CFD Education in Undergraduate Curriculum DG

(CFDEdUgCDG)

AIAA ASM 2010 Orlando5 January 2010

Objectives of this DG1. 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 reportExit 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 data1. MIT2. Univ. Illinois at Urbana-Champaign3. Univ. Michigan4. Purdue University5. Univ. Iowa6. Cal Poly SLO7. Univ. of Alabama Birmingham8. US Air Force Academy9. Michigan State University10. Notre Dame11. Western Michigan University12. UCLA13. Ohio State University14. Mississippi State University15. RPI

Greg Blaisdell

Russ Cummings

Bill Liou

Jeff Eldredge

Ravi Balasubramanian

MITMITMITMIT

CurriculumCurriculumCurriculumCurriculumCivil 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 MEAero 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 1.00 Introduction to Computers and Engineering Problem SolvingEngineering Problem Solving

• Fundamental software development and computational methods for engineering, scientific and managerial applications. Emphasis on object-oriented 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 2.086 Numerical Computation for Mechanical EngineersMechanical Engineers

1. Introduction to MATLAB2. Introduction to Computational Methods3. Probability and Statistics4. Integration5. Linear Algebra6. Regression7. Ordinary Differential Equations8. Eigenproblems9. Nonlinear Equations10. Partial Differential Equations

16.90 Computational Methods in Aero 16.90 Computational Methods in Aero EngineeringEngineering

• 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 IllinoisUniversity of IllinoisUniversity of IllinoisUniversity of Illinois

AE CurriculumAE CurriculumAE CurriculumAE 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

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 OutlineCourse Outline

1. Introduction1.1 Motivation for computational analysis1.2 Steps for PDE simulations1.3 Programming guidelines

2. Introduction to computational analysis2.1 Computational errors2.2 Interpolation and polynomial approximation2.3 Integration2.4 Root finding2.5 Solution of ODE

3. Numerical solution of linear systems3.1 Matrix characteristics3.2 Direct vs. iterative methods3.3 Direct methods3.4 Iterative methods

4. Finite difference method (FDM)4.1 Classification of PDE4.2 Initial and boundary conditions4.3 Taylor series to form finite-difference operators4.4 Finite difference of elliptic PDE4.5 Modeling boundary conditions4.6 Finite difference of parabolic PDE4.7 Finite difference of hyperbolic PDE

5. Finite element method (FEM)5.1 Reminder: energy formulation (PVM, PMPE)5.2 Rayleigh-Ritz method5.3 FEA of 1-D Poisson problem5.4 FEA of 2-D truss structures5.5 FEA of 2-D Poisson problem5.6 Additional topics on the FEM

AE 410 – Computational AerodynamicsAE 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 412ME 412Numerical Thermo-Fluid MechsNumerical 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 MichiganUniversity of MichiganUniversity of MichiganUniversity of Michigan

CurriculumCurriculumCurriculumCurriculum• 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 IIME 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. Open-ended design project.

• Topics:1. Internal compressible flow2. Pumps and compressors3. Fluid power systems4. Turbulence5. Computational fluid dynamics

Purdue UniversityPurdue UniversityPurdue UniversityPurdue University

CurriculumCurriculumCurriculumCurriculum• 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 CFDAAE 412 Intro. to CFDAAE 412 Intro. to CFDAAE 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 OutlineCourse OutlineI. 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

AcknowledgmentsSpecial 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*RequiredYesWhite?

Cal Poly SLO

• Undergrad CFD course?• Required/Elective?• Textbook?• If so, which book?• Students per year?

YesElectiveYesTannehill et al15

University of Alabama Birmingham

• Undergrad CFD course?• Required/Elective?• Textbook?• If so, which book?• Students per year?

YesElectiveNo

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

YesRequiredYesInstructor 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?