ROSE-HULMAN INSTITUTE OF TECHNOLOGY

ME 427  Introduction to Computational Fluid Dynamics --- Spring 2010–2011

 

 

Class

Date

Day

Topics

 HW Set Due

Lecture 1

3-7

M

Introduction to CFD: what it is and what it is not

  

Lecture 2

3-8

T

Conservation of mass - the continuity equation

  

Lab 1

3-9

W

MATLAB review - leap-frogging of vortex rings

  

Lecture 3

3-10

R

Conservation of linear momentum: the Navier-Stokes equation

 

Lecture 4

3-14

M

Conservation of energy

Set 2

Lecture 5

3-15

T

Road map of a CFD calculation

Set 3

Lab 2

3-16

W

Construction of a computational model

  

Lecture 6

3-17

R

 Solution strategy of the finite-difference method

Set 4

Lecture 7

3-21

M

Solution strategy of the finite-volume method - Treatment of convection

 

Lecture 8

3-22

T

Solution strategy of the finite-volume method - Treatment of viscous diffusion

Set 6

Lab 3

3-23

W

Solution to a steady-state problem - an indirect method

  

Lecture 9

3-24

R

Solution strategy of the finite-volume method - Treatment of pressure gradient

  

Lecture 10

3-28

M

Formal order of accuracy of spatial discretization

Set 8

Lecture 11

3-29

T

Effect of reduced order at domain boundaries: biased scheme

  

Lab 4

3-30

W

Solution to a one-dimensional problem with convection and diffusion - a finite-volume approach

  

Lecture 12

3-31

R

Modified wave number of spatial discretization

Set 10

Lecture 13

4-4

M

Wave resolution efficiency of spatial discretization

Set 11

Lecture 14

4-5

T

Numerical dispersion and dissipation

Set 12

Lab 5

4-6

W

2D Grid generation - a GAMBIT exercise (Tutorial 1, Tutorial 2)

  

Lecture 15

4-7

R

Introduction to non-uniform structured mesh - needs & basic ideas

Set 13

Lecture 16

4-11

M

Non-uniform structured mesh - examples of mapping function & metric terms

 

Lecture 17

4-12

T

Review of Exam 1

 

Lab 6

4-13

W

Exam 1

  

Lecture 18

4-14

R

Applications of structured mesh generation

Set 15

Spring Break

Lecture 19

4-25

M

Time advancement - explicit Euler (formal order of accuracy, stability analysis)

Set 16

Lecture 20

4-26

T

Higher-order predictor-corrector methods (formal order of accuracy & stability)

Set 18

Lab 7

4-27

W

CFD solver - a FLUENT exercise (Tutorial 1)

  

Lecture 21

4-28

R

Implicit time advancement: Euler & Trapezoid (formal order of accuracy & stability)

  

Lecture 22

5-2

M

Amplitude error & phase error of a time advancement scheme

Set 20

Lecture 23

5-3

T

Space-time coupling in convective problem

Set 21

Lab 8

5-4

W

More exercise on mesh generation & solver

  

Lecture 24

5-5

R

Space-time coupling in diffusive problem

 

Lecture 25

5-9

M

Issues of stability, accuracy, dispersion, dissipation of space-time scheme in convective and diffusive problems

 

Lecture 26

5-10

T

Hierarchy of numerical computations

Set 23

Lab 9

5-11

W

Project work

  

Lecture 27

5-12

R

The closure problem of turbulence

 

Lecture 28

5-16

M

Turbulence modeling - the eddy viscosity model

Set 24

Lecture 29

5-17

T

Turbulence modeling - the Reynolds stress model

  

Lab 10

5-18

W

Exam 2

  

Lecture 30

5-19

R

Course wrap up & evaluation

  

Final

 

 

 Project presentation to instructor during the week of final exams (special arrangement with graduating seniors)  

Vortex pairing in supersonic mixing layer
This laminar computation demonstrates the vortex pairing phenomenon in a supersonic mixing layer at a low Reynolds number of 1,000 (based on the inflow vorticity thickness and the speed of the lower stream.) The upper stream travels at Mach 2 while the lower stream is at Mach 1.2. The shear between the two fluid streams causes the fluid to roll up into individual vortices which further pair up to form larger vortices as they convect downstream. The following animation displays the vorticity (rotation of fluid particles) distribution of the flow field. The flow is perturbed by its fundamental and subharmonic modes.