Finite Volumes Lab II: Cooking a Simulation from Scratch

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Finite Volumes Lab II Cooking a Simulation from
Scratch

• R. Edwin García
• redwing_at_purdue.edu

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One Dimensional Diffusion
F(x, t0) 0
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Working Scripts for Todays Class can be are
diffusionX.py
diffusionI.py
diffusionCN.py
(explicit)
(implicit)
(semi-implicit)
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A PDE is Solved in Four Steps

• Variables Definitions
• Equation(s) Definition(s)
• Boundary Condition Specification
• Viewer Creation
• Problem Solving

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A PDE is Solved in Four Steps

• Variables Definitions
• Equation(s) Definition(s)
• Boundary Condition Specification
• Viewer Creation
• Problem Solving

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Variables Definitions

• nx 50
• dx 1.0/float(nx)
• from fipy.meshes.grid1D import Grid1D
• mesh Grid1D(nx, dx)
• from fipy.variables.cellVariable import
  CellVariable
• phi CellVariable(name"solution variable",
  meshmesh, value0)
• D 1.0
• valueLeft 1
• valueRight 0
• timeStepDuration 0.9(dx)2/(2D)
• steps 900

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A PDE is Solved in Four Steps

• Variables Definitions
• Equation(s) Definition(s)
• Boundary Condition Specification
• Viewer Creation
• Problem Solving

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Equation Definition

• from fipy.terms.explicitDiffusionTerm import
  ExplicitDiffusionTerm
• from fipy.terms.transientTerm import
  TransientTerm
• eqX TransientTerm() ExplicitDiffusionTerm(coe
  ff D)

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Other Equation Terms
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A PDE is Solved in Four Steps

• Variables Definitions
• Equation(s) Definition(s)
• Boundary Condition Specification
• Viewer Creation
• Problem Solving

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Boundary Conditions

• from fipy.boundaryConditions.fixedValue import
  FixedValue
• BCs (FixedValue(faces mesh.getFacesRight(),
  valuevalueRight),
• FixedValue(facesmesh.getFacesLeft(),va
  luevalueLeft))

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Other Type of BCs
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A PDE is Solved in Four Steps

• Variables Definitions
• Equation(s) Definition(s)
• Boundary Condition Specification
• Viewer Creation
• Problem Solving

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Viewer Creation

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

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A PDE is Solved in Four Steps

• Variables Definitions
• Equation(s) Definition(s)
• Boundary Condition Specification
• Viewer Creation
• Problem Solving

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Solving the Problem

• for step in range(steps)
• eqX.solve(var phi, boundaryConditions
  BCs, dt timeStepDuration)
• viewer.plot()

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Launching the Simulation

• Save file under adequate name (extension must be
  .py)
• Run it by calling python from the command line.
• You can cancel your simulation by typing CTRL-C

short-cut CTRL-X CTRL-S
Example coolSimulation.py
Example python coolSimulation.py
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Fun Things to Try

• Try changing the boundary and initial conditions.
  
• Try changing the Amplification factor in the time
  step.
• Try replacing the ExplicitDiffusionTerm with an
  ImplicitDiffusionTerm

Example initialize the field to 0.5
Example set A1.1
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Three Exercises

• Run diffusionX.py with an amplification factor of
  0.9
• Run diffusionX.py with an amplification factor of
  1.0
• Run diffusionX.py with an amplification factor of
  1.1

(Explicit Method)
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Three More Exercises

• Run diffusionCN.py with an amplification factor
  of 1
• Run diffusionCN.py with an amplification factor
  of 10
• Run diffusionCN.py with an amplification factor
  of 100

(Semi-Implicit Method)
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Three Final Exercises

• Run diffusionI.py with an amplification factor of
  0.9
• Run diffusionI.py with an amplification factor of
  1.0
• Run diffusionI.py with an amplification factor of
  1.1
• Run diffusionI.py with an amplification factor of
  2, 5, 7, 10, 100,...

(Implicit Method)
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FiPy Resources

• FiPy Manual (tutorials and useful examples)
• FiPy Reference (what every single command does)
• Mailing List fipy_at_nist.gov
• You can also email
• John Guyer guyer_at_nist.gov
• Dan Wheeler daniel.wheeler_at_nist.gov
• FiPy Website http//www.ctcms.nist.gov/fipy/