[格子boltzmann和ppt08.pptVIP

Basic Boltzmann Gas Concepts Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. Kinetic Theory Complete set of position (x) and momentum (p) coordinates for all individual particles gives exact dynamical state of system Together with classical mechanics, allows exact prediction of future states However, this level of description is essentially not possible Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. Statistical Mechanics Represent system by ensemble of many copies Describe by distribution function f(N)(xN,pN,t); N is number of particles Changes in f(N)(xN,pN,t) with time given by Liouville equation (6N variables) Usually interested in low order distribution functions (N = 1, 2) Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. First Order Distribution Function f(1)(x,p,t) gives probability of finding a particular molecule with given position and momentum; positions and momenta of remaining N-1 molecules unspecified No experiment can distinguish between molecules, so the choice of which molecule doesn’t matter ‘Single particle’ distribution function f(1) adequate for describing all gas properties that don’t depend on relative positions of molecules (dilute gas with long mfp平均自由路程) Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. External force Xi (small relative to intermolecular forces) For each component i there is an fi(1)(x,pi,t) such that probable number of type i molecules with position coordinates in the range x ±dx and momentum coordinates pi ±dpi is fi(1)(x,pi,t) dxdpi Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. Expected Evolution w/o Collisions(streaming) If no collisions, then at time t + dt, the new positions of m