Eulerian-Lagrangian models

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... 

Eulerian-Lagrangian model for gas-evolving processes based on supersaturation... 

The two-phase flow formulation can also be categorized into two groups, namely, the Eulerian-Eulerian models and Eulerian-Lagrangian model. In the Eulerian-Eulerian model, a set of transport equations is solved for the gas phase while in the Eulerian-Lagrangian model, the gas phase is treated as particles, which interact with the continuous phase. 

In the Eulerian-Lagrangian methods, Eulerian parts of the equations are generally solved with methods described previously for the quasi-single-fluid models. The bubble trajectory equations are solved by direct integration [33,74] of (9.51) and (9.52). The solution procedure employed by Johansen and Boysan to solve the Eulerian-Lagrangian model [33] can be summarized as follows ... 

The methods used for modeling pure granular flow are essentially borrowed from that of a molecular gas. Similarly, there are two main types of models the continuous (Eulerian) models (Dufty, 2000) and discrete particle (Lagrangian) models (Herrmann and Luding, 1998 Luding, 1998 Walton, 2004). The continuum models are developed for large-scale simulations, where the controlling equations resemble the Navier-Stokes equations for an ordinary gas flow. The discrete particle models (DPMs) are typically used in small-scale simulations or... 

Heberton, C.I., Russel, T.F., Konikow, L.F., and Hornberger, G.Z., A Three-Dimensional Finite-Volume Eulerian-Lagrangian Localized Adjoint Method (ELLAM) for Solute-Transport Modeling, Water Resources Investigations Report 00-4087, U.S. Geological Survey, Reston, VA, 2000. 

Two models have been presented which are based on the Lagrangian and Eulerian difference schemes respectively. These models were able to calculate in detail the interaction of acoustic waves with inclusions in discontinuous fluids. The Lagrangian model was able to consider the transfer of normal to shear stresses at fluid discontinuities. The Eulerian model is limited to the study of dilatation waves but its computational efficiency enables it to... 

For multiphase systems a rough distinction can be made between systems with separated flows and those with dispersed flows. This classification is not only important from a physical point of view but also from a computational perspective since for each class different computational approaches are required. For multiphase systems involving multiphase flow both Eulerian, mixed Eulerian-Lagrangian, and two-material free surface methods can be used. An excellent review on models and numerical methods for multiphase flow has been presented by Stewart and Wendroff (1984). A similar review with emphasis on dilute gas-particle flows has been presented by Crowe (1982). 

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