Post on 11-Jan-2016
description
ME614: COMPUTATIONAL FLUID DYNAMICS
Fall 2015, MWF 2:30 pm - 3:20 pm, ME2053
Instructor
Dr. Carlo ScaloAssistant Professor of Mechanical EngineeringRoom ME2195, ME BuildingWest Lafayette, IN 47907-2045Work: 765-496-0214, Mobile: 650-739-9506Email: scalo@purdue.eduOffice Hours: by appointmentTeaching Assistant: Mr. Kukjin Kim, kim1625@purdue.edu
Prerequisites
Prerequisites for the course include basic knowledge of fluid mechanics, linear algebra, partial differential equations andaverage programming skills. The use of Python is strongly recommended but not mandatory. The class content is structuredin such a way to allow talented undergraduate students to successfully complete the coursework.
Course Objectives
The course will cover traditional aspects of Computational Fluid Dynamics (CFD) while providing exposure to the latestgeneration of high-level dynamic languages and version-control software. The course will cover the following topics:
1. Spatial & Temporal Discretizations2. Linear Advection & Diffusion Equation3. Poisson and Heat Equations4. Navier-Stokes Solvers
with a focus on incompressible flow and turbulent simulations. Students will be expected to write their own completeNavier-Stokes solver from scratch as a final project.
Sample mesh (left) and flow visualization (right) from a transonic turbulent calculation of the flow around aMcDonnell-Douglas 30P/30N multi-body airfoil. Courtesy of Prof. Julien Bodart (Universite de Toulouse, ISAE, France)
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Grade Distribution
Homework assignments and final reports turned in LATEX and/or with supporting images generated in vector graphics arestrongly encouraged (points will be detracted from messy reports, with unclear figures and text). The grade distribution is:
• (5%) Homework 0: Computing Environment Setup• (25%) Homework 1: Spatial Discretization• (25%) Homework 2: Linear Advection & Diffusion Equation• (25%) Homework 3: First Incompressible Navier-Stokes Solver• (20%) Final Project
Examples of source code will be provided in Python only. The use of Python is strongly recommended but not mandatory.Collaboration on the homework assignment is encouraged but submissions need to be individual. Note that it is trivial tocheck whether parts of source code have been copied.
Textbooks
With the exception of programming tutorials, all of the lecture material will be explained at the blackboard to facilitate adynamic discussion. Some of the course material will be based on selected pages from the following textbooks:
• Ferziger, J., and M. Peric, Computational Methods for Fluid Dynamics, Third Edition, Springer, 2001• Pletcher, R. H., Tannehill, J. C., and Anderson, D., Computational Fluid Mechanics and Heat Transfer, Third Edition,
CRC Press, 2011.• R. Leveque, Finite Volume Methods For Hyperbolic Problems, Cambridge, 2004• Lloyd N. Trefethen, Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations, unpublished
text, 1996, available at http://people.maths.ox.ac.uk/trefethen/pdetext.htmlThe first two will be the main reference textbooks for the course. The last two cover more theoretical and advanced topics.
Tentative Schedule
A tentative schedule is included below. The instructor reserves the right to (frequently) update it.
Monday Wednesday Friday
Aug 24th Lecture 1
Introduction• Course Structure Overview• Homework 0:
Python, Linux, Git
26th Lecture 2
Principles of Discretization• Discrete Operators• Matrix Multiplication
Reading: review linear algebra (matrixmultiplications, eigenvalues, ...)
28th Lecture 3
Spatial Discretization• Polynomial Fitting• Taylor Expansion
Reading: review linear algebra;Pletcher, et al. (2011) pp. 43 – 75;Ferziger & Peric (2001) pp. 21 – 52.
31st Lecture 4
Spatial Discretization• Pade Approximants• Modified Wavenumber
Reading:Ferziger & Peric (2001) pp. 45 – 63;
Sep 2nd Lecture 5
Homework 0 Due
Spatial Discretization• Pade Approximants (cont’d)• Homework 1 overview
Reading:Ferziger & Peric (2001) pp. 45 – 63;
4th Lecture 6
Spatial Discretization• Python Session:
Homework 1 Starter
Reading:Python Tutorial, Sections 2,3,4, and 5
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Monday Wednesday Friday7th
LABOR DAY
9th Lecture 7
Spatial Discretization• Grid Transformations (1D)• Boundary Conditions:
periodic vs non-periodic
Reading:Pletcher et al. (2011) pp. 329 – 337;Ferziger & Peric (2001) pp. 47 – 58;
11th Lecture 8
Temporal Discretization• Explicit Euler & Upwind• Modified Equation
Reading:Pletcher et al. (2011) pp. 103 – 124;
14th Lecture 9
Spatial Discretization• Python Session:
“Best Practices in Python”
Reading:Python Tutorial, Sections 6,7 and 8
16th
NO CLASS
18th
NO CLASS
21st Lecture 10
Temporal Discretization• Fourier/Von Neumann Analysis• Implicit Euler, MacCormack,
