Fluid Closure

Lack of closure is an endemic problem in fluid theory. Because each moment is coupled to the next higher moment (for instance, the density evolution depends on the flow velocity, the flow velocity evolution depends on the viscosity tensor, and so on), any finite set of exact moment equations is bound to contain more unknowns than equations.

There are two basic types of fluid closure schemes. In *truncation schemes*,
higher order moments are arbitrarily
assumed to vanish, or simply prescribed in terms of lower
moments. Truncation schemes can often provide quick insight into fluid
systems, but always involve uncontrolled approximation. *Asymptotic schemes*, on the other hand,
depend on the rigorous exploitation of some small parameter.
Asymptotic closure schemes have the advantage of being systematic, and providing some
estimate of the error involved in the closure. On the other hand,
the asymptotic approach to closure is mathematically demanding, because it
inevitably involves working with the kinetic equation.