Numerical modelling approach

Reed, M.H. and Spycher, N.F. (1985) Boiling, cooling and oxidation to epithermal systems. A numerical modeling approach. In Berger, B.R. and Bethke, P.M. (eds.). Geology and Geochemistry of Epithermal System. Reviews in Economic Geology, 2, 249-272. 

There have been some attempts to overcome the analysis of compaction problems, mostly by introducing numerical modeling approaches. The modeling approaches often used in compaction analysis are (a) phenomenological continuum models, (b) micromechanically based continuum models, and (c) discrete-element models. The parameters that should be analyzed when tableting is under development are as follows ... 

Functional Nanostructures and Nanocomposites -Numerical Modeling Approach and Experiment... 

This paper is structured as follows in section 2, we recall the statement of the forward problem. We remind the numerical model which relates the contrast function with the observed data. Then, we compare the measurements performed with the experimental probe with predictive data which come from the model. This comparison is used, firstly, to validate the forward problem. In section 4, the solution of the associated inverse problem is described through a Bayesian approach. We derive, in particular, an appropriate criteria which must be optimized in order to reconstruct simulated flaws. Some results of flaw reconstructions from simulated data are presented. These results confirm the capability of the inversion method. The section 5 ends with giving some tasks we have already thought of. 

The benefit of such LFERs is that they establish patterns of regular behavior, isolating apparent simplicity and defining normal or expected reactivity. Against such patterns it becomes possible to detect widely deviant or unexpected behavior. As we saw in Chapter 7, we cannot expect great generality from the extrathermodynamic approach, so it may be necessary to define numerous model processes so as to fit a full range of situations. 

The numerical model consisted of two alternating procedures During the first one, the creep under applied dead load of a 2-dimensional bar, with an initial small deviation from the straight shape, was simulated the second procedure was the solution to the eigenvalue buckling problem for a bar with a shape developed due to the creep, this approach allowed a prediction of the buckling time with the assumption of the initial imperfection accepted as an unavoidable handicap. 

The Geothermal Response Test as developed by us and others has proven important to obtain accurate information on ground thermal properties for Borehole Heat Exchanger design. In addition to the classical line source approach used for the analysis of the response data, parameter estimation techniques employing a numerical model to calculate the temperature response of the borehole have been developed. The main use of these models has been to obtain estimates in the case of non-constant heat flux. Also, the parameter estimation approach allows the inclusion of additional parameters such as heat capacity or shank spacing, to be estimated as well. 

Only due to severe restrictions in these points the differential equations can be solved. For a detailed and more realistic analysis of real problems therefore a different approach has to be used. We have to use numerical models because there we only have to define the differential equations in the form of difference equations. These are then solved by a computer. 

Obviously, these two items are not strictly separated in contrast, the most fruitful approach is when they are simultaneously followed, so that they can mutually benefit from each other. In this chapter, we want to focus on the use of simulation methods as a design tool for gas-fluidized bed reactors, for which we consider gas-solid flows at four distinctive levels of modeling. However, before discussing the multilevel scheme, it is useful to first briefly consider the numerical modeling of the gas and solid phase separately. 

Such an experimental characterization is a necessary step to carry out a detailed comparison of emission properties as measured experimentally with the corresponding quantities as calculated by numerical models capable of describing transport and energy deposition of fast electrons in matter and consequent emission of characteristic X-ray emission. A possible modeling approach of fast electron transport experiments is given here, where the above results on Ka imaging were interpreted using the hybrid code PETRA [53] to... 

In the Lagrangian frame, droplet trajectories in the spray may be calculated using Thomas 2-D equations of motion for a sphere 5791 or the simplified forms)154 1561 The gas velocity distribution in the spray can be determined by either numerical modeling or direct experimental measurements. Using the uncoupled solution approach, many CFD software packages or Navier-Stokes solvers can be used to calculate the gas velocity distribution for various process parameters and atomizer geometries/configurations. On the other hand, somesimple expressions for the gas velocity distribution can be derived from... 

There have been books on droplet-related processes. However, the present book is probably the first one that encompasses the fundamental phenomena, principles and processes of discrete droplets of both normal liquids and melts. The author has attempted to correlate many diverse mechanisms and effects in a single and common framework in an effort to provide the reader with a new perspective of the identical basic physics and the inherent relationship between normal liquid and melt droplet processes. Another distinct and unique feature of this book is the comprehensive review of the empirical correlations, analytical and numerical models and computer simulations of droplet processes. These not only provide practical and handy approaches for engineering calculations, analyses and designs, but also form a useful basis for future in-depth research. Therefore, the present book covers the fundamental aspects of engineering applications and scientific research in the area. 

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