Ordnung im Chaos : Molekular-kinetische Simulationen in der Strömungsmechanik

Die Strömung eines Fluides kann entweder makroskopisch mittels Kontinuumstheorie oder mikroskopisch auf der Grundlage molekular-kinetischer Modelle beschrieben werden. Die Kontinuumsannahme versagt jedoch, wenn beispielsweise ein Gas stark verdünnt ist oder die Abmessungen mikroskopisch klein sind. Die Modellierung erfordert in diesen Fällen eine mikroskopische Betrachtung auf molekularer Ebene. In diesem Beitrag werden wichtige, molekular-kinetische Simulationsmethoden mit einigen Berechnungsbeispielen vorgestellt.

This contribution presents a brief overview of numerical concepts for molecular-kinetic simulations of fluid flows. In general, molecularkinetic methods offer a wider range of applicability than continuum approaches and enable the development of efficient and flexible simulation methods even for continuum flows. The kinetic approaches are based on a statistical interpretation of the chaotic Brownian movement of gas molecules, which is represented in the form of a probability function: the so-called velocity distribution function. The governing equation to determine this function is the famous Boltzmann equation. The mathe-matical difficulties for solving this non-linear partial integrodifferential equation analytically are very high. More general solutions for technical and scientific problems are achieved by numerical methods only. The three most commonly used numerical solution concepts are discussed here. The „Direct Simulation Monte Carlo“ (DSMC) method simulates the random motion of the Brownian movement directly on the computer without solving any differential equations. The DSMC method is widely used for problems of rarefied gasses as they appear in vacuum technique or at re-entry flights of space vehicles. The other two solution concepts presented here are based on a reduced phase space and offer therefore very simple but efficient methods for continuum and nearcontinuum problems. The „Cellular Automata“ or „Lattice-Gas“ methods are simplified direct-simulation methods but not very well suited for continuous problems due to inherent statistical fluctuations. An extension of this method is the „‘Lattice-Boltzmann“ method, which is intensively under development and application at the site of the author. This method is described here in more detail and demonstrated by a number of examples, as simulations for chemically reacting flow, for gas-particle flow in technical filters and in the nasal airways.

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