Lagrangian single-particle model

The Lagrangian steady drag force on a single particle is commonly expressed by (5.48). For Eulerian model formulations one normally employs (5.34), hence for the multifluid models the standard steady drag force parameterization 3delds ... 

Draxler, R.R. and Rolph, G.D., 2003. HYSPLIT (HYbrid Single-Particle Lagrangian Integrated Trajectory) Model access via NOAA ARL READY Website (http //www.arl.noaa.gov/ready/hysplit4.html). NOAA Air Resources Laboratory, Silver Spring, MD. 

The description is based on the previously defined single-particle (Lagrangian) or one-point (Eulerian) joint velocity-composition (micro-)PDF, /(r,yr). As mentioned in Section 12.4.1, in the one-point description no information on the local velocity and scalar (species concentrations, temperature,. ..) gradients and on the frequency or length scale of the fluctuations is included and the related terms require closure models. The scalar dissipation rate model has to relate the micro-mixing time to the turbulence field (see (12.2-3)), either directly or via a transport equation for the turbulence dissipation rate e. A major advantage is that the reaction rate is a point value and its behavior and mean are described exactly by a one-point PDF, even for arbitrarily complex and nonlinear reaction kinetics. 

In order to simulate the SDEs, we will introduce a large ensemble of notional particles that move through the simulation domain according to the Lagrangian PDF models. As an example, we will consider a single inert-scalar field in a one-dimensional domain. The position and composition of the th notional particle can be denoted by X n t) and 4i(n)(f), respectively. The SDEs for the Lagrangian composition PDF (with closures) become... 

It is remarked that in the standard literature on fluid dynamics and transport phenomena three different modeling frameworks, which are named in a physical notation rather than in mathematical terms, have been followed formulating the single phase balance equations [91]. These are (1) The infinitesimal particle approach [2, 3, 67, 91, 145]. In this case a differential cubical fluid particle is considered as it moves through space relative to some fixed coordinate system. By applying the balance principle to this Lagrangian control volume the conservation equations for... 

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