Numerical modelling couple

Li P.W., Schaefer L., Chyu M.K. (2004) A numerical model coupling the heat and gas species transport processes in a tubular SOFC. Journal of Heat Transfer 126, 219-229. 

P. W. Li, L. Schaefer, and M. K. Chyu. A Numerical Model Coupling the Heat and Gas Species Transport Processes in a Tubular SOFC. J. Heat Transfer 126, (2004) 219-229. 

A common feature in the models reviewed above was to calculate pressure and temperature distributions in a sequential procedure so that the interactions between temperature and other variables were ignored. It is therefore desirable to develop a numerical model that couples the solutions of pressure and temperature. The absence of such a model is mainly due to the excessive work required by the coupling computations and the difficulties in handling the numerical convergence problem. Wang et al. [27] combined the isothermal model proposed by Hu and Zhu [16,17] with the method proposed by Lai et al. for thermal analysis and presented a transient thermal mixed lubrication model. Pressure and temperature distributions are solved iteratively in a iterative loop so that the interactions between pressure and temperature can be examined. 

To extend the applicability of the SECM feedback mode for studying ET processes at ITIES, we have formulated a numerical model that fully treats diffusional mass transfer in the two phases [49]. The model relates to the specific case of an irreversible ET process at the ITIES, i.e., the situation where the potentials of the redox couples in the two phases are widely separated. A further model for the case of quasireversible ET kinetics at the ITIES is currently under development. For the case where the oxidized form of a redox species, Oxi, is electrolytically generated at the tip in phase 1 from the reduced species, Red], the reactions at the tip and the ITIES are ... 

Rathfelder, K.M., Lang, J.R. and Abriola, L.M., A numerical model (MISER) for the simulation of coupled physical, chemical and biological processes in soil vapor extraction and bioventing systems, J. Contam. Hydrol., 43, 239-270, 2000. 

Ge and Fan (2005) developed a 3-D numerical model based on the level-set method and finite-volume technique to simulate the saturated droplet impact on a superheated flat surface. A 2-D vapor-flow model was coupled with the heat-transfer model to account for the vapor-flow dynamics caused by the Leidenfrost evaporation. The droplet is assumed to be spherical before the collision and the liquid is assumed to be incompressible. 

Since publication of the first edition, the held of reaction modeling has continued to grow and hnd increasingly broad application. In particular, the description of microbial activity, surface chemistry, and redox chemistry within reaction models has become broader and more rigorous. Reaction models are commonly coupled to numerical models of mass and heat transport, producing a classification now known as reactive transport modeling. These areas are covered in detail in this new edihon. 

Compared to the situation in lakes, the sediment-water interactions in rivers are more complex. Because the flow velocity is constantly changing, particles may either settle at the bottom or be resuspended and deposited again further downstream. In order to adequately describe the effect of these processes on the concentration of a chemical in the river, we would need a coupled water-sediment model with which the profile of the chemical along the river of both the aqueous concentration in the river and the concentration in the sediment bed are described. This is a task to be left to numerical modeling. We choose a simpler approach by approximating the net deposition of the particles and the chemicals sorbed to them as a linear process (see Eqs. 23-16 and 23-17) ... 

For this reason, only highly reliable models coupled with accurate numerical routines such as those presented here are useful for the professional chemical/biological engineer. 

A better understanding of the behavior of FCC units can be obtained through mathematical models coupled with industrial verification and cross verification of these models. The mathematical model equations need to be solved for both design and simulation purposes. Most of the models are nonlinear and therefore they require numerical techniques like the ones described in the previous chapters. 

To understand the mechanisms of solids slug flows, a two-dimensional coupled DEM/CFD numerical model was built to simulate the motion of a pre-formed slug (ca. 0.3 m long) in a 1 m long horizontal 50 mm bore pipe as shown in Fig. 1. The pipe was initially filled with a layer of particles, approximately 15 mm thick at the bottom. (The thickness of this stationary layer was determined based on experience from previous experiments and computer test runs). 

Kuo, A.Y., and Park, K. (1995) A framework of coupling shoals and shallow embayments with main channels in numerical modeling of coastal plain estuaries. Estuaries 18, 341-350. 

Figure 3. Remanence enhancement in exchange-coupled single -phase nanostructures - ( ) Numerical modeling [117, 118] and (o) calculation according to Eq. 13.

Coupled methods (transport model coupled with hydrogeochemical code) For coupled models solving the transport equation can be done by means of the finite-difference method (and finite volumes) and of the finite-elements method. Algorithms based on the principle of particle tracking (or random walk), as for instance the method of characteristics (MOC), have the advantage of not being prone to numerical dispersion (see 1.3.3.4.1). 

When system (4.164)-(4.165) does not have any analytical solution, we can use numerical integration coupled with interpolation for each function Pk(z,s), k= 1,...N then we can obtain the originals Pk(z,t), k= 1,...N. However, this procedure gives an approximate result when compared to the direct numerical integration of the original model. 

Besides the scientific questions related to the coupling of models, the interaction of the numerical models is a big technical challenge. The transformation of data at different temporal and spatial resolutions as well as computational efficiency, memory consumption, data storage capacity, meta-data communication and code management are issues which have to be addressed. 

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