I am a fourth year PhD student under Professor Praveen Chandrashekar at Tata Institute of Fundamental Research - Centre for Applicable Mathematics. My work is on development of efficient numerical algorithms for simulation of advection dominated fluid flows. The broad class of numerical algorithms that I study are higher order methods. These methods are notable for having better accuracy with fewer grid points and doing more number crunching and lesser memory transfers, something that modern computers like.

The particular higher order methods that I work on are Lax-Wendroff Flux Reconstruction (LWFR) schemes. These simulate time dependent flows without depending on an Ordinary Differential Equation (ODE) solver and can thus achieve higher order accuracy in a single stage, minimizing memory transfers even more than standard higher order methods. During my PhD, my colleagues and I made the following contributions to the LWFR scheme

1. Enhancement of stability and accuracy: Article Preprint
2. Provably admissibility-preserving shock capturing with particular focus on maintaining the benefits of high order accuracy: Article Preprint
3. Embedded error-based time step computation, tested on adaptive curvilinear meshes. Preprint
4. Advection-diffusion equations like Navier-Stokes Preprint
5. Generalized framework for admissibility preservation, source terms Preprint
6. Proven linear equivalence with ADER schemes where local evolution is performing by solving an implicit equation Preprint

You can see my cv here. Thanks for visiting!

Presenting our work at ICOSAHOM 2023, Yonsei University, Seoul, Korea

Photo credits to Kedar Wagh