Editing Control volume (section)

==Overview==
Typically, to understand how a given [[physical law]] applies to the system under consideration, one first begins by considering how it applies to a small, control volume, or "representative volume". There is nothing special about a particular control volume, it simply represents a small part of the system to which physical laws can be easily applied. This gives rise to what is termed a volumetric, or volume-wise formulation of the mathematical model.

One can then argue that since the [[physical law]]s behave in a certain way on a particular control volume, they behave the same way on all such volumes, since that particular control volume was not special in any way. In this way, the corresponding point-wise formulation of the [[mathematical model]] can be developed so it can describe the physical behaviour of an entire (and maybe more complex) system.

In [[continuum mechanics]] the [[Conservation laws|conservation equations]] (for instance, the [[Navier-Stokes equations]]) are in integral form. They therefore apply on volumes. Finding forms of the equation that are ''independent'' of the control volumes allows simplification of the integral signs. The control volumes can be stationary or they can move with an arbitrary velocity.<ref>
{{Cite journal 
|last1=Nangia
|first1=Nishant 
|last2=Johansen 
|first2=Hans
|last3=Patankar 
|first3=Neelesh A. 
|last4=Bhalla 
|first4=Amneet Pal S.
|title=A moving control volume approach to computing hydrodynamic forces and torques on immersed bodies
|journal=Journal of Computational Physics
|volume=347
|pages=437–462
|year=2017
|doi=10.1016/j.jcp.2017.06.047|arxiv=1704.00239|bibcode=2017JCoPh.347..437N|s2cid=37560541 
}}
</ref>