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Use En dash throughout for Navier–Stokes
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gforsyth committed Jul 11, 2018
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2 changes: 1 addition & 1 deletion lessons/00_Quick_Python_Intro.ipynb
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"cell_type": "markdown",
"metadata": {},
"source": [
"Hello! This is a quick intro to programming in Python to help you hit the ground running with the _12 Steps to Navier-Stokes_. \n",
"Hello! This is a quick intro to programming in Python to help you hit the ground running with the _12 Steps to NavierStokes_. \n",
"\n",
"There are two ways to enjoy these lessons with Python:\n",
"\n",
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6 changes: 3 additions & 3 deletions lessons/01_Step_1.ipynb
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"cell_type": "markdown",
"metadata": {},
"source": [
"12 steps to Navier-Stokes\n",
"12 steps to NavierStokes\n",
"======\n",
"***"
]
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"cell_type": "markdown",
"metadata": {},
"source": [
"Hello! Welcome to the **12 steps to Navier-Stokes**. This is a practical module that is used in the beginning of an interactive Computational Fluid Dynamics (CFD) course taught by [Prof. Lorena Barba](http://lorenabarba.com) since Spring 2009 at Boston University. The course assumes only basic programming knowledge (in any language) and of course some foundation in partial differential equations and fluid mechanics. The practical module was inspired by the ideas of Dr. Rio Yokota, who was a post-doc in Barba's lab, and has been refined by Prof. Barba and her students over several semesters teaching the course. The course is taught entirely using Python and students who don't know Python just learn as we work through the module.\n",
"Hello! Welcome to the **12 steps to NavierStokes**. This is a practical module that is used in the beginning of an interactive Computational Fluid Dynamics (CFD) course taught by [Prof. Lorena Barba](http://lorenabarba.com) since Spring 2009 at Boston University. The course assumes only basic programming knowledge (in any language) and of course some foundation in partial differential equations and fluid mechanics. The practical module was inspired by the ideas of Dr. Rio Yokota, who was a post-doc in Barba's lab, and has been refined by Prof. Barba and her students over several semesters teaching the course. The course is taught entirely using Python and students who don't know Python just learn as we work through the module.\n",
"\n",
"This [Jupyter notebook](https://jupyter-notebook.readthedocs.io/en/stable/) will lead you through the first step of programming your own Navier-Stokes solver in Python from the ground up. We're going to dive right in. Don't worry if you don't understand everything that's happening at first, we'll cover it in detail as we move forward and you can support your learning with the videos of [Prof. Barba's lectures on YouTube](http://www.youtube.com/playlist?list=PL30F4C5ABCE62CB61).\n",
"This [Jupyter notebook](https://jupyter-notebook.readthedocs.io/en/stable/) will lead you through the first step of programming your own NavierStokes solver in Python from the ground up. We're going to dive right in. Don't worry if you don't understand everything that's happening at first, we'll cover it in detail as we move forward and you can support your learning with the videos of [Prof. Barba's lectures on YouTube](http://www.youtube.com/playlist?list=PL30F4C5ABCE62CB61).\n",
"\n",
"For best results, after you follow this notebook, prepare your own code for Step 1, either as a Python script or in a clean Jupyter notebook.\n",
"\n",
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4 changes: 2 additions & 2 deletions lessons/02_Step_2.ipynb
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"cell_type": "markdown",
"metadata": {},
"source": [
"12 steps to Navier-Stokes\n",
"12 steps to NavierStokes\n",
"======\n",
"***"
]
