CFD Education in Undergraduate
Curriculum DG
(CFDEdUgCDG)
AIAA ASM 2010 Orlando
5 January 2010
Objectives of this DG
1.
Should there be undergraduate CFD education?
2.
Information gathering: Examine and discuss the current
computation-related curricula of mechanical and aerospace
engineering departments. Also, discuss current texts and their
relative strengths/merits for undergrad CFD education.
3.
Discussion: Itemize the basic curriculum elements that will best
prepare undergraduate students for informed and thoughtful
application (‘intelligent users and observers’) of CFD tools in their
career (including graduate school).
4.
Expert recommendation: Work together to formulate a
recommendation report that can eventually be used by
departments, particularly those undergoing curriculum reform
processes.
Objective 3: Recommendation report
Exit strategy of this DG (-->WG):
A publicly available document that recommends the
necessary curricular elements for preparing
engineering students for a variety careers in which CFD
is an actively-used tool.
•This document should also provide ideas/examples about how such
elements might be incorporated into the existing curriculum, with as little
upset as possible.
•Also, a bibliography of textbooks (and reviews?) could be included.
•What else?
Towards Objective 1: What is out there?
Poll ~10 ME, AE or MAE departments and provide
details of their computation-related curricula, including
•Programming courses
•Numerical algorithms
•CFD courses
•Fluid dynamics/aerodynamics courses (and in particular, those
that include CFD related elements in their syllabi)
•Computational structural mechanics (e.g. FEM) courses
•Design courses with CFD or CSM components
Towards Objective 1
Some questions to ask:
• Are these courses required for undergraduates?
• In CFD units of fluids or design courses, are the students
getting instruction with the algorithms themselves, or
applying a commercial/shareware code as a black box?
• If there is an undergrad-level numerical algorithms and CFD
course, what topics are included on the syllabus? What
textbook is used?
• Who are some of the most important employers of recent
graduates of this department? Is CFD a commonly used tool
in typical career paths of these graduates?
Universities polled for data
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
MIT
Univ. Illinois at Urbana-Champaign
Univ. Michigan
Purdue University
Univ. Iowa
Cal Poly SLO
Univ. of Alabama Birmingham
US Air Force Academy
Michigan State University
Notre Dame
Western Michigan University
UCLA
Ohio State University
Mississippi State University
RPI
Greg Blaisdell
Russ Cummings
Bill Liou
Jeff Eldredge
Ravi Balasubramanian
MIT
Curriculum
Civil Engineering:
• 1.00 Introduction to Computers and Engineering Problem Solving –
part of Aero core curriculum
ME courses:
• 2.086 Numerical Computation for Mechanical Engineers – Newly
approved as a required course in ME
Aero courses:
• 16.100 Aerodynamics – “Elementary MATLAB usage expected”
• 16.13 Aerodynamics of Viscous Flows – Includes “numerical solution
techniques and exercises”
• 16.90 Computational Methods in Aero Engineering – UG elective
(several graduate CFD/numerical courses available)
1.00 Introduction to Computers and
Engineering Problem Solving
• Fundamental software development and computational methods for
engineering, scientific and managerial applications. Emphasis on objectoriented software design and development. Active learning using laptop
computers (available on loan). Assignments cover programming concepts,
graphical user interfaces, numerical methods, data structures, sorting and
searching, computer graphics and selected advanced topics. The Java
programming language is used.
2.086 Numerical Computation for
Mechanical Engineers
1. Introduction to MATLAB
2. Introduction to Computational Methods
3. Probability and Statistics
4. Integration
5. Linear Algebra
6. Regression
7. Ordinary Differential Equations
8. Eigenproblems
9. Nonlinear Equations
10. Partial Differential Equations
16.90 Computational Methods in Aero
Engineering
• Description: Introduction to computational techniques arising in
aerospace engineering. Techniques include numerical integration of
systems of ordinary differential equations; numerical discretization of
partial differential equations; and probabilistic methods for quantifying
the impact of variability. Specific emphasis will be given to finite volume
methods in fluid mechanics, and energy and finite element methods in
structural mechanics.
University of Illinois
AE Curriculum
•
•
•
•
•
Sophomore course introduces MATLAB
MATLAB used in several courses
Systems course includes real-time programming
AE 470 Numerical Methods is required
Undergraduate Electives:
–
–
–
–
AE 410 Computational Aerodynamics
ME 412 Numerical Thermo-Fluid Mechs
TAM 470 Computational Mechanics
CS 450 Numerical Analysis
AE 470 - Computational Methods in
Aerospace Engineering
•
•
•
•
•
Required senior course
Text: Published course notes and many references
MATLAB based
Students write their own programs
Sample homework problems available
– Include using finite difference methods to solve the wave equation
and structural vibration equations in 1-D and 2-D
Course Outline
1. Introduction
1.1 Motivation for computational analysis
1.2 Steps for PDE simulations
1.3 Programming guidelines
2. Introduction to computational analysis
2.1 Computational errors
2.2 Interpolation and polynomial
approximation
2.3 Integration
2.4 Root finding
2.5 Solution of ODE
3. Numerical solution of linear systems
3.1 Matrix characteristics
3.2 Direct vs. iterative methods
3.3 Direct methods
3.4 Iterative methods
4. Finite difference method (FDM)
4.1 Classification of PDE
4.2 Initial and boundary conditions
4.3 Taylor series to form finite-difference
operators
4.4 Finite difference of elliptic PDE
4.5 Modeling boundary conditions
4.6 Finite difference of parabolic PDE
4.7 Finite difference of hyperbolic PDE
5. Finite element method (FEM)
5.1 Reminder: energy formulation (PVM,
PMPE)
5.2 Rayleigh-Ritz method
5.3 FEA of 1-D Poisson problem
5.4 FEA of 2-D truss structures
5.5 FEA of 2-D Poisson problem
5.6 Additional topics on the FEM
AE 410 – Computational Aerodynamics
• Elective senior course
• Description: Introduction to computational technologies as
solution tools for various aerodynamic problems; modeling
and solution of one-and two-dimensional, incompressible and
compressible, steady and unsteady inviscid external flow
fields. Computational laboratory for practical experience.
