Numerical Fluid Mechanics

As taught in: Spring 2007

Level:

Graduate

Instructors:

Prof. Henrik Schmidt

Course Features

Course Highlights

Course Description

Technical Requirements

A computer simulation of high velocity air flow around a space shuttle during re-entry. (Image courtesy of NASA.)

Course Features

• Selected lecture notes
• Assignments and solutions
• Exams and Solutions

Course Highlights

This course features complete lecture notes and course MATLAB® scripts on the lecture notes page.

Course Description

This course introduces students to MATLAB®. Numerical methods include number representation and errors, interpolation, differentiation, integration, systems of linear equations, and Fourier interpolation and transforms. Students will study partial and ordinary differential equations as well as elliptic and parabolic differential equations, and solutions by numerical integration, finite difference methods, finite element methods, boundary element methods, and panel methods.

Lecture Notes

This section contains documents created from scanned original files, which are inaccessible to screen reader software. A "#" symbol is used to denote such documents.

Special software is required to use some of the files in this section: .zip, and .m.

SES #	TOPICS	LECTURE NOTES	MATLAB® SCRIPTS
1	Introduction to numerical methods in engineering MATLAB® proficiency evaluation First day of classes	(PDF)	(ZIP) (The ZIP file contains: dudt.m, piv.m, and sph_drag_2.m.)
2	Number representations Errors of numerical operations Recursion	(PDF)	(ZIP) (The ZIP file contains: heron.m, horner.m, radd.m, recur.m, sbfj.m, sbfj_3.m, sbfj_f.m, sbfy.m, and tsbfj.m.)
3	Error analysis Error propagation Condition numbers	(PDF)
4	Roots of non-linear equations General/Bisection/Secant/Newton-Raphson methods	(PDF)	(ZIP) (The ZIP file contains: bisect.m, cube.m, div.m, heron.m, and sqr.m.)
5	Linear systems Gaussian elimination	(PDF)	(ZIP) (The ZIP file contains: tbt.m, tbt2.m,tbt3.m, and tbt4.m.)
6	Linear systems Multiple right-hand-sides LU factorization	(PDF)	(ZIP) (The ZIP file contains: tbt6.m, tbt7.m, and tbt8.m.)
7	Special matrices Examples	(PDF)	(ZIP) (The ZIP file contains: vib_string.m.)
8	Linear systems Iterative techniques Gauss-Seidel	(PDF - 1.0 MB) (Courtesy of Reza Karimi. Used with permission.)
9	Root finding and linear systems Examples and applications	(PDF) (Courtesy of Dr. Yuming Liu. Used with permission.)
10	Optimization Curve fitting	(PDF)	(ZIP) (The ZIP file contains: cost.m, curve.m, lstsq.m, and salesman.m.)
11	Interpolation Polynomial interpolation Lagrange polynomials Splines	(PDF)	(ZIP) (The ZIP file contains: interp_test.m, lagrange.m, newton.m, and newton_coef.m.)
12	Fourier interpolation Fourier transforms	(PDF)	(ZIP) (The ZIP file contains: tpcoef.m, tpeval.m, tptest.m, trig_poly.m, and ts.m.)
13	Quiz 1
14	Numerical integration Newton-Cotes Gaussian quadratutre	(PDF)
15	Numerical differentiation Finite differences Ordinary differential equations Initial value problems Euler's method	(PDF)	(ZIP) (The ZIP file contains: dudt.m, sph_drag_2.m, and sph_param.m.)
16	ODE-IVP Runge-Kutta methods	(PDF)	(ZIP) (The ZIP file contains: pcm.m, stiff.m, and stiff_imp.m.)
17	Higher order ODEs Boundary value problems	(PDF)	(ZIP) (The ZIP file contains: back_tri.m, dudy.m, forw_tri.m, lu_fact.m, lu_tri.m, plate_flow.m, and sou_flow.m.)
18	Partial differential equations Introduction Examples	(PDF)	(ZIP) (The ZIP file contains: waveeq.m and wavei.m.)
19	PDE review
20	PDEs Parabolic equations	(PDF)	(ZIP) (The ZIP file contains: back_tri.m, forw_tri.m, heat_cn.m, heat_cn_sin.m, heat_fw.m, heat_fw_2.m, and lu_tri.m.)
21	PDEs Elliptic equations	(PDF)	(ZIP) (The ZIP file contains: duct.m, duct_fs.m, duct_oil.m, and heat_plate.m.)
22	Finite element methods	(PDF)	(ZIP) (The ZIP file contains: duct_galerkin.m, and exp_eq.m.)
23	Boundary element methods Panel methods (1)	(PDF)# (Courtesy of Dr. Yuming Liu. Used with permission.)	(ZIP) (The ZIP file contains: cpm_main.m, cylinder_geom.m, gxy.m, inflcoef.m, localize.m, matrices.m, setbcs.m, and setpanels.m.)
24	Boundary element methods Panel methods (2)
25	Review	(PDF - 1.0 MB)
26	Quiz 2