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{\Large \bf EML 5725 \hfill Spring 2003 } \\
{\Large \bf Intro to C.F.D.} \\
{\Large \it Van Dommelen }
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\section{Catalog Description}
\label{catalog}

Topics for this course include introduction to conservation laws in
fluid dynamics; weak solutions; solving the full potential equations
for subsonic, transonic, and supersonic flows; solving system of
equations. In particular, upwind schemes and flux splitting will be
introduced in solving the Euler equations. Coordinate transformation
and grid generation methods will also be covered.

\section{Credit Hours}
\label{credit}

3

\section{Prerequisites}
\label{prereqs}

\begin{itemize}
\item EML 5060 Analysis in M.E.
\item EML 5709 Fluid Mechanics
\end{itemize}

Or permission of instructor.

\section{Textbook}
\label{books}

Tannehill, John C, Anderson, Dale A \& Pletcher, Richard H
{\it Computational Fluid Mechanics and Heat Transfer.}
Taylor \& Francis, 2nd edition 1997.  ISBN 1-56032-046-X

\section{Instructor}
\label{instructor}

Dr. Leon Van Dommelen:

\begin{description}

\item[Office hours]
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M 1-2 pm, T 3-4 pm, in A 242 CEB.
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</A>
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\item[Phone]
(850) 410-6324. I tend to forget to check my voice mail.

\item[E-mail]
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<A HREF="mailto:dommelen@eng.fsu.edu">
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dommelen@eng.fsu.edu
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</A>
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\item[Web page]
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http://www.eng.fsu.edu/$\sim$dommelen/index.html.\
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\item[Contact information]
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See web page
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\end{description}

\section{Teaching Assistant}
\label{TA}

None

\section{Schedule}
\label{schedule}

Class times: MWF 10:45-11:35 in A 226 CEB or as announced.

Predetermined dates:

\begin{itemize}
\item 01/13/03 HW 2.1, 2 due
\item 01/15/03 HW 2.5 (assume a-f all constant), 8, 9(a) due
\item 01/22/03 HW Describe typical properly posed problems for the Laplace,
  heat, and wave equations.  Describe what the CFL condition tells us
  about how to solve those equations on a mesh of points.
\item 01/27/03 HW 2.12 (write as $\vec u_y = A \vec u_x$), 14
\item 01/31/03 HW: Derive the exact solution of groups project 1 using
  the method of separation of variables.  Compare with the functions
  {\tt 
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exact
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} on the web page and comment on the questions in the comments.
\item 02/03/03 HW 3.2 3.16 ($\Delta x_+ \equiv x_{i+1}-x_i$ and
  $\Delta x_- \equiv x_i-x_{i-1}$.)
\item 02/05/03 Project 1 due.
\item 02/07/03 For the finite difference formula
  $(u_j^{n+1}-u_j^n)/\Delta t = c (u_j^n-u_{j-1}^n)/\Delta x$, find
  the PDE with which this FDE is consistent and find the order of
  accuracy.  Note: the Courant number is defined as $C=c\Delta
  t/\Delta x$.  Use many terms in the Taylor series.
\item 02/10/03 Use operators to derive a {\em second order accurate}
  finite difference formula for $(u_{xxx})_j^n$ that is {\em as
    compact as possible}, i.e. that only uses $u$ values at {\em mesh}
  points as close as possible to $j$ itself.  Write it out both in
  terms of operators and in terms of mesh point values.  Derive the
  truncation error of your formulae using Taylor series.  Verify that
  the same truncation error is obtained from multiplying the
  expansions on the formula sheet. \\
  \strut\\
  Also, use your program at $N=0.5$ and $j_{\rm max}=4, 8, 16,$ and 32
  to examine whether the maximum error at time $t_{n_{\rm out}}$
  (i.e., about 0.5) is really $O(\Delta x)^2$ as it should be.  Also
  examine whether the error is $O(\Delta x)^4$ for $N=1/6$.  Repeat
  both for the case that $V_1$ is 1 instead of 2.  Explain the
  results.
\item 02/14/03 Use both the second order and the fourth order compact
  scheme to evaluate $u_{xx}$ between $x=0$ and $x=2$, using $\Delta
  x=0.5$.  Take $u=e^x$. For the compact scheme, you can use the exact
  values of the second derivative at the end points $x=0$ and $x=2$.
  Is the compact scheme more accurate?
\item 02/21/03 Exam I
\item 02/24/03 Crank-Nicholson consistency and accuracy using Taylor
  series due.
\item 03/05/03 HW 3.4 due.
\item 03/19/03 Group project 2 due.
\item 03/21/03 3.11, 17, 18, 19 due.
\item 03/26/03 3.25, 26, 27 due.
\item 04/02/03 Exam II
\item 04/07/03 (a) Do McCormack scheme stability as stands.
  (b) Reduce the scheme to LW.
\item 04/09/03 Derive the conservative form of the equations of
  axisymmetric inviscid nonconducting flow.  Make sure there are no
  nonconservative {\em derivative} terms.
\item 04/11/03 Convert coordinates and bring the equations back into
  conservative form.
\item 04/25/03 Individual project 1 due.
\item 04/30/03: Wednesday 12:00 Final Project due
\end{itemize}

\section{Goals}
\label{goals}

This course will familiarize the student with basic ideas and techniques
of computational fluid dynamics.

