compressible flows
- Meshless method
- Finite volume method
- Finite element and Discontinuous Galerkin Method
- Compressible flows, MHD, Shallow water
- Well-balanced scheme
- Adjoint equations and solvers
- Automatic differentiation
- Shape optimization
- Simplex method
- Particle swarm optimization
- Metamodelling, surrogate models
- Parallel computing
Organizational activities
- Instructional workshop on FEM, 2-13 July 2012
- International conference on conservation laws and applications, 1-3 July 2013
- IFCAM Summer school on numerics and control of PDEs, 22 July - 2 August, 2013
- Workshop on optimization with PDE constraints, Nov 25 - Dec 6, 2013
- Finite element meet, 18-20 Dec, 2014
- Advanced Summer School on Control and Numerics for Fluid-Structure Interaction Problems, 22-26 June, 2015
- Workshop on Control and Numerics for Fluid-Structure Interaction Problems, 29 June - 1 July, 2015
- Conference on Computational PDE, 21-23 Dec, 2015
- Compact course on compressible Navier-Stokes equations, May 2016.
- GIAN course on Computational Solution of Hyperbolic PDE at IIT Delhi, 4-15 December, 2017.
- Conference on PDE and Numerical Analysis, 28-30 April 2022, online conference organized in memory of Prof. A. S. Vasudeva Murthy.
- NCM Workshop on Finite Volume and Spectral Methods for Hyperbolic Problems, December 2023.
Fun in research
- Will the wind tunnel replace the computer ?
- The Wine Snobs Guide To Flux Functions
- The Fitted Mesh Story...,
- A one-sided view
- The Turbulent History of Fluid Mechanics
Computing
- Computing on Mac OSX
- Amrex | Bash | cchpc19 | Chapel | Clawpack | Debian | Docker | Fenics | Firedrake | Git HowTo | Gnuplot | Homebrew | Julia | Jupyter | Latex | LFTP | Make | Matplotlib | OpenSuse | PBS | Python | Screen | SLURM | Spack | SSH | TeXMacs | Vim | VisIt | WSL | xmgrace
- Computers at TIFR-CAM