Modelling of Multiphysics Systems




3L-0T-0L-0D (9 Credits)



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)

  • 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)

  • 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)

  • 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)

  • Development of simple Multiphysics models in MATLAB and COMSOL; Fragmentation and analysis of complex problems. [3 Lecture]

V. Multiscale modelling (5 Lectures)

  • Introduction to Multiscale modelling approaches; Project discussion. [5 Lectures]


  1. Modeling MEMS and NEMS, Pelesko and Bernstein, Chapman & Hall/CRC.

  2. Partial Differential Equations: An Introduction, Walter A. Strauss, Wiley.

  3. Computational Partial Differential Equations Using MATLAB, Li and Chen, CRC.

  4. Multiphysics and Multiscale Modeling Techniques and Applications, Young W. Kwon, CRC.

  5. Multiphysics Modeling Numerical Methods and Engineering Applications, Zhang and Cen, Elsevier.

  6. Applied Mechanics of Solids, Allan F. Bower, CRC.

  7. A Compendium of Partial Differential Equation Models Method of Lines Analysis with Matlab, Schiesser and Griffiths, Cambridge.