Introduction to Numerical Method

Introduction to Computational Fluid Mechanics

Instructor: Leon Kaganovskiy
Office: HNS 110 or HNS 204 (Physics Computer Lab), Office Phone: 487-4118
Office Hours:

Mon: 11-12:30 and 4-6, Tue : 4-6 (office/computer lab HNS 204), Wed: 11-12:30 and 4-6, Thu : research day, Fri : 4:30-6:30 (office/computer lab HNS 204)

I am available at other times by appointment.

email: lkaganovskiy@ncf.edu - best way to ask a question. Also if you need me ASAP: (941) 366-6134; (941) 961-3896

Book: I will follow a set of Lecture Notes due to Prof L. Trigwasson and H. Im.

Books for reference

Title:	Computational Fluid Mechanics and Heat Transfer
ISBN:	156032046X
Publisher:	Taylor francis (UK)
Author(s):	John C Tannehill, Dale A Anderson, Richard H Pletcher

Charles Hirsch, Publisher: Wiley. Volume I, II

Numerical Computation of Internal and External Flows, Computational Methods for Inviscid and Viscous Flows

Course Goals and Objectives:

Computational Fluid Mechanics

This course is an interdisciplinary introduction to Computational Fluid Mechanics. The course focuses on Physical and Mathematical foundations of computational fluid mechanics with emphasis on applications. We will consider solution methods for model equations and the Euler and the Navier-Stokes equations; the finite volume formulation of the equations; classification of partial differential equations and solution techniques; truncation errors, stability, conservation, and monotonicity. The main programming language is Matlab. The work required of students includes approximately biweekly homework and substantial programming projects which counts 60% of the grade. The other 40% comes from two tests.

Minimal Prerequisites: The course is at the intermediate - sophomore/junior level. It should be accessible for the students in Science and Mathematics majors. The specific prerequisites are Calculus and Differential Equations;

Programming Language: The predominant programming languages used in numerical analysis are Fortran and MATLAB. In this course we will focus on Matlab. Many numerical analysis programs in Matlab will be provided. For students unacquainted with MATLAB, a short introduction is available from the following sources: Matlab Tutorial Brief, Matlab Primer (more comprehensive, but longer), Matlab Intro Plotting, Matlab Tutorial MIT, or just Google it.

A student version of MATLAB can be obtained from the company Mathworks, Inc. at a somewhat reduced price (>100$). This student version is essentially the full version, without some special add-on toolboxes. Matlab is available at the second floor Physics Computer Lab. Programs in languages other than Fortran and Matlab are also sometimes acceptable, but no programming assistance will be given in the use of such languages.

Grading Policy: The final grade will be based on tests and problems, as follows:

There will be two exams, and each will count 20% of the course grade.

1^st exam – 1 week before Spring break, Final – exam week. Exact dates and times will be announced in class.

Homework assignments and projects will count 60% of the course grade. Late homework will be accepted only by special permission of the instructor.

Attendance Policy:

There are no specific attendance credit points, but you are responsible for attending all the classes and keeping abreast of all the material presented in class.

Special Need Students:

Students with the need for special accommodations must work with the Counseling and Wellness Center, which will establish the specific accommodations and communicate them to me.

Academic Dishonesty Policy:

Any suspected instance of plagiarism will be reported to the office of the Provost and handled in accordance with the College’s policy.

Topics to be covered and Homework Assigned (exact due dates will be announced in class).

This course plan may be modified during the semester. Such modifications will be announced in advance during class periods, and the students are responsible for keeping abreast of such changes. The WWW page for the course will also be used to list assignments and other notes, and students are responsible for checking this web page regularly.

HW1 - due Mar 1

HW2 - due Mar 19

HW3 - due Apr 10

HW4 - due May 12

For HW4 we need two additional programs: Laplace equation and Heat. I will distribute them in class.

Finite difference approximations for ODEs

Finite difference approximations for PDEs, advection-diffusion equations, stability

Advection-Diffusion Movie: Exact Solution, Numerical Solution, Numerical Unstable

Review of Fluid Dynamics, Navier-Stokes equations

Vorticity-streamfunction formulation

Velocity-pressure formulation, MAC grid

Finite Volume formulation