Praveen Chandrashekar
Associate Professor (G)
Education
- BE, Mechanical Engg., KREC, Surathkal (Now NIT)
- ME, Aerospace Engg., IISc, Bangalore
- PhD, Aerospace Engg., IISc, Bangalore
Websites
Research Interests
- Computational Fluid Dynamics
- Finite element and Discontinuous Galerkin Methods
- Parallel Computing
Computational methods for PDE
Partial differential equations arise as models of real world systems in many areas like aerospace, mechanical, civil, chemical, weather modelling and of course in many physics problems. Except in some simple situations, we cannot solve PDEs with analytical techniques and we have to use a computer to obtain an approximate solution. The construction of accurate and stable numerical methods requires a combination of PDE theory, numerical analysis and computer programming ideas. The approximation techniques must be constructed to be consistent with the PDE, satisfy additional structural properties of the solutions and be capable of being efficiently implemented on modern computers. Linear and non-linear PDEs arising in modelling of fluid flows also pose challenges in terms of developing waves, shocks and turbulent solutions, which require special techniques. At CAM, we are interested in developing novel, robust and high order techniques for PDEs in compressible flow of a gas, magnetohydrodynamics, plasma flow models, Maxwell's equations, shallow water flows, etc. We also place emphasis on developing structure preserving schemes in terms of maintaining positivity of solutions, satisfying entropy and energy conservation, divergence-free property, etc., so that the resulting methods are more consistent with the PDE model and the physics of the problem. The methods developed are also implemented in computer codes and since their computational cost can be quite high, we also aim to make them faster by using parallel programming concepts, so they can be run on clusters of computers. Some recent work on high order Lax-Wendroff methods for compressible flows can be see in these videos (part of the PhD thesis work of Arpit Babbar)
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https://www.youtube.com/playlist?list=PLHg8S7nd3rfvifIGkW4a6fpvy-0PbGCbv
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https://youtube.com/playlist?list=PLHg8S7nd3rfvI1Uzc3FDaTFtQo5VBUZER
Since mathematical modelling and computer simulation is an integral part of most industries, students who are trained in these areas will be well equipped to pursue careers in many application domains, either as researchers/scientists or as academics in universities.