### finite volume method

**(FVM)**
(computational method to PDEs especially suited to fluid dynamics)

**Finite volume method** (**FVM**) refers to a means of calculating
solutions to partial differential equations which happens to be especially suited to
fluid dynamics (hydrodynamics).
It divides a volume with a three-dimensional grid into small
volumes and uses the **divergence theorem** to allow tractable
calculation to produce good results.

The divergence theorem relates divergence
within a volume to flow
in/out of the volume. That fact along with the fact that flow
in/out of a volume matches that of the volumes to which it is
adjacent allow calculations regarding the interfaces to represent
activity within the volume.

FVMs have the advantage that it is relatively easy to deal with
volumes of different sizes and shapes, i.e., in an irregular
pattern, more easily than others, e.g., a finite difference method.

FVMs are particularly adapted to fluid dynamics because they
involve flow of material which would be between the volumes,
which is exactly what FVMs deal with. Also, the fact that
they can deal with irregular or moving volumes assists in
devising ways to handle discontinuities in fluid flow,
such as shock waves.

(*mathematics,physics,computation,fluid dynamics*)
**Further reading:**

http://en.wikipedia.org/wiki/Finite_volume_method

http://en.wikipedia.org/wiki/Divergence_theorem

http://cfd.mace.manchester.ac.uk/twiki/pub/Main/TimCraftNotes_All_Access/cfd1-finvols1.pdf

http://www.scholarpedia.org/article/Finite_volume_method

**Referenced by pages:**

Godunov scheme

MITgcm

numerical analysis

Riemann problem

Index