Finite Volume

Don’t just review the notes to answer these questions, literally write the answers down on paper, as if you were taking a quiz.

  • A finite difference method uses a grid of points. What is used in a finite volume method?
  • The finite difference method works with a differential conservation law (PDE). What does the finite volume method work with?
  • What are three equivalent approaches for obtaining the governing transport equation for a finite volume method?
  • T/F: in a finite volume method we work directly with fluxes, rather than substitute fluxes into the governing equation and discritizing the result.
    • (Rather than answer this as a T/F question, see if you can turn it around, like, how does a finite volume method differ from a finite difference method in terms of the treatment of fluxes?)
  • What is the main advantage of formulating problems in terms of fluxes and finite volumes?
  • T/F: we still use finite difference approximations to evaluate the fluxes themselves?
  • What are the assumptions we make regarding the variations of quantities within a volume and along a face?
  • What is the difference between Practice A and Practice B?
    • Which is more accurate for evaluating fluxes?
    • Which is more accurate for evaluating source terms?
    • Which naturally includes a grid point on the boundary?
    • Which naturally includes a full cell in contact with the boundary?