Research Projects

Working under the guidance of Dr. Anand Jacob Abraham (Asst. Prof., Industrial and Systems Engineering, Indian Institute of Technology (IIT), Kharagpur). My research focuses on a two-period inventory management model for phasing out products, where players anticipate an increase in wholesale prices during the second period. We examine how the pricing and inventory strategies are affected in a competing retailer environment when there is a possibility of demand disruption for a specific retailer under a commitment contract. A paper detailing this work is under review in the Journal of the Operational Research Society. 

An extension of an already published work (link) by my supervisor, Dr. Satyananda Panda (Prof. NIT Calicut), discussing the modeling of tidal movement of water in the Gulf of Khambhat, a bay on the Arabian Sea coast of India, using shallow water equations with turbulent friction. 

In this work, with the goal of producing a much more efficient scheme, we discretized implicitly using the finite volume method and solved using MATLAB's nonlinear solver. The results indicate a sharp fall in the solution, specifically in the elevation and velocity of the tidal waves, but it presents a much more promising outcome than the Method of Lines. It is noted that a sharp discontinuity emerges in the solutions over time due to the exponential decay of the channel, and the solver fails to capture this phenomenon. To address this discontinuity, WENO (Weighted Essentially Non-Oscillatory), a shock-capturing scheme, is incorporated into the discretization of the flux function. It is found that the shocks could be identified by the higher-order implicit WENO scheme. The simulated results are in perfect agreement with the known physical facts associated with the waves in the Gulf, thus validating the work.

In addition, in order to check the efficiency of the WENO scheme compared to an upwind method (zero-order WENO scheme), we implemented both the fifth-order WENO method and the upwind method to solve the Burgers equation. The observation leads to the conclusion that with increasing order and the use of WENO, the solution effectively captures more discontinuities. Consequently, WENO proves to be a suitable method for problems characterized by discontinuities or shocks. 

My first research experience was a reading internship under the guidance of Dr. Sachindranath Jayaraman (Assoc. Prof., IISER Thiruvananthapuram) on the topic of Matrix Theory. We specifically worked on Jordan Canonical Forms, covering two different approaches to prove the existence of Jordan Canonical Forms: one an algebraic method and the other a more algorithmic approach. This experience helped me learn more about linear algebra, and the two-month experience involved weekly presentations, discussions with my guide, and a lot of learning and unlearning about the nuances of a research career. 

 📌  Report Copy submitted to Science Academies 

 📌 SRFP Certificate