Date 
Topics covered: 
1/15 
Introduction to the
Class 

Use of Numerical Methods 

Initial Mathematical Model 

Transformation of Model
Equations 

Steps for Use of Finite Difference 
1/17

Classification
of PDEs ( Examples) 
1/22 
Formation of Finite Volume
Equations 
1/24, 1/29

Verification
and Validation of
Codes and Results 
1/31

Formation of Finite Difference Equations 
2/5

Finite Difference Equation Examples 
2/7 
Predictor Corrector Method 
2/12, 2/14

Iterative Solution of Linear
Equations, Basics 
2/19 
Domain Decomposition and
Multigrid
Iteration 
2/21 
Krylov Subspace Methods 

Some considerations for
direct matrix
solution 
2/26 
Introduction to Time
Dependent
Conduction 
2/28

More Time Dependent
Conduction, (also check this link to Slides)

3/4

Review for Exam 
3/6 
More Stability
Analysis 
3/11, 3/13

Spring
Break

3/18, 3/20 
The AdvectionDiffusion
Equation 
3/25 
QUICKEST and effects of Source Terms 
3/27 
Quantifying Numerical Diffusion
Wiggles 
4/1

Full Flow Equation Set 
4/3

Use
of Numerically Generated
Jacobians 
4/8

A sample testbed
program 
4/10

Nonorthogonal
Grids 
4/15, 4/17

Use of
Overset Grids in Computational Fluid Dynamics (presented by Dr.
Eric Paterson)

4/22 
Final Project Discussions 
4/24, 4/29

Application to Multiphase and/or reacting flow 
5/1

Semester Summary 

Review
for the Second Exam
