University of Toronto Institute for Aerospace Studies

(for research in the design of environmentally friendly aircraft)

**"Education is the most powerful weapon which you can use to change the world."
**

Nelson Mandela

Address:

University of Toronto Institute for Aerospace Studies (UTIAS)

4925 Dufferin St.,
Toronto, Ontario,
Canada M3H 5T6

Phone: (416) 667-7709, Fax: (416) 667-7799

Email: dwz(at)oddjob(dot)utias(dot)utoronto(dot)ca

**Table of Contents**

(scroll down or click on an item from the list below)

Textbook: Fundamental Algorithms in Computational Fluid Dynamics

Textbook: Fundamentals of Computational Fluid Dynamics

Technology Developments and Renewable Fuels for Sustainable Aviation (with Omer Gulder)

The following journal papers since 1999 can be downloaded (see below for downloadable conference papers):

Brown, D.A., and Zingg, D.W., "Monolithic homotopy continuation with predictor based on higher derivatives," J. of Computational and Applied Mathematics, Vol. 346, Jan. 2019, pp. 26-41.

Brown, D.A., and Zingg, D.W., "Matrix-Free Monolithic Homotopy Continuation Algorithm with Application to Computational Aerodynamics," Numerical Algorithms, Vol. 78, Issue 4, August 2018, pp. 1303-1320.

Koo, D., and Zingg, D.W., "Investigation into Aerodynamic Shape Optimization of Planar and Nonplanar Wings," AIAA J., Vol. 56, Jan. 2018, pp. 250-263.

Witherden, F.D., Jameson, A., and Zingg, D.W., "The Design of Steady State Schemes for Computational Aerodynamics," Handbook of Numerical Analysis, Vol. 18, Handbook of Numerical Methods for Hyperbolic Problems: Applied and Modern Issues, 2017, pp. 303-349.

Brown, D.A., and Zingg, D.W., "Design and Evaluation of Homotopies for Efficient and Robust Continuation," Applied Numerical Mathematics, Vol. 118, 2017, pp. 150-181.

Brown, D.A., and Zingg, D.W., "Efficient numerical differentiation of implicitly-defined curves for sparse systems," Journal of Computational and Applied Mathematics, 304 (2016) 138-159.

Brown, D.A., and Zingg, D.W., "A Monolithic Homotopy Continuation Algorithm with Application to Computational Fluid Dynamics," Journal of Computational Physics, 321 (2016) 55-75.

The following conference papers can be downloaded in postscript form (pdf for papers dated 2003 and later):

Lassaline, J.V., and Zingg, D.W., "Development of an Agglomeration Multigrid Algorithm with Directional Coarsening," AIAA 99-3338, June 1999.

Driver, J., and Zingg, D.W., "Optimized Natural-Laminar-Flow Airfoils," AIAA Paper 2006-247, 2006.

**Second Textbook: Fundamental Algorithms in Computational
Fluid Dynamics**

The textbook *Fundamental Algorithms in Computational Fluid Dynamics*,
by Thomas H. Pulliam, and David W. Zingg, was published in 2014 by
Springer-Verlag in the series Scientific Computation.
The book is intended for a first or second course in computational fluid dynamics, in the latter case in conjunction with our earlier textbook (see below).
It is an entirely new book, not a new edition of the earlier book. For further information, click
here.

The textbook *Fundamentals of Computational Fluid Dynamics*,
by Harvard Lomax, Thomas H. Pulliam, and David W. Zingg, was published in June 2001 by
Springer-Verlag in the series Scientific Computation, ISBN 41607-2.
The book is intended for a first course in computational fluid dynamics.
For further information, click
here.

From a review in Contemporary Physics:

"[The book] is much needed to fill a gap in the market for texts that try to cover some of the fundamental mathematical aspects of the subject. The book is aimed at graduate students and concentrates on analysing the properties of approximations produced by finite-difference and finite-volume methods. ... The main strengths of the book are that the theoretical aspects are treated in an elegant and simple manner, making it easy for the reader to appreciate the subtle links between the discrete and continuous operators and linear algebra. The mathematics is self-contained and not daunting. Most of the sections are well written and the section on ordinary differential equations and time marching methods is particularly good."

