1/13
Course mechanics, introduction to Computational Fluid Dynamics (CFD).
Sections 1.1-1.7
 

1/15
Conservation laws in fluid mechanics, strong conservation law form, mathematical classification.
Sections 1.8-1.9, 2.1-2.4
 

1/20
Mathematical classification continued, components of a numerical method. Properties of numerical solutions.
Chapter 2 of Tannehill, Anderson, and Pletcher, Section 2.5 of Ferziger and Peric.
 

1/22
Properites of numerical solutions, discretization approaches.
Section 2.5, 2.6
 

1/27
Introduction to finite difference methods. Taylor series, polynomial fitting, approximation to an arbitrary derivative, error analysis.
Sections 3.1-3.6
 

1/29
Boundary conditions for finite difference approaches, spectral methods.
Sections 3.7-3.8
 

2/3
Algebraic system resulting from finite difference approximations.
Section 3.9
 

2/5
In depth error analysis, examples of finite difference methods.
Sections 3.10-3.11
 

2/10
Introduction to finite volume methods, approximations of volume and surface integrals.
Sections 4.1-4.3
 

2/12
Interpolation schemes for estimating fluxes.
Section 4.4
 

2/17
Interpolation schemes continued, time lagging, boundary conditions for finite volume methods.
Sections 4.4-4.6
 

2/19
Algebraic equation system resulting from finite volume approximations, relation to finite difference methods. Examples of finite volume methods.
Sections 4.7-4.8
 

2/24
More examples of finite volume methods.
Section 4.8
 

2/26
Introduction to time marching methods, accuracy, stability.
Section 6.1
 

3/3
Stability analysis.
Notes provided.
 

3/5
Explicit time marching methods.
Section 6.2
 

3/10
Implicit time marching methods.
Section 6.3
 

3/12
Time marching examples.
Section 6.4
 

3/17
Midterm exam.
 

3/19
Euler and Navier-Stokes equations. Conservation properties, conservation law form, dangers of non-conservative forms.
Course notes.
 

3/31
Wave motion, characteristic analysis, upstream and downstream propagation of information.
Course notes.
 

4/2
Difficulty in obtaining a stable differencing scheme for the Euler equations.
Course notes.
 

4/7
Upwind differencing, flux splitting.
Course notes.
 

4/9
Flux difference splitting.
Course notes.
 

4/14
Detailed information on setting up a finite volume method for the Euler equations.
Course notes.
 

4/16
Finite volume method for the Euler equations continued.
Course notes.
 

4/20
Finite volume method for the Euler equations continued.
Course notes.
 

4/23
Incompressible Navier-Stokes equations. Staggered grids.
Sections 7.1-7.2
 

4/27
Incompressibility constraint, Poisson equation for the pressure.
Section 7.3
 

4/30
Fractional step method.
Section 7.4