Introduction to Computational Fluid Dynamics (CFD)


Week 1

The need for CFD, applications, historic perspective, different methods for CFD, stateoftheart, challenges, future directions
Introduction to NavierStokes (NS) equations, physical and mathematical classification of PDEs, system of equations, some key PDEs of interest in CFD


Basics of Finite Difference Method (FDM))


Week 2

Numerical approximation of derivatives using Taylor series, orderofaccuracy, modified wavenumber analysis of numerical derivatives, finite difference representation of a PDE, truncation error, consistency, stability


FDM for Parabolic PDEs


Week 3

Numerical solution of 1D transient diffusion equation, explicit methods, modified wavenumber analysis, von Neumann stability analysis, modified equation method for accuracy and consistency, DuFort Frankel method, implicit methods, types of boundary conditions and their implementation

Week 4

CrankNicolson method, 2D and 3D transient diffusion equations, approximate factorization and alternate direction implicit (ADI) methods for computational efficiency


FDM for Hyperbolic PDEs


Week 5

Numerical solution of 1D advection equation, upwind explicit and FTCS implicit methods, Courant condition, von Neumann stability analysis, amplitude and phase errors

Week 6

LaxFriedrichs method, LaxWendroff method, trapezoidal method, boundary conditions, linear Burger's equation, advectiondiffusion equation, matrix structure for implicit method in 2D

Week 7

Review for Midterm exam
Midterm exam


FDM for Elliptic Partial Differential Equations


Week 8

Some common elliptic PDEs, solution using direct methods such as Gauss elimination, iterative methods: point Jacobi, Gauss Seidel, SOR, boundary conditions
LineSOR, method of steepest descent, multigrid acceleration


FDM for NavierStokes (NS) Equations


Week 9

Derivation of mass, momentum and energy equations, macroscopic and microscopic views
Conservative vs nonconservative forms of NS equations, some other simple fluids equations, FDM for incompressible NS equations

Week 10

FDM for incompressible NS equations, vorticitystream function formulation for 2D incompressible flows

Week 11

FDM for incompressible NS equations, premitive variable formulation

Week 12

Introduction to Direct Numerical Simulations (DNS), ReynoldsAveraged Navier Stokes (RANS) and largeeddy simulation (LES) techniques for modeling of incompressible turbulent flows, introduction to numerical methods for compressible flows


Unstructured Grids and Finite Volume Method (FVM)


Week 13

Introduction to complex geometry and grids, need for unstructured grids, grid generation and storage of grid connectivity, implimentation of boundary conditions, conversion of PDE into numerical equations using FVM


Project Office Hours


Week 14

Inclass help with projects


Project Presentations and Submission of Project Reports


Week 15

1520 minutes presentation to the class