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"cell_type": "markdown",
"metadata": {},
"source": [
"This IPython notebook continues the presentation of the **12 steps to Navier-Stokes**, the practical module taught in the interactive CFD class of [Prof. Lorena Barba](http://lorenabarba.com). You should have completed [Step 1](./01_Step_1.ipynb) before continuing, having written your own Python script or notebook and having experimented with varying the parameters of the discretization and observing what happens.\n"
"This IPython notebook continues the presentation of the **12 steps to NavierStokes**, the practical module taught in the interactive CFD class of [Prof. Lorena Barba](http://lorenabarba.com). You should have completed [Step 1](./01_Step_1.ipynb) before continuing, having written your own Python script or notebook and having experimented with varying the parameters of the discretization and observing what happens.\n"
]
},
{
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2 changes: 1 addition & 1 deletion lessons/03_CFL_Condition.ipynb
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"cell_type": "markdown",
"metadata": {},
"source": [
"12 steps to Navier-Stokes\n",
"12 steps to NavierStokes\n",
"=====\n",
"***"
]
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4 changes: 2 additions & 2 deletions lessons/04_Step_3.ipynb
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"cell_type": "markdown",
"metadata": {},
"source": [
"12 steps to Navier-Stokes\n",
"12 steps to NavierStokes\n",
"======\n",
"***"
]
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"cell_type": "markdown",
"metadata": {},
"source": [
"You should have completed Steps [1](./01_Step_1.ipynb) and [2](./02_Step_2.ipynb) before continuing. This IPython notebook continues the presentation of the **12 steps to Navier-Stokes**, the practical module taught in the interactive CFD class of [Prof. Lorena Barba](http://lorenabarba.com). "
"You should have completed Steps [1](./01_Step_1.ipynb) and [2](./02_Step_2.ipynb) before continuing. This IPython notebook continues the presentation of the **12 steps to NavierStokes**, the practical module taught in the interactive CFD class of [Prof. Lorena Barba](http://lorenabarba.com). "
]
},
{
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4 changes: 2 additions & 2 deletions lessons/05_Step_4.ipynb
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"cell_type": "markdown",
"metadata": {},
"source": [
"12 steps to Navier-Stokes\n",
"12 steps to NavierStokes\n",
"=====\n",
"***"
]
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"cell_type": "markdown",
"metadata": {},
"source": [
"We continue our journey to solve the Navier-Stokes equation with Step 4. But don't continue unless you have completed the previous steps! In fact, this next step will be a combination of the two previous ones. The wonders of *code reuse*!"
"We continue our journey to solve the NavierStokes equation with Step 4. But don't continue unless you have completed the previous steps! In fact, this next step will be a combination of the two previous ones. The wonders of *code reuse*!"
]
},
{
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4 changes: 2 additions & 2 deletions lessons/06_Array_Operations_with_NumPy.ipynb
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"cell_type": "markdown",
"metadata": {},
"source": [
"12 steps to Navier-Stokes\n",
"12 steps to NavierStokes\n",
"=====\n",
"***"
]
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"cell_type": "markdown",
"metadata": {},
"source": [
"This lesson complements the first interactive module of the online [CFD Python](https://github.com/barbagroup/CFDPython) class, by Prof. Lorena A. Barba, called **12 Steps to Navier-Stokes.** It was written with BU graduate student Gilbert Forsyth."
"This lesson complements the first interactive module of the online [CFD Python](https://github.com/barbagroup/CFDPython) class, by Prof. Lorena A. Barba, called **12 Steps to NavierStokes.** It was written with BU graduate student Gilbert Forsyth."
