Hello, I'm Kshitij.
I am an Engineer In Love With Math (EILWM). Currently pursuing research into the Variational Projection of Navier Stokes under the guidance of Dr. Haithem E. Taha. My work presents a fresh perspective on the age-old field of incompressible fluid dynamics — it turns out this field is not stagnant, and we have only scratched the surface.
About Me
I had most of my formal education in India. I pursued Aerospace Engineering and Computer Science at IIT Kharagpur. As an undergraduate, I was always fascinated with the ability to control movement in robots. Hence, naturally I was attracted towards robotics and control theory. However, as it happened to be, the aerospace department at IIT Kharagpur could not match me with a potential advisor whose specialization was in control theory. At this point in my life, I am grateful for this event (back then, I was not). This led to me working on flapping wing micro-aerial vehicles with Dr. Sunil Manohar Dash. He introduced me to unsteady aerodynamics and the scope of numerical computing. Next, I moved on to do my summer internship with Dr. Sophie Armanini at TU Munich, and then later she was my co-advisor for my Master's Thesis with Dr. Dash.
Publications
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Variational Projection of Navier Stokes (VPNS): A Novel Optimization Based Solver for Incompressible Fluid Flows
Introduces VPNS, a novel computational framework that reformulates incompressible flow simulation using variational mechanics. By leveraging the Principle of Minimum Pressure Gradient, the method transforms fluid mechanics into a Convex Quadratic Programming problem with a closed-form solution, eliminating the need for iterative Pressure Poisson solvers.
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Variational Projection of Navier-Stokes: Fluid Mechanics as a Quadratic Programming Problem
Gauss's principle of least constraint is extended to fluid mechanics through the principle of minimum pressure gradient (PMPG), transforming incompressible flow problems into pure minimization frameworks and enabling new computational approaches.
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Formulating Constrained Mechanics As Quadratic Programming Enables Explicit Navier-Stokes Projection
Demonstrates how constrained mechanics formulated as convex quadratic programming enables explicit Navier-Stokes projection, transforming fluid mechanics into an optimization problem that bypasses direct equation solving.
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Mechanics as a Convex Quadratic Programming Problem With Application to Incompressible Flows
Establishes that the principle of minimum pressure gradient transforms incompressible fluid mechanics into a strongly convex quadratic programming problem, providing a computationally tractable framework for flow evolution.
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A Generic Tool for Simulating Two-Dimensional Ideal Flows Over Arbitrary Shapes Using the Principle of Minimum Pressure Gradient
Development of a computational tool that simulates two-dimensional ideal flows over arbitrary geometries by leveraging variational principles, eliminating the need for traditional Poisson equation solvers.
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Aerodynamic Modelling of 3-DOF Flapping Kinematics and Dynamic Modelling of 2-DOF FWMAV
Investigates dragonfly flight dynamics through numerical simulations and develops a mechanical model for two-degree-of-freedom flapping-wing micro air vehicles, analyzing vortex interaction effects and stability characteristics.