One-dimensional numerical model

One-Dimensional Numerical Model. The equations are in finite difference form and are based on the model described by Selim and Iskandar (17). The water flow equation was solved in terms of soil water pressure head, h, rather than water content, 0, giving... 

R.L. Adams and X Roy. A one-dimensional numerical model of a drop-on-demand inkjet. Journal of Applied Mechanics, 53 (1986) 193-197. 

The previous section showed that the one-dimensional numerical model can predict the average breakthrough times but is not able to explain the differences between the temperature measurements in the radial centre and the zone close to the wall of the bed. The difference in temperature profiles between these locations is particularly pronounced for the cooling step. The temperature development close to the wall is very disperse, which cannot be predicted by the one-dimensional model. 

The determination of the diffusion coefficient of al-kanethiol ink in PDMS stamps is possible by means of simple linear-diffusion experiments, in which the basic parameters of//CP (ink concentration, printing time, and stamp geometry) are taken into account. Ink transport is monitored by direct adsorption on gold substrates from consecutive prints. We showed that the ink transport through the PDMS slab follows Pick s law of diffusion. A simplified analytical model was found to be accurate for experiments with high initial concentrations (saturation) but is likely to become inaccurate at low initial concentrations. Therefore, a more precise one-dimensional, numerical model based on the finite-difference method was developed, which also proved to be accurate at low concentrations. 

A mathematical model for reservoir souring caused by the growth of sulfate-reducing bacteria is available. The model is a one-dimensional numerical transport model based on conservation equations and includes bacterial growth rates and the effect of nutrients, water mixing, transport, and adsorption of H2S in the reservoir formation. The adsorption of H2S by the roek was considered. 

In the present study, two-dimensional Two-Fluid Eulerian model was used to describe the steady state, dilute phase flow of a wet dispersed phase (wet solid particles) in a continuous gas phase through a pneumatic dryer. The predictions of the numerical solutions were compared successfully with the results of other one-dimensional numerical solutions and experimental data of Baeyens et al. [5] and Rocha [13], Axial and the radial distributions of the characteristic properties were examined. 

The numerical solution to the advection-dispersion equation and associated adsorption equations can be performed using finite difference schemes, either in their implicit and/or explicit form. In the one-dimensional MRTM model (Selim et al., 1990), the Crank-Nicholson algorithm was applied to solve the governing equations of the chemical transport and retention in soils. The web-based simulation system for the one-dimensional MRTM model is detailed in Zeng et al. (2002). The alternating direction-implicit (ADI) method is used here to solve the three-dimensional models. 

A number of one dimensional computer models have been developed to analyze thermionic converters. These numerical models solve the nonlinear differential equations for the thermionic plasma either by setting up a finite element mesh or by propagating across the plasma and iterating until the boundary conditions are matched on both sides. The second of these approaches is used in an analytical model developed at Rasor Associates. A highly refined "shooting technique" computer program, known as IMD-4 is used to calculate converter characteristics with the model ( ). 

They subsequently (2) developed a one-dimensional mathematical model in the form of coupled differential and integro-differential equations, based on a gross mechanism for the chemical kinetics and on thermal feedback by wall-to-wall radiation, conduction in the tube wall, and convection between the gas stream and the wall. This model yielded results by numerical integration which were in good agreement with the experimental measurements for the 9.53-mm tube. For this tube diameter, the flows of unbumed gas for stable flames were in the turbulent regime. 

A refined one-dimensional numerical ocean model of the southern Baltic Sea was used by Axell (2002) to investigate suitable parameterizations of unresolved turbulence and compared it with available observations. The turbulence model is a k- model that includes extra source terms of turbulent kinetic energy production by internal waves and Langmuir circulation due to unresolved, breaking internal waves and Langmuir... 

The sequence of models used in these studies constituted a progression from a simple analytical model of the convection-dispersion type with fixed parameters, associated with the assumption of a semi-infinite homogenous profile, to a convection-dispersion numerical model, which incorporated dynamic water and solute movement through a multilayered profile. In brief, the sequence was as follows (a) one-dimensional analytical model with an upper boundary... 