\section{Course Outline}

\begin{itemize}
\item We will quickly go over the introduction in chapter 1.
\item We will quickly go over chapter 2 on partial differential
  equations (already largely known from EML 5060.)
\item We will study chapter 3
\item We will study section 4.1 in some detail followed by
  4.2.13 and selected parts of 4.4
\item We will study sections 6.3-5.
\end{itemize}

\section{Methods of Instruction}

Lectures, programs, examinations.

\section{Student Evaluation}
\label{evaluation}

The course grade will be computed as:

\begin{itemize}
\item 20\% Homework
\item 10\% Group projects
\item 10\% Individual project
\item 20\% Exam 1
\item 20\% Exam 2
\item 20\% Final Project
\end{itemize}

\section{Important Regulations} \
\label{regulations}

\begin{enumerate}
\item Immediately check the dates listed above for any conflicts.
\item Homework must be handed in at the {\em start} of the lecture at
  which it is due.  It may {\em not} be handed in at the departmental
  office or at the end of class.  Homework that is not received at the
  start of class on the due date listed above cannot be made up unless
  permission to hand in late has been given {\it before} the homework
  is due, or it was not humanly possible to ask for such permission
  before the class.  If there is a chance you may be late in class,
  hand the homework in to the instructor the day before it is due.
  (Shove it under his door if necessary.) This also applies to Web
  students: they must E-mail the homework before the time the class
  starts.
\item Homework should be neat.
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\item Students are bound by the rules and regulations in their
  University bulletin, as well as by those specified in this syllabus,
  and by the usual standards applied by the College of Engineering.
  Read your academic bulletin. Violations of the rules and regulations
  in your bulletin may result in reduced grades and/or other actions.
\item Students are bound by the honor code of their university.  It
  requires you to uphold academic integrity and combat academic
  dishonesty.  Please see your student handbook.  Violations of your
  honor code may result in reduced grades and/or other actions.
\item {\it Copying} of homework, assignments, or tests is never
  allowed and will result in a failing or zero grade for the copied
  work.  It will also result in a failing or zero grade of the person
  whose work is being copied if that person could reasonably have
  prevented the copying.  However, {\it working together} is typically
  allowed and encouraged for most homeworks, (and sometimes for other
  take-home assignments,) as long as you present the final results in
  your own words and using your own line of reasoning.  Since close
  similarities between solutions will reduce credit, it is better not
  to formally put down anything until you have figured out the
  problem, and then let each person write their own solution.  If it
  is unclear whether working together is allowed on any assignment,
  check with the instructor beforehand.
\item Attendance is required.  Exams missed, even when rescheduled
  from the original date and surprise tests, or homework not handed in
  on time due to unexcused absence or lateness will result in a zero
  grade for that exam and/or homework.  Failure to properly complete
  homework, tests, assignments, etcetera due to changes in date,
  assignment, etcetera, that you did not know about due to unexcused
  absence, lateness, or inattentiveness will not be excused and cannot
  be made up.
\item For excused absences where the student has given advanced notice
  of the absence at the earliest opportunity, the instructor will work
  with the student to arrange for make-up work and tests.
\item In undergraduate classes, the total grade is further reduced due
  to unexcused absences or lateness.  See the instructor for details.
  Even a few absences will make it impossible to pass the class.
  Typically, four unexcused absences result in an F grade regardless
  of numerical performance.  Conscientious attendance is required for
  a confident determination of your mastery of the subject matter to
  be made. In other words, this class cannot be taken like a DIS
  unless a faculty member will allow you to do so under formal DIS
  rules with appropriately modified grading and testing standards.
\item The College of Engineering has a restrictive interpretation of
  what is considered a valid excuse for an absence.  If an absence is
  to be excused, make sure you at least get official confirmation by
  phone that it will be granted beforehand.
\item The instructor will make sure that make-up tests are no simpler
  than the original, but he will try to make them similarly difficult.
  However, he cannot make allowances for increased difficulty due to
  the small sample size.
\item The College of Engineering has a more restrictive drop-add
  period than you might think based on your bulletin.  Check both your
  bulletin and the Dean's office to determine whether drop-add will be
  allowed.
\item Some of these rules may not apply if you fall under the
  Americans with Disabilities Act.  FAMU students with disabilities
  needing academic accommodations should contact Student Health
  Services for confirmation of permanent physical disability, FSU
  students should register with and provide documentation to the
  Student Disability Resource Center. Next bring a letter to the
  instructor from the Services or Center indicating you need academic
  accommodations.  This should be done during the first week of
  classes.
\item The instructor might wave some regulation on a case-by-case
  basis depending on his subjective determination of fairness and
  appropriateness.  This will occur only under exceptional
  circumstances and should not be assumed. Especially, never assume
  that a seemingly minor regulation will be waved because the
  instructor has waved it in the past.  A second appeal to wave a
  minor regulation will probably indicate to the instructor that the
  regulation is not being taken seriously and most likely refused.
  Any appeal to the instructor will further be refused apriori unless
  it is done at the earliest possible moment by phone and/or by
  E-mail. Do not wait until you are back in town, say.
\end{enumerate}

\section{Computer Requirements}
\label{computer}

Students must be able to program in a decent scientific programming
language.  Fortran is recommended, but C or C++, Pascal, Algol, PL 1,
ADA, and Matlab are also acceptable.  Students must have an E-mail
address and daily check their E-mail.  Students must be able to use a
Web browser such as Netscape.  The class web page can be accessed at

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If you are taking this class remotely, see the
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for requirements.

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