Benefit of using Nodal method instead of finite difference method?

[libertad]

Nodal Method??

What's the benefit of using Nodal method instead of finite difference method in solving a diffusion problem?

 

[Astronuc]

What's the benefit of using Nodal method instead of finite difference method in solving a diffusion problem?

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.

 

[libertad]

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 want to 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.

 

[Morbius]

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 want to 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.

libertad,

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:

http://dspace.mit.edu/handle/1721.1/15979

Dr. Gregory Greenman
Physicist

 

[libertad]

Dr. Gregory Greenman

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

Regards,
Libertad