]
},
{
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2 changes: 1 addition & 1 deletion lessons/07_Step_5.ipynb
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"cell_type": "markdown",
"metadata": {},
"source": [
"12 steps to Navier-Stokes\n",
"12 steps to NavierStokes\n",
"=====\n",
"***"
]
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2 changes: 1 addition & 1 deletion lessons/08_Step_6.ipynb
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"cell_type": "markdown",
"metadata": {},
"source": [
"12 steps to Navier-Stokes\n",
"12 steps to NavierStokes\n",
"=====\n",
"***"
]
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2 changes: 1 addition & 1 deletion lessons/09_Step_7.ipynb
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"cell_type": "markdown",
"metadata": {},
"source": [
"12 steps to Navier-Stokes\n",
"12 steps to NavierStokes\n",
"=====\n",
"***"
]
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2 changes: 1 addition & 1 deletion lessons/10_Step_8.ipynb
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"cell_type": "markdown",
"metadata": {},
"source": [
"12 steps to Navier-Stokes\n",
"12 steps to NavierStokes\n",
"=====\n",
"***"
]
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6 changes: 3 additions & 3 deletions lessons/11_Defining_Function_in_Python.ipynb
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"cell_type": "markdown",
"metadata": {},
"source": [
"12 steps to Navier-Stokes\n",
"12 steps to NavierStokes\n",
"=====\n",
"***"
]
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"cell_type": "markdown",
"metadata": {},
"source": [
"This lesson complements the first interactive module of the online [CFD Python](https://github.com/barbagroup/CFDPython) class, by Prof. Lorena A. Barba, called **12 Steps to Navier-Stokes.** The interactive module starts with simple exercises in 1D that at first use little of the power of Python. We now present some new ways of doing the same things that are more efficient and produce prettier code.\n",
"This lesson complements the first interactive module of the online [CFD Python](https://github.com/barbagroup/CFDPython) class, by Prof. Lorena A. Barba, called **12 Steps to NavierStokes.** The interactive module starts with simple exercises in 1D that at first use little of the power of Python. We now present some new ways of doing the same things that are more efficient and produce prettier code.\n",
"\n",
"This lesson was written with BU graduate student Gilbert Forsyth.\n"
]
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"\n",
"Well, there are a few more ways to make your scientific codes in Python run faster. We recommend the article on the Technical Discovery blog about [Speeding Up Python](http://technicaldiscovery.blogspot.com/2011/06/speeding-up-python-numpy-cython-and.html) (June 20, 2011), which talks about NumPy, Cython and Weave. It uses as example the Laplace equation (which we will solve in [Step 9](./12_Step_9.ipynb)) and makes neat use of defined functions.\n",
"\n",
"But a recent new way to get fast Python codes is [Numba](http://numba.pydata.org). We'll learn a bit about that after we finish the **12 steps to Navier-Stokes**.\n",
"But a recent new way to get fast Python codes is [Numba](http://numba.pydata.org). We'll learn a bit about that after we finish the **12 steps to NavierStokes**.\n",
"\n",
"There are many exciting things happening in the world of high-performance Python right now!\n",
"\n",
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4 changes: 2 additions & 2 deletions lessons/12_Step_9.ipynb
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"cell_type": "markdown",
"metadata": {},
"source": [
"12 steps to Navier-Stokes\n",
"12 steps to NavierStokes\n",
"=====\n",
"***"
]
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"cell_type": "markdown",
"metadata": {},
"source": [
"In the previous step, we solved the [2D Burgers' equation](./10_Step_8.ipynb): an important equation in the study of fluid mechanics because it contains the full convective nonlinearity of the flow equations. With that exercise, we also build the experience to incrementatlly code a Navier-Stokes solver.\n",
"In the previous step, we solved the [2D Burgers' equation](./10_Step_8.ipynb): an important equation in the study of fluid mechanics because it contains the full convective nonlinearity of the flow equations. With that exercise, we also build the experience to incrementatlly code a NavierStokes solver.\n",
"\n",
"In the next two steps, we will solve Laplace and then Poisson equation. We will then put it all together!"
