Numerical simulation approach

In general, the numerical simulation approach has several advantages in predicting and simulating local impact effects, due to its capabihty to capture the details of the impact process, time and cost-effectiveness, and reliability. However, it should be noted that the stabihty and accuracy of algorithms for the application of the constitutive equations must be assured, because the sensitivity of some material parameters is often unknown to the user, requiring a detailed and comprehensive parameter analysis. The successftd modelling of an impact event is based on vahd boundary descriptions and material models with parameters obtained from rehable material tests. 

Seidler, T., Stadnicka, K., and Champagne, B. (2014) Second-order nonlinear optical susceptibilities and refractive indices of organic crystals from a multiscale numerical simulation approach. Adv. Opt Mater.,... 

The alternative simulation approaches are based on molecular dynamics calculations. This is conceptually simpler that the Monte Carlo method the equations of motion are solved for a system of A molecules, and periodic boundary conditions are again imposed. This method pennits both the equilibrium and transport properties of the system to be evaluated, essentially by numerically solvmg the equations of motion... 

Mitsoulis, E., 1986. The numerical simulation of Boger fluids a viscometric approximation approach. Polym. Eng. Sci. 26, 1552-1562. 

Accident simulation Large-scale accidents normally cannot be staged for experimental purposes. It is impossible to put a building on fire in order to see how smoke spreads. In this case, numerical simulation is the sensible approach. 

Due to the very low volumetric concentration of the dispersed particles involved in the fluid flow for most cyclones, the presence of the particles does not have a significant effect on the fluid flow itself. In these circumstances, the fluid and the particle flows may be considered separately in the numerical simulation. A common approach is to first solve the fluid flow equations without considering the presence of particles, and then simulate the particle flow based on the solution of the fluid flow to compute the drag and other interactive forces that act on the particles. 

Products of nickel aluminides are also observed along the axis of the sample over a diameter of about 1 mm where the numerical simulations show radial focusing of the pressure to values approaching 50 GPa for times of about 200 ns. 

For adsorbates out of local equilibrium, an analytic approach to the kinetic lattice gas model is a powerful theoretical tool by which, in addition to numerical results, explicit formulas can be obtained to elucidate the underlying physics. This allows one to extract simplified pictures of and approximations to complicated processes, as shown above with precursor-mediated adsorption as an example. This task of theory is increasingly overlooked with the trend to using cheaper computer power for numerical simulations. Unfortunately, many of the simulations of adsorbate kinetics are based on unnecessarily oversimplified assumptions (for example, constant sticking coefficients, constant prefactors etc.) which rarely are spelled out because the physics has been introduced in terms of a set of computational instructions rather than formulating the theory rigorously, e.g., based on a master equation. 

R. Kobayashi. Modeling and numerical simulations of dendritic crystal growth. Physica D (55 410, 1993 R. Kobayashi. A numerical approach to three-dimensional dendritic solidification. Exp Math 5 59, 1994. 

In general, discontinuities constitute a problem for numerical methods. Numerical simulation of a blast flow field by conventional, finite-difference schemes results in a solution that becomes increasingly inaccurate. To overcome such problems and to achieve a proper description of gas dynamic discontinuities, extra computational effort is required. Two approaches to this problem are found in the literature on vapor cloud explosions. These approaches differ mainly in the way in which the extra computational effort is spent. 

In this section we briefly outline a general mean-field theory approach to arbitrary PCA and then apply the formalism to a particular class of one-parameter rules. We then compare the theoretical predictions to numerical simulations on lattices of dimension 1 < d < 4. 

It is now well-established that for atomic fluids, far from the critical point, the atomic organisation is dictated by the repulsive forces while the longer range attractive forces serve to maintain the high density [34]. The investigation of systems of hard spheres can therefore be used as simple models for atomic systems they also serve as a basis for a thermodynamic perturbation analysis to introduce the attractive forces in a van der Waals-like approach [35]. In consequence it is to be expected that the anisotropic repulsive forces would be responsible for the structure of liquid crystal phases and numerous simulation studies of hard objects have been undertaken to explore this possibility [36]. 

Here again, no precise instructions can be given because each situation will demand a tailored approach. Note Numerical simulation in many ways resembles the what-if scenario technique available in spreadsheets programs. Several programs supplied with this book allow the reader to play with functions and noise levels.)... 

Simulation Approach The numerical simulations were carried out using program SIMGAUSS, see data file TABLET C.dat for content uniformity, respectively TABLET W.dat for weight uniformity. The mean weights and contents were varied over a range covering the nominal values. 

Multiscale modeling is an approach to minimize system-dependent empirical correlations for drag, particle-particle, and particle-fluid interactions [19]. This approach is visualized in Eigure 15.6. A detailed model is developed on the smallest scale. Direct numerical simulation (DNS) is done on a system containing a few hundred particles. This system is sufficient for developing models for particle-particle and particle-fluid interactions. Here, the grid is much smaller... 

Yeoh, S.L., Papadakis, G., and Yianneskis, M. (2004) Numerical simulation of turbulent flow characteristics in a stirred vessel using the les and rans approaches with the sliding/deforming mesh methodology. Chem. Eng. Res. Des., 82 (A7), 834-848. 

Regions of stable and unstable operation determined by numerical simulation of mass and heat balances equations first- and second-order, autocatalytic, and product-inhibited kinetics graphically presented boundaries in co-ordinates in practice. safe operation if l/5e>2. Equality of heat generation and heat removal rates Semenov approach modified for first-order kinetics. 

Takeno, N. (1989) The effect of temperature gradient on the interaction between geothermal water and rock — an approach by numerical simulation. Mining Geology, 39, 295-304. 

The coupling of the component and energy balance equations in the modelling of non-isothermal tubular reactors can often lead to numerical difficulties, especially in solutions of steady-state behaviour. In these cases, a dynamic digital simulation approach can often be advantageous as a method of determining the steady-state variations in concentration and temperature, with respect to reactor length. The full form of the dynamic model equations are used in this approach, and these are solved up to the final steady-state condition, at which condition... 

The approach that we use is based on the principles of statistical mechanics and the techniques of numerical simulations. 

The resin system selected to initiate these studies is a step-growth anhydride cured epoxy. The approach to the kinetic analysis is that which is prevalent in the chemical engineering literature on reactor design and analysis. Numerical simulations of oligomeric population density distributions approximate experimental data during the early stages of the cure. Future research will... 

Using this approach, the hopping transport was modeled as a quasi-Marcovian process. The details of the analytical formulas forming the basis of the modeling and the numerical simulation procedure are given elsewhere.62 The values of parameters included in the hopping transport model are listed in Table 7. 

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