Adams-Bashforth, Leap Frog,Crank-Nicholson
Reading:Pletcher et al. (2011) pp. 82– 95
23rd Lecture 11
Homework 1 Due
Temporal Discretization• Runge-Kutta schemes
Reading:Handouts, Chapter 4Pletcher et al. (2011) pp. 124 – 125
25th Lecture 12
Temporal Discretization• σ-roots
Reading:Handouts, Chapter 4
28th Lecture 13
Linear Advection & Diffusion• Homework 2 overview
30th Lecture 14
Linear Advection & Diffusion• Python Session:
Homework 2 Starter
Oct 2nd Lecture 15
Poisson and Heat Equations• 2D spatial operators (DivGrad
operator)• Direct Methods
Reading:Pletcher et al. (2011) pp. 147 –152
5th Lecture 16
Linear Systems of Equations• Iterative Methods: Jacobi,
Gauss-Seidel, Line Relaxation
Reading:Handouts, Chapter 3Pletcher et al. (2011) pp. 152 – 162
7th Lecture 17
Linear Systems of Equations• Iterative Methods:
Over-Relaxation, ADI,Multi-Grid
Reading:Handouts, Chapter 3Pletcher et al. (2011) pp. 152 – 162
9th Lecture 18
Linear Systems of Equations• Iterative Methods: Multi-Grid
(cont’d), Conjugate Gradient
Reading:Handouts, Chapter 3Pletcher et al. (2011) pp. 166 – 175
12th
October Break
14th Lecture 19
Poisson and Heat Equations• Homework 3 overview (Part I)• Python Session: 2D
arrays/operators, fast indexing,Homework 3 Starter
16th Lecture 20
Homework 2 Due
Poisson and Heat Equations• Python Session
(cont’d)
19th Lecture 21
Navier-Stokes Solvers• A traumatic introduction to the
incompressible Navier-Stokes(MoureauBP JCP 2007) insteadof Ham JCP 2002
21st Lecture 22
Navier-Stokes Solvers• Incompressible Navier-Stokes
equations: conservative vsnon-conservative form,Lagrangian derivative
23rd Lecture 23
Navier-Stokes Solvers• Finite-Volume Approach,
Staggered Variable Collocation
Reading: Harlow & Welch (1965)
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Monday Wednesday Friday26th
NO CLASS
28th
NO CLASS
30th Lecture 24
Navier-Stokes Solvers• Projection Method: Fractional
Step Method
Reading:Chorin (1969), Kim & Moin (1985)
Nov 2nd Lecture 25
Navier-Stokes Solvers• Algebraic Pressure Segregation
4th Lecture 26
Navier-Stokes Solvers• Semi-Implicit Methods• suggested 2nd-order
discretization foradvection/diffusion terms
6th Lecture 27
Navier-Stokes Solvers• Semi-Implicit Time
Advancement, prediction step:Explicit-Euler, Runge-Kutta
9th Lecture 28
Homework 3 Due
Navier-Stokes Solvers• Kinetic energy conservation
properties of the incompressibleNavier-Stokes equations
11th Lecture 29
Navier-Stokes Solvers• Discrete kinetic energy
conservation, review of Ham,et al. (2002)
13th Lecture 30
Navier-Stokes Solvers• Homework 3 tutorial
16th Lecture 31
Navier-Stokes Solvers• Vorticity-Streamfunction
(Ψ − ω) formulation (in 2D)
18th Lecture 32
Navier-Stokes Solvers• Boundary conditions in Ψ − ω:
solenoidal condition
20th Lecture 33
Navier-Stokes Solvers• Boundary conditions for
velocity-pressure formulation• Mass conservation in boundary
layers
Reading: : Orlanski (1976),Piomelli & Scalo (2010)
23rd
NO CLASS
25th Lecture 34
Navier-Stokes Solvers• Discussion of Final Project
27th Lecture 35
Navier-Stokes Solvers• Pseudo-spectral methods:
introduction to DFT
Reading: : Pope (2000), Section 6.4;Ferziger & Peric (2001), Section 3.10
30th Lecture 36
Navier-Stokes Solvers• Pseudo-spectral methods
(cont’d)• De-aliasing
Dec 2nd Lecture 37
Navier-Stokes Solvers• Python Session: Advection
diffusion equation and Poissonequation with FFT
4th Lecture 38
Navier-Stokes Solvers• Final Project:
office hours (2:00 - 3:30 pm)
7th Lecture 39
Navier-Stokes Solvers• Final Project:
office hours (2:00 - 3:30 pm)
9th Lecture 40
Navier-Stokes Solvers• Final Project:
office hours (2:00 - 3:30 pm)
11th Lecture 41
Final Project Due
Grades Due:December 22
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References
A. J. Chorin (1969). ‘On the convergence of discrete approximations to the Navier-Stokes equations’. Math. Comp. 23:341– 353.
J. Ferziger & M. Peric (2001). Computational Methods for Fluid Dynamics. Springer.
F. Ham, et al. (2002). ‘A fully conservative second-order finite difference scheme for incompressible flow on nonuniform grids’.J. Comput. Physics 177(1):117–133.
Harlow & Welch (1965). ‘Numerical calculation of time-dependent viscous incompressible flow of fluid with free surfaces’8(21).
J. Kim & P. Moin (1985). ‘Application of a Fractional-Step Method to Incompressible Navier-Stokes Equations’. J. Comput.Phys. 59:308 – 323.
I. Orlanski (1976). Journal of Computational Physics 21:251 – 269.
U. Piomelli & C. Scalo (2010). ‘Subgrid-scale modelling in relaminarizing flows’. Fluid Dynamics Research 42(4):045510.
R. H. Pletcher, et al. (2011). Computational Fluid Mechanics and Heat Transfer. CRC Press.
S. Pope (2000). Turbulent flows. Cambridge Univ Pr.
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