Two-dimensional numerical model

Festa, J.F., and Hansen, D.V. (1978) Turbidity maxima in partially mixed estuaries A two-dimensional numerical model. Estuar. Coastal Shelf Sci. 7, 347-359. 

The effects of aquifer anisotropy and heterogeneity on NAPL pool dissolution and associated average mass transfer coefficient have been examined by Vogler and Chrysikopoulos [44]. A two-dimensional numerical model was developed to determine the effect of aquifer anisotropy on the average mass transfer coefficient of a 1,1,2-trichloroethane (1,1,2-TCA) DNAPL pool formed on bedrock in a statistically anisotropic confined aquifer. Statistical anisotropy in the aquifer was introduced by representing the spatially variable hydraulic conductivity as a log-normally distributed random field described by an anisotropic exponential covariance function. 

A two-dimensional numerical model was developed to describe the transport of dissolved organics originating from nonaqueous phase liquid pool dissolution in saturated porous media in the presence of dissolved humic substances. The model assumes that the dissolved contaminant (NAPL dissolved in the aqueous phase) may sorb onto the solid matrix as well as onto humic substances suspended in the aqueous phase, contaminant-humic particles and humic substances may sorb onto the solid matrix, the dissolved contaminant may undergo first-order decay, and humic substances are introduced into the aquifer from a line source. 

Two-dimensional numerical modelling of hydrogen diffusion assisted by stress and strain... 

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... 

Jones, R.L., and J.A. Pyle, Observations of CH4 and N2O by the NIMBUS 7 SAMS A comparison with in-situ data and two dimensional numerical model calculations. J Geophys Res 89, 5263, 1984. 

Karnahl, J. and Westrich, B. (2007) Two-dimensional numerical modeling of Hue sediment transport behavior in regulated rivers. In Westrich, B. and Forstner, U. (eds) Sediment Dynamics and Pollutant Mobility in Rivers An Interdisciplinary Approach, Springer, Berhn, Germany, Chapter 4.2, pp. 130-142. 

As a part of the international DECOVALEX III project, several independent research teams have analysed coupled HM effects during TBM drilling of the FEBEX tunnel. This paper presents the analyses conducted by two different research teams Institut de Radioprotection et de Surete Nucleaire (IRSN) in collaboration with Ecole des Mines de Paris (EMP), who conducted a two-dimensional numerical modelling, and the Lawrence Berkeley National Laboratory (Berkeley Lab), who conducted a three-dimensional transient numerical modelling. The paper focuses on the pressure responses in borehole section P4, which are most distinct. 

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. 

Kulikovsky AA (2000) Two-dimensional numerical modeling of a direct methanol fuel cell. J Appl Electrochem 30 1005-1014... 

With the goal of simulating as best as possible the real-life conditions in a wave rotor channel (Fig. 4), a two-dimensional numerical model... 

In Chap. 7, the investigation on combustion stabihty is extended to propane-fueled catalytic microreactors, using the catalytic and gas-phase chemical reaction schemes of propane combustion on platinum proposed and validated in Chap. 4. The steady hetero-Zhomogeneous combustion of lean propaneZair and methaneZair mixtures in a platinum-coated, catalytic plane channel-flow microreactor were investigated at pressures of 1 and 5 bar, channel heights of 1.0 and 0.3 mm, and wall thermal conductivities of 2 and 16 WZmK. Stability limits were assessed as a function of fuel type, inlet velocity, and imposed external heat losses. Parametric studies were performed with a full-eUiptic, two-dimensional numerical model employing detailed gas-phase (homogeneous) reaction schemes for both fuels. 

Blasco et al. [12] proposed two-dimensional mathematical model for the drying process of dense phase pneumatic conveying. However, heat and mass transfer were not considered and therefore their model may be used for dense phase pneumatic transport only. In their paper, both experimental and numerical predictions for axial and radial profiles for gas and solid velocity, axial profiles for solid concentration and pressure drop were presented. 

There are numerous practical applications of membranes coated with a very thin, nearly impermeable surface layer. Such thin coatings often have holes in the surface film causing the coatings to exist as flakes or strips with spaces between strips. For simplicity, we solve a two dimensional lattice model (Figure 6). 

Our results suggest that the spin correlation functions decay exponentially with a correlation length 1 for an arbitrary parameter a. We also assume that the decay of the correlation function is of the exponential type for the 14 parameter model as well, i.e., for any choice of site spinor I>A/u/p. This assumption is supported in special cases 1) the partition of the system into one-dimensional chains with exactly known exponentially decaying correlation functions 2) the two-dimensional AKLT model, for which the exponential character of the decay of the correlation function has been rigorously proved [32], Further evidence of the stated assumption lies in the numerical results obtained for various values of the parameter in the one-parameter model. 

Thus, two-dimensional numerical quadrature is sufficient. Further simplification follows by noting that the correlation function should satisfy Rj(Xj, Xj) = 1 when modeling a continuous function. 

An analysis of radial flow, fixed bed reactor (RFBR) is carried out to determine the effects of radial flow maldistribution and flow direction. Analytical criteria for optimum operation is established via a singular perturbation approach. It is shown that at high conversion an ideal flow profile always results in a higher yield irrespective of the reaction mechanism while dependence of conversion on flow direction is second order. The analysis then concentrates on the improvement of radial profile. Asymptotic solutions are obtained for the flow equations. They offer an optimum design method well suited for industrial application. Finally, all asymptotic results are verified by a numerical experience in a more sophisticated heterogeneous, two-dimensional cell model. 

---