Quasistatic approximation

Quasistatic approximation(s) refers to different domains and different meanings. In the most common acceptance, quasistatic approximation refers to equations that keep a static form (do not involve time derivatives) even if some quantities are allowed to vary slowly with time. In electromagnetism it refers to mathematical models that can be used to describe devices that do not produce significant amounts of electromagnetic waves. For instance the capacitor and the coil in electrical networks.

The quasistatic approximation can be understood through the idea that the sources in the problem change sufficiently slowly that the system can be taken to be in equilibrium at all times. This approximation can then be applied to areas such as classical electromagnetism, fluid mechanics, magnetohydrodynamics, thermodynamics, and more generally systems described by hyperbolic partial differential equations involving both spatial and time derivatives. In simple cases, the quasistatic approximation is allowed when the typical spatial scale divided by the typical temporal scale is much smaller than the characteristic velocity with which information is propagated. The problem gets more complicated when several length and time scales are involved. In the strict acceptance of the term the quasistatic case corresponds to a situation where all time derivatives can be neglected. However some equations can be considered as quasistatic while others are not, leading to a system still being dynamic. There is no general consensus in such cases.

In fluid dynamics, only quasi-hydrostatics (where no time derivative term is present) is considered as a quasi-static approximation. Flows are usually considered as dynamic as well as acoustic waves propagation.

In thermodynamics, a distinction between quasistatic regimes and dynamic ones is usually made in terms of equilibrium thermodynamics versus non-equilibrium thermodynamics. As in electromagnetism some intermediate situations also exist; see for instance local equilibrium thermodynamics.

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