Langevin equation

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The stochastic differential equation (SDE) for velocity component $U(t)$ , the Langevin equation is

$dU(t) = - U(t) \frac{dt}{\tau} + \frac{2 u'}{\tau}^{1/2} dW(t)$

where $dW(t)$ is a Wiener process. $u'$ is the turbulence intensity and $\tau$ a Lagrangian time-scale.

Th finite difference approximation of the above equation is

$U(t+\Delta t) = U(t) - U(t) \frac{\Delta t}{\tau} + \frac{2 u' \Delta t}{\tau}^{1/2} \mathcal{N}$

where $\mathcal{N}$ is a standardized Gaussian random variable with 0 mean an unity variance which is independent of $U$ on all other time steps (Pope 1994). The Wiener process can be understood as Gaussian random variable with 0 mean and variance $dt$

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Langevin equation

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Revision as of 09:29, 14 November 2005 (view source) Salva (Talk \| contribs) ← Older edit	Latest revision as of 14:30, 15 June 2007 (view source) Jola (Talk \| contribs) m (Reverted edits by YlzEnr (Talk); changed back to last version by Salva)
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