Can anyone tell me the main areas of application for the finite difference, element and volume discretisation methods? I have information on the methods themselves, but typically under what conditions does one adopt each method?

Thanks in advance, JonS

finite difference is easy to implement and straighforwardly exentends to three-dimensional space and usually used in structure grids. Also easy to use multigrid methods as a solver.

finite element is good for irregular grid such as unstructured adaptive mesh methods.

Junseok

See previous discussion http://www.cfd-online.com/Forum/main...cgi?read=13743

all these methods are not satisfactory and outdated.

I will give them grade C.

use discontinuous epctral element method, which can have grade B+ or A-

Thanks, both!

JonS

I did not realize there existed a central and objective grading system for numerical discretisation methods, but I am very interested in hearing the background. Could you please point me to the references (peer-reviewed publications, book chapters, conference papers and similar) which contain the information on numerical methods you have tested, grading criteria, test cases, implementation details, robustness, performance (CPU time), accuracy, error convergence, mesh sensitivity examples of success/failure etc. on which you base this judgement. I am particularly interested in "real life" simulations, including complex 3-D geometries, coupled systems of PDEs describing complex physics and large mesh sizes.

Thanks,

Hrv

Dear Sir,

It depnds on the School of thought you are in, the area of application and above all on the irregularity of the domain you are modelling.

Finite element method is best suited to irregular boundaries where local refinement is mostly needed. It has the advantage of generating grids automatically.

Finite difference is more accurate but not best suited for irregular boundaries.

Finite volume extracts the positive features of both finite difference and finite element.

Sincerely,

sorry, that was my personal view, but very reliable.

look for my comments following the original thread

look for comments on numerical method