Acceleration mesoscale

Fio. 4. Types of multiscale modeling and solution strategies. Hybrid models (one model at each scale) apply well when there is separation of scales (onion or nested-type models). When there is lack of separation of scales, mesoscale models need to be developed where the same technique (e.g., MD or MC) is accelerated. Alternatively, multigrid (heterogeneous) hybrid models can be employed where the unresolved degrees of freedom are determined from a finer scale model and passed to a coarser scale model. 

In order to complete our discussion on momentum transfer, we must consider the final forms of the mesoscale acceleration models in the presence of all the fluid-particle forces. When the virtual-mass force is included, the mesoscale acceleration models must be derived starting from the force balance on a single particle ... 

As can be seen from Eq. (5.100), the virtual-mass force reduces the drag and lift forces by a factor of 1 /y. The buoyancy force is not modified because we have chosen to define it in terms of the effective volume Vpy. We remind the reader that the mesoscale acceleration model for the fluid seen by the particle A j must be consistent with the mesoscale model for the particle phase A p in order to ensure that the overall system conserves momentum at the mesoscale. (See Section 4.3.8 for more details.) As discussed near Eq. (5.14) on page 144, this is accomplished in the single-particle model by constraining the model for Apf given the model for Afp (which is derived from the force terms introduced in this section). Thus, as in Eqs. (5.98) and (5.99), it is not necessary to derive separate models for the momentum-transfer terms appearing in Apf. 

The simulated result shows that the low vortex with shear line developed to the strongest on 06UTC/24, there were four p-mesoscale systems A, B, C and D on the head of the low vortex at the level of 850 hPa (Fig. 1). The distribution of X shows that intense X almost coupled with intense ascend motion, p-mesoscale system D has hardly been accelerated, so the development level is lowest. The distribution of E suggested that the area of E > 0 and E < 0 were alternating, it indicated the energy transfer was very complicated between large... 

Atmospheric features which are smaller than the mesoscale have pressure fields in which wind acceleration is a significant component (which is referred to as the dynamic wind). The pressure gradient which causes this dynamic wind is called the nonhydiostatic pressure. 

Particle-based simulation techniques include atomistic MD and coarse-grained molecular dynamics (CG-MD). Accelerated dynamics methods, such as hyperdynamics and replica exchange molecular dynamics (REMD), are very promising for circumventing the timescale problem characteristic of atomistic simulations. Structure and dynamics at the mesoscale level can be described within the framework of coarse-grained particle-based models using such methods as stochastic dynamics (SD), dissipative particle dynamics (DPD), smoothed-particle hydrodynamics (SPH), lattice molecular dynamics (LMD), lattice Boltzmann method (IBM), multiparticle collision dynamics (MPCD), and event-driven molecular dynamics (EDMD), also referred to as collision-driven molecular dynamics or discrete molecular dynamics (DMD). 

It is the author s conviction that in many (turbulent) dispersed multiphase flows—except probably in very dense multiphase flow systems—the origin of mesoscale structures is in the fluid—particle interaction, with a secondary role for particle-particle interaction (coUisions, coalescence, breakup). Clustering of particles is believed to be intimately connected with the chaotic dynamics of fluid accelerations, as particles converge toward each other where and when the divergence of the acceleration field is positive (Goto... 

On the basis of all information gathered, it is fair to conclude that one of the major drivers behind the occurrence, the shape, and the dynamics of these mesoscale structures is the fluid—particle interaction force that plays a dominant role, both in stability analyses and in CFD simulations of any type. This role is related to the difference in inertia of the two phases and, as a result, to the temporally and spatially varying difference in velocities of dispersed phase (particles) and carrier (or continuous) phase. Cluster and strand formation seem to be closely related to the continuous chaotic accelerations in a turbulent carrier fluid (in the Euler—Lagrange approach) or a turbulent continuous phase (in the Euler-Euler or two-fluid approach). An interesting explanation for cluster formation is the sweep-stick mechanism proposed by Goto and Vasillicos (2008). 

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