Conservation form

Conservation form refers to an arrangement of an equation or system of equations, usually representing a physical system, that show that a property represented is conserved by making overall change equal to zero.

An example of a set of equations written in conservation form could be the Euler equations of fluid flow:

${\partial \rho \over \partial t}+\nabla \cdot (\rho {\mathbf {u}})=0$

${\partial \rho {\mathbf {u} } \over \partial t}+\nabla \cdot (\rho {\mathbf {u} }){\mathbf {u} }+\nabla p=0$

${\partial E \over \partial t}+\nabla \cdot ({\mathbf {u}}(E+p))=0$

Each of these represents the conservation of mass, momentum and energy, respectively.