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Nodal Method?

  1. Sep 19, 2008 #1
    Nodal Method??

    What's the benefit of using Nodal method instead of finite difference method in solving a diffusion problem?
  2. jcsd
  3. Sep 19, 2008 #2


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    Staff: Mentor

    Re: Nodal Method??

    Do you mean finite element method?

    IIRC, it has to do with the representation of the boundary conditions.

    I believe FEM can uses larger cells (elements), and therefore would be more computationally efficient.

    I learned the difference 25 years ago when part of the course work was develop FD / FE methods for diffusion, fluid flow and heat transfer. Back then, available computers were severely memory limited, and the emphasis was on computational efficiency (both in terms of memory and time) and accuracy.
  4. Sep 19, 2008 #3
    Re: Nodal Method??

    FEM is mostly used for solving transport equation whereas barely used for diffusion equation.
    Nodal method was developed in 70s decade in order to evade the lack of memory of those time computers.

    I wanna know that in this era in which the super computers are solving the complicated mathematical problems in a few seconds, the use of nodal method is recommended or not.
  5. Oct 7, 2008 #4


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    Re: Nodal Method??


    As one of the co-developers [ along with Kord Smith ] of the "Analytic Nodal Method" at MIT; I can
    speak to your question.

    A nodal method reduces both the amount of storage and the computational work. There's no
    supercomputer today that is solving time-dependent transport or time-dependent diffusion in just
    a few seconds.

    In essence; both the finite difference method and the finite element method make very simple
    approximations to either the transport and / or diffusion equations. Because of that, one may be
    forced to use relatively fine mesh-spacing in order to capture the relavant physics.

    A nodal method makes use of a higher order approximation or a higher order discretization of the
    transport or diffusion equation. Because of that, one doesn't need as fine a resolution in order to
    get equivalent accuracy as the low order finite difference and finite element methods.

    Nobody has so much computer power that the difference isn't advantageous in favor of the nodal
    method. As long as one "homogenizes" fuel assemblies; which is almost universally done; there
    really isn't a reason NOT to use a nodal method. If one desires to find the peak "pin power" and
    consequent heat fluxes; a whole core calculation is done with homogenized assemblies in order
    to find the high power assemblies. One can then do a calculation on the high power assemblies
    with the geometry represented explicitly and surface currents from the nodal calculation used as
    boundary conditions.

    A good reference to the "Analytic Nodal Method" is Kord's Engineer's Thesis which describes the
    3-D implementation in the computer code, QUANDRY. It is available at:


    Dr. Gregory Greenman
  6. Oct 9, 2008 #5
    Re: Nodal Method??

    Dr. Gregory Greenman

    Thanks a lot for your information.
    I will study the Engineer's Thesis you mentioned.

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