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计算流体力学(CFD)领域,基本理论,数值方法,典型应用
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CFD经典读物之一。该教材涵盖了本科生、研究生所需学习的基本知识,内容丰富,其中所使用的应用均为开源软件,适合从事CFD相关领域的初学者、开发者阅读。 主要内容包括: 1.理论推导 2.数值计算方法 3.典型应用场景
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An Open Source Approach
Brian C. Vermeire
Carlos A. Pereira
Hamidreza Karbasian
Fluid Dynamics
Computational
![](https://csdnimg.cn/release/download_crawler_static/89077540/bg2.jpg)
An Open Source Approach
Fluid Dynamics
Computational
![](https://csdnimg.cn/release/download_crawler_static/89077540/bg3.jpg)
Copyright
c
2020 Brian C. Vermeire
PUBLISHED BY CONCORDIA UNIVERSITY
BOOK-WEBSITE.COM
Licensed under the Creative Commons Attribution-NonCommercial 3.0 Unported License (the
“License”). You may not use this file except in compliance with the License. You may obtain
a copy of the License at
http://creativecommons.org/licenses/by-nc/3.0
. Un-
less required by applicable law or agreed to in writing, software distributed under the License is
distributed on an “AS IS” BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either
express or implied. See the License for the specific language governing permissions and limitations
under the License.
First printing, October 2020
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Foreword
This book evolved out of my lecture notes for the undergraduate and graduate computational fluid
dynamics courses that I teach at Concordia University. In combination with an open-educational
resources grant from the library, it is provided to you completely free of charge. It uses entirely
open-source tools including Python, Jupyter Notebooks, SU2, Gmsh, Paraview, L
A
T
E
X, and many
others. This means that all of the examples and applications can be run on your computer using any
common operating system and without purchasing any licenses - CFD for free!
The book itself is even open-source, available as a public repository on Gitlab. As such, you
may want to think of this book more as a software development project, rather than a conventional
hard cover textbook. All of the content needed to run the chapter examples and final applications
are stored in the repository, and you can even contribute to the book and its examples via a pull
request if you think of a useful addition. Just like any software development project, this book may
contain a few “bugs”, mostly in the form of minor typos. If you find one of these please feel free to
give back and submit a pull request to correct them.
In terms of content, the book is designed with enough material to cover an advanced under-
graduate course, or an introductory course for graduate students. For an undergraduate course I
recommend a more hands-on computer lab experience, focusing on Part 1, some of Part 2, and Part
3. In Part 2 I find it useful to cover finite difference methods, consistency, stability, convergence,
time stepping, iterative methods, and then return to introduce finite volume methods. Part 3 is
designed as a bi-weekly computer lab, where students get hands-on experience with practical CFD
simulations. For a graduate course I recommend focusing on Parts 1 and 2, with a final project to
write a two-dimensional compressible solver for lid driven cavity flow. If you are studying CFD on
your own then I recommend covering the whole book.
Finally, I would like to thank my undergraduate and graduate students over the years for
their useful discussions and contributions to the core ideas in this book. In particular, I need to
acknowledge my co-authors Carlos and Hamid for their hard work in developing the first version. I
also thank the students in my classes for using the first “experimental” editions and their useful
feedback. Finally, I would like to thank you the reader for your interest in this project and for
learning CFD.
Dr. Brian C. Vermeire
![](https://csdnimg.cn/release/download_crawler_static/89077540/bg5.jpg)
Contents
I
Part 1: Physics
1 Conservation Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.1 Reynolds Transport Theorem 13
2 The Navier Stokes Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1 Integral Form 15
2.1.1 Conservation of Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1.2 Conservation of Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1.3 Conservation of Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.1.4 Compact Integral Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2 Divergence Form 18
2.2.1 Conservation of Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.2 Conservation of Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.3 Conservation of Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2.4 Compact Divergence Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3 Simplified Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.1 Euler Equations 21
3.2 Linear Advection 21
3.3 Burgers Equation 22
3.4 Linear Diffusion 23
3.5 PDE Classification 25
3.5.1 First Order Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.5.2 Second Order Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
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