IST - Principles of Continuum Mechanics (2024)

Venue: J.C. Bose University of Science & Technology, Faridabad

Dates: 3 Jun 2024 to 15 Jun 2024


Name: Prof. Neetu Gupta Dr. Suraj Goyal
Mailing Address: Chairperson & Dean Sciences Department of Mathematics
J.C. Bose University of Science & Technology, YMCA Faridabad-1210 06, Haryana
Assistant Professor
Department of Mathematics
J.C. Bose University of Science & Technology, YMCA Faridabad-1210 06, Haryana
Email:  neetuymca [at] yahoo [dot] co [dot] in  surajgoyal87 [at] jcboseust [dot] ac [dot] in

In this school, we will learn the basic principles of continuum mechanics and their use to study propagation of time harmonic waves in simple media. In particular, we will learn about Eulerian and Lagrangian coordinate systems, stress-strain tensors and their properties, governing differential equations of continuum mechanics, conservation laws for the mass, linear momentum, angular momentum, energy; Basic concepts of theory of elasticity: Hooke’s law and its generalization, symmetry of stress tensor; Waves in uniform elastic medium, Helmholtz decomposition of vector, body waves, reflections/ refraction phenomena; Surface waves - Rayleigh, Love and stoneley; Non-Local Elasticity.
Computational Fluid Dynamics: Need and Applications; concept of finite difference, finite difference discretization, convergence, consistency, and stability; second order wave equation using explicit method and its von-Neumann stability; vorticity – stream function formulation; flow over a backward-facing step problem. Convection problems in fluid Dynamics, Hydrodynamics of Rayleigh-Benard convection and Couette-Taylor problem, Numerical methods for hydrodynamic and the flow problems.

After learning these topics one can pursue research in solid and fluid mechanics. Through these topics we will discuss some current problems to have an idea of ongoing research in these areas. We will also learn how to use software like MATLAB for computations and graphical interpretation of results.
Our motivation is to promote applied mathematics in our region and improve the quality of teaching which is essential for motivating participants for research in mathematics. We hope that after attending this school, our participants will be able to motivate and encourage their students to study mathematics at a higher level.