ME687A
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Modelling of Multiphysics Systems
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Credits:
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3L-0T-0L-0D (9 Credits)
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Course Content:
Introduction and dimensional analysis and review of numerical method: Review on vector calculus, scalar/vector fields, linear algebra, notation system, Taylor series, numerical methods for simultaneous linear equations, first/second order ODE and PDE, dimensional analysis; Review and modelling of simple systems: Conservation laws of mass, momentum and energy, thermal transport (Fourier’s Law and Diffusion Equation), mass transport (Fick’s Law, diffusive and convective mass balance), definitions of displacement gradient, strain (Euler/Lagrange), stress (nominal, PK-1/2), momentum conservation, Generalized Hooke’s Law and Navier’s equation, plane stress/strain, continuity and Navier Stokes equations, steady and transient flow models, electrodynamics, Maxwell’s equations, electrochemical transport and kinetics, Butler Volmer and Tafel models, applied numerical problems for each physics; Modelling of coupled multiphysics systems: Thermal-elastic systems, gas-driven and thermal strain-driven actuating devices, Electrostatic-elastic systems, capacitive mass-spring and plate systems, stability analysis and bifurcation diagrams, Fluid-thermal systems, natural convection, Fluid-structural systems, Electrochemical-thermal-mechanical systems; Computational application of multiphysics problems: Numerical modelling of coupled systems in Matlab and COMSOL, one-way and two-ways coupling, dimensional analysis and problem simplification; Multiscale modelling: Introduction to molecular dynamics.
Lecture-wise Breakup (based on 50 min per lecture)
I. Introduction and dimensional analysis and review of numerical method (4 Lecture)
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Introduction to Multiphysics systems; Review of vector calculus; Notation system (conventional/Einstein summation); Scaling and dimensional analysis; Review of numerical methods; Taylor series; 1st and 2nd order ODE; PDE – Euler method, Crank Nicholson; Basic model development in MATLAB. [4 Lecture]
II. Review and modelling of simple systems (15 Lectures)
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Conservation laws and constitutive equations for thermal, mechanical, fluid, electrochemical and electromagnetic systems. Development of analytical solutions for transient thermal diffusion, deformation of membrane, string and plate; Revision of Navier Stokes, Nernst and Maxwell’s equations; PDE solutions using separation of variable, Green’s theorem, calculus of variations, etc.; Effect of scaling on modelling. [15 Lectures]
III. Modelling of coupled Multiphysics systems (15 Lectures)
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Thermo-mechanical system – membranes, thermal actuators (bi-metallic), piezo; Fluid-thermal system; Electro/magneto-mechanical system – charged mass/spring, membranes/actuated-combs; Electrochemical-thermal-mechanical system – modelling energy storage devices, ion transport, surface kinetics, deposition dynamics, heat generation modes and thermal diffusion, diffusion-induced stresses. [15 Lectures]
IV. Computational application of Multiphysics problems (3 Lectures)
V. Multiscale modelling (5 Lectures)
References:
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Modeling MEMS and NEMS, Pelesko and Bernstein, Chapman & Hall/CRC.
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Partial Differential Equations: An Introduction, Walter A. Strauss, Wiley.
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Computational Partial Differential Equations Using MATLAB, Li and Chen, CRC.
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Multiphysics and Multiscale Modeling Techniques and Applications, Young W. Kwon, CRC.
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Multiphysics Modeling Numerical Methods and Engineering Applications, Zhang and Cen, Elsevier.
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Applied Mechanics of Solids, Allan F. Bower, CRC.
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A Compendium of Partial Differential Equation Models Method of Lines Analysis with Matlab, Schiesser and Griffiths, Cambridge.
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