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Research Seminar by Dr. Surya Narayan Maharana, on 29 July, at 11:00 AM

Title of the talk: Numerical Simulations of Convection Dominated Flow Problems

Date , Time & Venue: 29 July 2025, 11:00 AM ,Seminar Hall, Dept. of Mathematics

Abstract: Convection-dominated fluid flow problems frequently occur in nature and engineering, particularly in systems where solute concentration significantly alters the fluid’s viscosity and density. These flows arise in diverse contexts, from porous media governed by Darcy¹ or Brinkman equations²'³ to complex channel flows modelled by the Navier–Stokes equations⁴'⁵.. In such regimes, convective transport can dominate diffusion, producing steep gradients and numerical challenges. Despite their widespread occurrence, the governing equations for these flows remain poorly understood in terms of well-posedness. Moreover, the underlying flow instability phenomena, often critical in determining flow behaviour, require more rigorous investigation through improved linear stability analysis. Current numerical methods struggle to capture the full dynamics of these systems, especially under strong convection, highlighting the need for more robust and physically consistent simulation frameworks. This talk presents a range of representative flow problems to illustrate the mathematical and computational challenges of modelling convection dominated systems. It emphasizes open questions in theory and simulation and points to promising directions for future research.

About the Speaker: Dr. Surya Narayan Maharana is currently a postdoctoral research fellow at the Université libre de Bruxelles, Belgium, where he has been working since February 2023. He obtained his Ph.D. in Mathematics from  I.I.T. Ropar, in Feb'23. His doctoral research focused on the linear and nonlinear analysis of reaction-induced shear instabilities in Navier-Stokes flow. His research interests lie in numerical methods for partial differential equations, theoretical PDE, and scientific computing.

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