1. CFD Education in Undergraduate Curriculum DG (CFDEdUgCDG) AIAA ASM 2010 Orlando 5 January 2010

2. 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.

3. 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?

4. 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

5. 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?

6. Universities polled for data 1.MIT 2.Univ. Illinois at Urbana-Champaign 3.Univ. Michigan 4.Purdue University 5.Univ. Iowa 6.Cal Poly SLO 7.Univ. of Alabama Birmingham 8.US Air Force Academy 9.Michigan State University 10.Notre Dame 11.Western Michigan University 12.UCLA 13.Ohio State University 14.Mississippi State University 15.RPI Greg Blaisdell Russ Cummings Bill Liou Jeff Eldredge Ravi Balasubramanian

7. MITMIT

8. CurriculumCurriculum 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)

9. 1.00 Introduction to Computers and Engineering 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.

10. 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

11. 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.

12. University of Illinois

13. 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

14. 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

15. 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

16. 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.

17. 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

18. University of Michigan

19. CurriculumCurriculum 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

20. 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. Open- ended design project. Topics: 1. Internal compressible flow 2.Pumps and compressors 3.Fluid power systems 4.Turbulence 5.Computational fluid dynamics

21. Purdue University

22. CurriculumCurriculum 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

23. 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

24. 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

25. Acknowledgments Special thanks to: Luis Bernal (Michigan) Dan Bodony (UIUC) Philippe Geubelle (UIUC) Hong Im (Michigan) Tony Patera (MIT) Bram van Leer (Michigan)

26. 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 ?

27. Cal Poly SLO Undergrad CFD course? Required/Elective? Textbook? If so, which book? Students per year? Yes Elective Yes Tannehill et al 15

28. University of Alabama Birmingham Undergrad CFD course? Required/Elective? Textbook? If so, which book? Students per year? Yes Elective No 25

29. 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

30. 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.

31. Discussion on survey Brainstorming of questions?

32. 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?