From a review by P. Wesseling in Structural and Multidisciplinary Optimization:

"An introduction to finite volume methods for initial-boundary value problems for partial differential equations, developed with applications in CFD in mind ... The student who has mastered this material will be well equipped for further study and use of numerical methods in the computational disciplines, where one's only guide is often analogy with simple cases. ... I found the book pleasant to read, and good for students. The level is that of a course for students studying for a Masters degree in their final year. Teachers of similar courses will find the
book useful. A good collection of exercises is included."

From a review in Applied Mechanics Reviews:

"The book is well written and organized. It can be easily adopted as a textbook for senior or graduate students studying numerical methods of fluid mechanics. Practice exercises are provided at the end of each chapter, some of them expecting the reader to write his own computer codes. This reviewer would regard Fundamentals of Computational Fluid Dynamics as essential to anyone planning to use CFD modelling."

From a book review by Datta V. Gaitonde, U.S. Air Force Research Laboratory,
in the American Institute for Aeronautics and Astronautics Journal:

"The unaffected style adopted by the authors makes the book very readable and brings a
surprising degree of freshness to the mature concepts that are its emphasis.
For this reason, in addition to graduate students, the book may appeal to
professionals who do not have formal training in CFD but who wish to learn more
theory than is found in cookbook-oriented code manuals."

"... sharp focus on ideas and analysis rather than tips and techniques ..."

From a book review by Randall J. LeVeque, University of Washington,
in the SIAM Review:

"... the book covers a good set of introductory material and includes some topics
and insights not found in other books at this level, along with numerous
exercises. In the hands of a knowledgeable instructor, it could form the basis for an
excellent course and would be a useful supplement in general."

**AER 1316H Fundamentals of Computational Fluid Dynamics**

This course presents the fundamentals of numerical methods for inviscid and viscous flows. The following topics are covered: finite-difference and finite-volume approximations, the semidiscrete approach to the solution of partial differential equations, time-marching methods for ordinary differential equations, stability of linear systems, relaxation methods, multigrid, flux splitting, and approximate factorization.

The course textbook, *Fundamentals of
Computational Fluid Dynamics*, by H. Lomax, T.H. Pulliam, and D.W. Zingg,
is available at the textbook store or online, e.g. Indigo.

The first class for fall 2020 will be on Wednesday, September 9 from 10:00-12:00. All subsequent classes will be on Wednesdays from 10 to 12. Assignments are up to date for 2020. THE FINAL TEST WILL BE HELD ON DECEMBER 16.

**Assignment 1 (Due Sept. 30)**

Problems 1, 2, 3 and 4 from Chapter 2, problems 1, 5, 6, 8, 9, and 10 from Chapter 3.

**Assignment 2 (Due Nov. 4)**

Problems 7 through 12 from Chapter 6.

**Assignment 3 (Due Nov. 18)**

Problem 4 from Chapter 5, problems 1, 2, 5, and 6 from Chapter 6, problems 4 and 5 from Chapter 7, problem 1 from Chapter 8.

**Assignment 4 (Due Dec. 2)**

Problem 4 from Chapter 9, problem 2 from Chapter 10.

**AER 1318H Topics in Computational Fluid Dynamics**

This course follows AER 1316H, which is a prerequisite. The course first concentrates on the algorithmic details of two specific codes for solving the compressible Navier-Stokes equations, ARC2D and FLOMG. Topics to be covered include generalized curvilinear coordinates, approximate factorization, artificial dissipation, boundary conditions, and various convergence acceleration techniques, including multigrid. Finally, the course covers high-resolution upwind schemes.

The first meeting will be in the UTIAS lecture hall at 10:00 on January 15. The course outline and assignments are up to date for 2020.

The
schedule for the oral exam on April 15 is as follows. Please be ready a few minutes ahead of your scheduled time. Also, please do not discuss the exam questions
with your classmates until after everyone has completed the exam. The exam will
be held via Zoom. Please contact me if you do not have Zoom.

10:00 Zijun

10:15 Gregory

10:30 Mohamed

10:45 Anthony

11:00 Alex

11:15 Chris

11:30 Jose

** Assignment 1 **

Problems 3.1, 3.2, and 3.3 in the course text

** Assignment 2 **

Problems 4.1, 4.2, and 4.3 in the course text

** Assignment 3 **

Problems 5.1 and 5.2 in the course text

** Assignment 4 **

Problem 6.1 in the course text

**Micemen**

(1998 Metro Toronto Touch Football League AA Conference Champs)