Abstract
Recently a mesoscopic approach to computational fluid dynamics has been proposed which is based on a stochastic description defined by a discrete master equation. Applying van Kampen's system size expansion to one-dimensional flows, the deterministic macroscopic equations, i.e., the Navier-Stokes and continuity equation are obtained. The velocity and density fluctuations around the macroscopic dynamics are governed by a Fokker-Planck equation. From the assumption of local thermodynamic equilibrium, a relation between the velocity fluctuations and the temperature is obtained which allows to derive the linear Langevin equations of fluctuating hydrodynamics. Thus, the suggested stochastic approach makes possible the simultaneous numerical simulation of both the macroscopic balance equations and the hydrodynamic fluctuations.
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