Finite volume method vs finite difference method?
 

Dear friend,

what is the difference between the FVM and FDM? Any information is appreciated! Thanks!

Re: Finite volume method vs finite difference meth
 

You can see the differences in mathematical formulations for FDM and FVM in any CFD book.

I would mention the conceptual difference:

In FD, you concentrate on one point in space and see how its values are changing due to neighboring points in space.

However, in FV our focus is on a fixed volume in space, which we term as cell. We chose a cell center, usually centroid of this cell. We assign a value U to this point which represents average of the variable u over the whole volume.

We study how this cell centered value changes due to the neighboring volumes, or cells. If you see the mathematical formulations you will learn that FV method is conservative in nature, while FD is not.

In terms of application, what I know is FD is not as accurate for complex geometries as FV is. If someone can confirm this, it would be great.

-Sunny

Re: Finite volume method vs finite difference meth
 

At a very simple level:

FDM - based upon a differential formulation of the governing equations

FVM - based upon an integral formulation of the governing equations

The reasons why one might be preferred over the other are explained in almost every CFD text book.

Re: Finite volume method vs finite difference meth
 

In finite difference method, the partial derivatives are replaced with a series expansion representation, usually a Taylor series.The series is truncated usually after one or two terms. The more term u include, the more accurate the solution.But it causes complxity and increase of nodes.

In finite volume method, governing eqns are integrated over a volume assuming piecewise linear variation of dependent variables. Using these integrations, you essentially balance fluxes across the boundaries of individual volumes.

Re: Finite volume method vs finite difference meth
 

Problem with Finite voume method is that, it is NOT for equations that are not based on conservation of physical laws. If you are equation is essentially not conservation over a volume,, then you are not supposed to use FVM. In this regard, FDM is more general.