Two-Dimensional Numerical Model, Application of DBCP by shank injection in a pineapple bed (Maui fields) provides a line source of pesticide at a depth of about 30 cm which cannot be modeled in a one-dimensional mode without first evaluating the impact of initial concentration distribution. The geometry of the system is indicated by the cross-sectional diagram of two pineapple beds in Figure 1, The section of Figure 1 delineated by AA-BB represents a typical section. The objective was to model the movement of DBCP from an assumed source zone (8 cm wide x 10 cm deep section centered at 30 cm depth) to determine the approximate time required to justify the assumption of a uniform lateral distribution of DBCP in the plow layer for subsequent one-dimensional modeling. An appropriate model and numerical solution for this case was given by Hemwell (15) and the details of the present application are presented elsewhere C3 ). In brief, the two-dimensional equation solved is... 

Simulated DBCP Movement in Plow Laver — Two Dimensional Numerical Model. Of the several input parameters required for Equations 3 and 4 (Hemwell model) the most difficult to specify with confidence are Kd and D. Our objective in using the 2-D model was to calculate initial DBCP concentration in the upper layer in order to specify initial conditions for the one-dimensional models used to predict deep penetration of DBCP. For this reason the 2-D model was calibrated with field data by adjusting Kd and D within reasonable limits. Combinations of parameters used and the results are shown in Table III. The use of Kd = 4.10 was based on a calibration of the Jury et al. analytical model with field surface layer data six months after application as described earlier. This value is obviously too... 

The way we have presented the one-dimensional dispersion model so far has been as a modification of the plug-flow model. Hence, u is treated as uniform across the tubular cross section. In fact, the general form of the model can be applied in numerous instances where this is not so. In such situations the dispersion coefficient D becomes a more complicated parameter describing the net effect of a number of different phenomena. This is nicely illustrated by the early work of Taylor [G.I. Taylor, Proc. Roy. Soc. (London), A219, 186 (1953) A223, 446 (1954) A224, 473 (1954)], a classical essay in fluid mechanics, on the combined contributions of the velocity profile and molecular diffusion to the residence-time distribution for laminar flow in a tube. 

We summarize a number of simulations aimed at deciphering some of the basic effects which arise from the interaction of chemical kinetics and fluid dynamics in the ignition and propagation of detonations in gas phase materials. The studies presented have used one- and two-dimensional numerical models which couple a description of the fluid dynamics to descriptions of the detailed chemical kinetics and physical diffusion processes. We briefly describe, in order of complexity, a) chemical-acoustic coupling, b) hot spot formation, ignition and the shock-to-detonation transition, c) kinetic factors in detonation cell sizes, and d) flame acceleration and the transition to turbulence. 

The study of the configurational statistics of polymers in ideal solutions has already reached a high level of sophistication. This arises in part from the fact that many problems of this kind are soluble in closed form and the resultant expressions are readily evaluated by numerical techniques. The maturity of this field is a tribute to the matrix methods of the one-dimensional Ising model. As this subject is thoroughly presented in the literature, " it is not necessary to repeat the material here, except insofar as it is convenient to introduce the notation and concepts that arc necessary in any discussion of polymer systems. Before proce ing with a brief discussion of the configurational statistics of ideal polymer chains, wc should also indicate an additional motivation for considering this subject in a... 

The results of a blast wave simulation—that is, pressure-time histories on the solid plate (described previously)—are presented in Fig. 5. Curve 1 (solid line) represents data from a piezogauge mounted in the plate, covered by a 55-im layer of PUR foam with an average density of pQ 25.0 kg/m3. Curve 2 corresponds to the results of one-dimensional numerical simulation using a model of a one-fluid, two-temperature continuum. In order to reproduce initial conditions in our numerical simulations for blast wave/foam interaction, we used density distribution in a nonsteady jet from the shock tube experiment. Other gasdynamical parameters recjuired for the system of Eqs. (2a)-(2c) were derived using the assumption of the Riemann invariant being constant. Curve 3 illustrates pressure gauge data for the same plate without the foam. Mach number of the shock in the end of the tube was about 1.85 in all cases, Pq-I bar. 

In Chapter 1, the results were described of studies done on the time-dependent reaction zones of an ideal gas, nitromethane, and liquid TNT, using one-dimensional numerical hydrodynamics with the Arrhenius rate law. A similar study was made of the reaction zone in spherically diverging geometry. The reaction zone in nitromethane that was overdriven enough to be stable in the plane case, and in an ideal gas that was stable in the plane case at C-J velocity has been modeled. Figures 2.41 and 2.42 show that the detonation process depends upon the rarefaction process that follows it. The pressure at the front and back of the reaction zone quickly drops below the plane-wave C-J values. 

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