Computational Turbulent Reacting Flow

330T Engineering Building
Brigham Young University
Provo, UT 84602
801-422-1772
davidlignell@byu.edu

Parabolic Partial Differential Equations


  • Write the canonical parabolic PDE, the unsteady 1D diffusion equation
  • What ODE method is FTCS similar to?
  • What ODE method is BTCS similar to?
  • What ODE method is Crank Nicholson (CN) similar to?
  • What are the time and space discretization orders of FTCS, BTCS, and CN?
  • Consider the stencils for the methods discussed.
    • What do these imply about the domain coupling and rate of propagation of information?
    • How would this change if you used a higher order stencil?
  • Why is the method of lines called that?
  • True or False: the treatment of boundary conditions for simple PDEs is basically the same as for ODE BVPs.
  • Consider how index arrays can be used to good effect in Python (or Julia) to simplify the implementation and avoid loops (which are costly in Python).