]
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4 changes: 2 additions & 2 deletions lessons/13_Step_10.ipynb
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"cell_type": "markdown",
"metadata": {},
"source": [
"12 steps to Navier-Stokes\n",
"12 steps to NavierStokes\n",
"=====\n",
"***"
]
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"cell_type": "markdown",
"metadata": {},
"source": [
"For a moment, recall the Navier-Stokes equations for an incompressible fluid, where $\\vec{v}$ represents the velocity field:\n",
"For a moment, recall the NavierStokes equations for an incompressible fluid, where $\\vec{v}$ represents the velocity field:\n",
"\n",
"\\begin{eqnarray}\n",
"\\nabla \\cdot\\vec{v} &=& 0\\\\\\\n",
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8 changes: 4 additions & 4 deletions lessons/14_Step_11.ipynb
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"cell_type": "markdown",
"metadata": {},
"source": [
"12 steps to Navier-Stokes\n",
"12 steps to NavierStokes\n",
"=====\n",
"***"
]
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"cell_type": "markdown",
"metadata": {},
"source": [
"The final two steps in this interactive module teaching beginning [CFD with Python](https://bitbucket.org/cfdpython/cfd-python-class) will both solve the Navier-Stokes equations in two dimensions, but with different boundary conditions.\n",
"The final two steps in this interactive module teaching beginning [CFD with Python](https://bitbucket.org/cfdpython/cfd-python-class) will both solve the NavierStokes equations in two dimensions, but with different boundary conditions.\n",
"\n",
"The momentum equation in vector form for a velocity field $\\vec{v}$ is:\n",
"\n",
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"cell_type": "markdown",
"metadata": {},
"source": [
"Step 11: Cavity Flow with Navier-Stokes\n",
"Step 11: Cavity Flow with NavierStokes\n",
"----\n",
"***"
]
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"cell_type": "markdown",
"metadata": {},
"source": [
"The interactive module **12 steps to Navier-Stokes** is one of several components of the Computational Fluid Dynamics class taught by Prof. Lorena A. Barba in Boston University between 2009 and 2013. \n",
"The interactive module **12 steps to NavierStokes** is one of several components of the Computational Fluid Dynamics class taught by Prof. Lorena A. Barba in Boston University between 2009 and 2013. \n",
"\n",
"For a sample of what the other components of this class are, you can explore the **Resources** section of the Spring 2013 version of [the course's Piazza site](https://piazza.com/bu/spring2013/me702/resources).\n",
"\n",
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10 changes: 5 additions & 5 deletions lessons/15_Step_12.ipynb
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"cell_type": "markdown",
"metadata": {},
"source": [
"12 steps to Navier-Stokes\n",
"12 steps to NavierStokes\n",
"=====\n",
"***"
]
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"cell_type": "markdown",
"metadata": {},
"source": [
"Did you make it this far? This is the last step! How long did it take you to write your own Navier-Stokes solver in Python following this interactive module? Let us know!"
"Did you make it this far? This is the last step! How long did it take you to write your own NavierStokes solver in Python following this interactive module? Let us know!"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Step 12: Channel Flow with Navier-Stokes\n",
"Step 12: Channel Flow with NavierStokes\n",
"----\n",
"***"
]
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"cell_type": "markdown",
"metadata": {},
"source": [
"The only difference between this final step and Step 11 is that we are going to add a source term to the $u$-momentum equation, to mimic the effect of a pressure-driven channel flow. Here are our modified Navier-Stokes equations:"
"The only difference between this final step and Step 11 is that we are going to add a source term to the $u$-momentum equation, to mimic the effect of a pressure-driven channel flow. Here are our modified NavierStokes equations:"
]
},
{
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"cell_type": "markdown",
"metadata": {},
"source": [
"The interactive module **12 steps to Navier-Stokes** is one of several components of the Computational Fluid Dynamics class taught by Prof. Lorena A. Barba in Boston University between 2009 and 2013. \n",
"The interactive module **12 steps to NavierStokes** is one of several components of the Computational Fluid Dynamics class taught by Prof. Lorena A. Barba in Boston University between 2009 and 2013. \n",
"\n",
"For a sample of what the othe components of this class are, you can explore the **Resources** section of the Spring 2013 version of [the course's Piazza site](https://piazza.com/bu/spring2013/me702/resources).\n",
"\n",
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