Introduction to Finte Volume, Finite Element, and Finite Difference Methods


Jan 18  Jan 23

Discretization of 2D general transport equation using FV, FE, and FD methods, explicit vs implicit time advancement, direct vs iterative solvers, solution residuals, programming assignment on implimentation of FD method in 2D


Stability and Accuracy of Numerical Schemes


Jan 25

Numerical diffusion, modified wavenumber analysis, orderofaccuracy, numerical stabilization, computational assignment using CAE tool


Mesh Quality and Boundary Conditions


Jan 30  Feb 03

Unstructured vs structured mesh, assessment of mesh quality, effect of element shape on accuracy and stability, false diffusion due to mesh alignment, types of boundary conditions, computational assignment using CAE tool


Momentum Transport in Laminar Flows


Feb 06  Feb 10

Introduction to NavierStokes (NS) equations in dimensional and nondimensional form, special cases of creeping and inviscid flows, iterative and noniterative methods for numerical solution of NS equations (SIMPLE, PISO, FSM methods), computational assignment using CAE tool


Heat Conduction and Convection in Laminar Flows


Feb 13

Steady and unsteady heat condition equations, natural and forced convection in laminar flows, introduction to relevant nondimensional numbers, difficulties faced in numerical solution of energy equation, coupling of energy and momentum equations, computational assignment using CAE tool


Mass Transport in Laminar Flows


Feb 15

Fick's law of mass diffusion, equations of change for multicomponent gasphase diffusive and convective mass transport, introduction to relevant nondimensional numbers, solution procedure for mass transport equation, computational assignment using CAE tool


Calculation of Source Term for Chemically Reacting Flows


Feb 20

Introduction to multicomponent chemically reacting flows, multistep chemistry mechanisms, calculation of production and destruction rates of chemical species as a system of ODEs, coupling of chemical reactions with energy and multicomponent mass transrpot equations


Introduction to Turbulent Flows and their Simulations


Feb 23  Feb 27

Practical examples of turbulent flows, statistical description of turbulent flows, scales of turbulent motion, transition from laminar to turbulent flows, examples of free shear flows and wall flows, turbulence modelling approaches (RANS, LES, DNS), choice of an approach based on computational cost and relevant physics, examples of most commonly used turbulence models, computational assignment using CAE tool


Project Proposal Presentations


Mar 01

A 15minute presentation to the class by each team


Meshing Training


Mar 06

Meshing training from ANSYS in MechE Computing Cluster (HH C101)


Midterm Exam


Mar 08

Midterm exam


Computational Project


Mar 13  May 03

Team project in computational analysis using CAE tool, project proposal presentation, midproject presentation, weekly meetings with TA and instructor

April 05

Meshing training from ANSYS in MechE Computer Cluster (HH C101)

April 10

A 15minute project update presentation to the class by each team

May 09

Final project presentation and submission of written report
