Lagrangian transport

Leip A, Lammel G (2004) Indicators for persistence and long-range transport potential as derived from multicompartment chemistrytransport modelling. Environ Poll 128 205-221 Lin SJ, Rood RB (1996) Multidimensional flux form semi-Lagrangian transport. Mon Wea Rev 124 2046-2068... 

Lin S-J, Rood RB (1996) Multidimensional flux-form semi-Lagrangian transport schemes. Mon Weather Rev 124 2046-2070... 

A Lagrangian transport model implemented in BOLCHEM (BOLTRAJ variant) can be used in conjunction with the Eulerian part (DTsidoro et al., 2005). This is... 

Kaas E (2008) A simple and efficient locally mass conserving semi-Lagrangian transport scheme. Tellus 60A 305-320... 

Manney, G.L., R.W. Zurek, L. Froidevaux, J.W. Waters, A. O Neill, and R. Swinbank, Lagrangian transport calculations using UARS data. Part II Ozone. J Atmos Sci 52, 3069, 1995b. 

J. Saltzman and P. Colella, Second-Order Corner Coupled Upwind Transport Methods for Lagrangian Hydrodynamics, LA-UR-85-678, Los Alamos National Laboratory, Los Alamos, NM, 1987. 

MESOPUFF is a Lagrangian model suitable for modeling die transport, diffusion and removal of air pollutants from multiple point and area sources at transport distances beyond 10-50 KM. 

Taylor, J. A. (1989). A stochastic Lagrangian atmospheric transport model to determine global CO2 sources and sinks - a preliminary discussion, Tellus, Ser. B, 41,272-285. 

Dispersion in packed tubes with wall effects was part of the CFD study by Magnico (2003), for N — 5.96 and N — 7.8, so the author was able to focus on mass transfer mechanisms near the tube wall. After establishing a steady-state flow, a Lagrangian approach was used in which particles were followed along the trajectories, with molecular diffusion suppressed, to single out the connection between flow and radial mass transport. The results showed the ratio of longitudinal to transverse dispersion coefficients to be smaller than in the literature, which may have been connected to the wall effects. The flow structure near the wall was probed by the tracer technique, and it was observed that there was a boundary layer near the wall of width about Jp/4 (at Ret — 7) in which there was no radial velocity component, so that mass transfer across the layer... 

Aerosol production and transport over the oceans are of interest in studies concerning cloud physics, air pollution, atmospheric optics, and air-sea interactions. However, the contribution of sea spray droplets to the transfer of moisture and latent heat from the sea to the atmosphere is not well known. In an effort to investigate these phenomena, Edson et al.[12l used an interactive Eulerian-Lagrangian approach to simulate the generation, turbulent transport and evaporation of droplets. The k-e turbulence closure model was incorporated in the Eulerian-Lagrangian model to accurately simulate... 

Chapter 7 deviates from the rest of the book in that it describes computational methods for solving the transported PDF transport equation. Although Lagrangian PDF codes are... 

For canonical turbulent flows (Pope 2000), the flow parameters required to complete the CRE models are readily available. However, for the complex flow fields present in most chemical reactors, the flow parameters must be found either empirically or by solving a CFD turbulence model. If the latter course is taken, the next logical step would be to attempt to reformulate the CRE model in terms of a set of transport equations that can be added to the CFD model. The principal complication encountered when following this path is the fact that the CRE models are expressed in a Lagrangian framework, whilst the CFD models are expressed in an Eulerian framework. One of the main goals of this book... 

We shall see that a conditional acceleration model in the form of (6.48) is equivalent to a stochastic Lagrangian model for the velocity fluctuations whose characteristic correlation time is proportional to e/k. As discussed below, this implies that the scalar flux (u,

joint velocity, composition PDF level, and thus that a consistent scalar-flux transport equation can be derived from the PDF transport equation. 

Since the mean velocity and Reynolds-stress fields are known given the joint velocity PDF /u(V x, t), the right-hand side of this expression is closed. Thus, in theory, a standard Poisson solver could be employed to find (p)(x, t). However, in practice, (U)(x, t) and (u,Uj)(x, t) must be estimated from a finite-sample Lagrangian particle simulation (Pope 2000), and therefore are subject to considerable statistical noise. The spatial derivatives on the right-hand side of (6.61) are consequently even noisier, and therefore are of no practical use when solving for the mean pressure field. The development of numerical methods to overcome this difficulty has been one of the key areas of research in the development of stand-alone transported PDF codes.38... 

A transported PDF extension of the Hamelet model can be derived in a similar manner using the Lagrangian spectral relaxation model (Fox 1999) for the joint scalar dissipation rate. 

V, ip, x, and t) in the PDF transport equation makes it intractable to solve using standard discretization methods. Instead, Lagrangian PDF methods (Pope 1994a) can be used to express the problem in terms of stochastic differential equations for so-called notional particles. In Chapter 7, we will discuss grid-based Eulerian PDF codes which also use notional particles. However, in the Eulerian context, a notional particle serves only as a discrete representation of the Eulerian PDF and not as a model for a Lagrangian fluid particle. The Lagrangian Monte-Carlo simulation methods discussed in Chapter 7 are based on Lagrangian PDF methods. 

B B. By correctly choosing the coefficient matrices (a u, a 7, By, and B ), (6.159) can be made to correspond with the Eulerian velocity, composition PDF transport equation (6.19). However, it is important to note that /L / Thus it remains to determine how the Lagrangian notional-particle PDF /,( is related to the Eulerian velocity, composition PDF fn,0. This can be done by considering Lagrangian fluid particles. 

Lagrangian characteristics of turbulence and scalar transport in direct numerical simulations. Journal of Fluid Mechanics 427, 241-274. 

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