ME 412
Numerical Thermo-Fluid Mechs
• Senior elective
• Description: Numerical techniques for solving the equations
governing conduction and convective heat transfer in steady
and unsteady fluid flows: finite-difference and finite-volume
techniques, basic algorithms, and applications to real-world
fluid-flow and heat-transfer problems.
• Uses Fluent
University of Michigan
Curriculum
• ME/AE 523 Computational Fluid Dynamics I –
Graduate course in CFD, taken by some but not many
undergrads
• ME 420 Fluid Mechanics II – Senior elective, not
usually taken by AE students
• MATH 371 & 471 Numerical Methods – electives
• MATLAB and other codes (AVL-vortex lattice, XFOIL)
used in Aerodynamics and other courses
• Algorithms are taught before the tools are used
• Fluent used by some students in aircraft design
• Faculty interested in offering more computational
sciences courses to undergrads
ME 420 Fluid Mechanics II
• Senior elective
• Text: none
• Description: Use of commercial CFD packages for solving realistic fluid
mechanics and heat transfer problems of practical interest. Introduction to
mesh generation, numerical discrimination, stability, convergence, and
accuracy of numerical methods. Applications to separated, turbulent, and
two-phase flows, flow control, and flows involving heat transfer. Openended design project.
• Topics:
1. Internal compressible flow
2. Pumps and compressors
3. Fluid power systems
4. Turbulence
5. Computational fluid dynamics
Purdue University
Curriculum
• MATLAB taught to freshmen, used extensively in
many courses
• Algorithms generally not taught, but the theory
behind the physics is taught
• CFD used in senior design courses (with mixed
success)
• AAE 412 Intro. to CFD – senior elective
• Graduate CFD and numerical methods courses
available in AAE, ME, CS and MATH; some UGs take
the grad AAE CFD course
AAE 412 Intro. to CFD
• Senior elective (Fall 2009: 56 students)
• Text: An Intro. to Computational Fluid Dynamics – the
Finite Volume Method, Versteeg & Malalasekera
• Homework based on modifying and running simple
Fortran codes
• 4-week team project using Fluent (limited to 2-D)
• Most students do not attend graduate school; they will
be users of CFD codes
• Try to emphasize understanding numerical error and
modeling error
• I am not sure where to land in balancing hands-on
experience and theory
Course Outline
I. Introduction and Basic Numerical Methods
•
Introduction to CFD
•
Approximation and interpolation
•
Numerical integration
•
Finite difference approximations of derivatives
II. The Finite Volume Method for Model Problems
•
1-D diffusion – tri-diagonal systems
•
1-D convection-diffusion – von Neumann stability analysis
•
2-D diffusion, potential flow – iterative solvers
III. Computational Fluid Dynamics (CFD)
•
Staggered grids
•
Pressure-velocity coupling – the SIMPLE algorithm
•
Commercial CFD codes (Fluent)
•
RANS equations and turbulence modeling
Acknowledgments
Special thanks to:
• Luis Bernal (Michigan)
• Dan Bodony (UIUC)
• Philippe Geubelle (UIUC)
• Hong Im (Michigan)
• Tony Patera (MIT)
• Bram van Leer (Michigan)
University of Iowa
•
•
•
•
•
•
Undergrad CFD course?
Required/Elective?
Textbook?
If so, which book?
Students per year?
*Fluids course with CFD projects
Yes*
Required
Yes
White
?
Cal Poly SLO
•
•
•
•
•
Undergrad CFD course?
Required/Elective?
Textbook?
If so, which book?
Students per year?
Yes
Elective
Yes
Tannehill et al
15
University of Alabama Birmingham
•
•
•
•
•
Undergrad CFD course?
Required/Elective?
Textbook?
If so, which book?
Students per year?
Yes
Elective
No
25
U.S. Air Force Academy
•
•
•
•
•
•
Undergrad CFD course?
Required/Elective?
Textbook?
If so, which book?
Students per year?
*to be published by Cambridge
Press
Yes
Required
Yes
Instructor Notes*
70
Objective 2: ‘Customer’ survey?
• Survey targeting the ‘customers’ of recent graduates from
mechanical or aerospace departments. What should be
expected of such graduates in terms of their CFD background
when they enter the workforce or proceed to graduate
school.
– What questions would go on such a survey? Multiple choice?
– Who would receive such a survey? (Industry/govt labs/grad faculty
advisors/recent alumni)
– How would we compile the data?
• Some thoughts on this:
– Separate what is expected from what is merely desired.
– Must balance these survey responses with the underlying mission of a
university: to educate, not to train.
Discussion on survey
• Brainstorming of questions?
What else?
• It would useful to coordinate our activities with other
similarly-scoped efforts (e.g. Russ mentioned Fred
Stern at Univ. Iowa)
• What else should we be doing?