Getting Acquainted with the Python and FiPy: A Crash Course

1
Getting Acquainted with the Python and FiPy A
Crash Course

• R. Edwin García
• redwing_at_purdue.edu

2
Goal for Today

• An extremely brief xemacs overview
• A very simple python example
• Introduction to FiPy solving the diffusion
  equation in 25 (or less) lines of code

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The Interface xemacs
4
Setting Up xemacs Options
line numbers
highlight syntaxis
save options
5
Running Something Simple helloWorld.py

• this is a comment
• import math this is how you import modules
• num_items 10 this is an integer variable
• dx 0.1 this is a float (real) variable
• x 0 this is another float variable
• array this is an empty array
• next is a for loop
• for index in range(num_items)
• print "Hello World!" this is a print
  statement
• note that only indented things are part of
  the
• for loop
• x x dx this increases the value of x by
  dx
• array.append(x) this adds x to the list
• print "array", array this prints the list

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What is FiPy?

• Simply put
• Is a set of python libraries to solve PDEs
• In more detail
• Provides a numerical framework to solve for
  partial differential equations by using the
  finite volumes technique
• The emphasis is on microstructural evolution

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1D Diffusion The Big Picture
F(x, t0) 0
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Creating the Mesh

• import fipy imports fipy, a finite volumes set
  of libraries
• sometimes there are modules within modules and
  you can import them
• by typing
• from fipy.meshes import grid1D this imports
  the grid1D module from fipy
• you can define variables of any kind in
  python.
• For example, the mesh size
• mesh_size 50 this is an integer
• or the size of the domain
• length 1.0 this is a float (real) number
• or the size of the control volume
• deltax length/float(mesh_size) note that I
  just forced an integer to become float
• you can create an instance of a one
  dimensional mesh by typing
• mesh_example grid1D.Grid1D(nx mesh_size, dx
  deltax)

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Defining the Concentration Field

• create a field with initial values
• phi_o 0
• from fipy.variables.cellVariable import
  CellVariable
• phi CellVariable(name"solution variable",
  meshmesh_example, valuephi_o)

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Specifying Boundary Conditions

• Define boundary condition values
• leftValue 1.0
• rightValue 0
• Creation of boundary conditions
• from fipy.boundaryConditions.fixedValue import
  FixedValue
• BCs (FixedValue(faces mesh_example.getFacesRig
  ht(), valuerightValue),
• FixedValue(facesmesh_example.getFacesLeft(
  ),valueleftValue))

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Creating the Diffusion Equation
transient term

• D 1.0 diffusivity (m2/s)
• Transient diffusion equation is defined next
• from fipy.terms.explicitDiffusionTerm import
  ExplicitDiffusionTerm
• from fipy.terms.transientTerm import
  TransientTerm
• eqX TransientTerm() ExplicitDiffusionTerm(coe
  ff D)

diffusion term
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Specifying the Time Stepping of the Model

• timeStep 0.09deltax2/(2D) size of time
  step
• steps 9000 number of time-steps

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Creating a Viewer

• create a GUI
• from fipy import viewers
• viewer viewers.make(vars phi,
  limits'datamin'0.0, 'datamax'1.0)

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Looping Over Time

• iterate until you get tired
• for step in range(steps)
• eqX.solve(var phi, boundaryConditions
  BCs, dt timeStep) solving the equation
• viewer.plot() update the GUI

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Launching Our Simulation

• Save your script and assign a descriptive name,
  e.g., diffusion1D.py
• Type python diffusion1D.py in the command line
• You should get something like this

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Final Comments

• You can cancel your calculation by typing
  CTRL-C in the command line
• You can re-do this calculation and make it 2D by
  using a grid2D.Grid2D class instead