Numerical simulations are designed to solve, for the material body in question, the system of equations expressing the fundamental laws of physics to which the dynamic response of the body must conform. The detail provided by such first-principles solutions can often be used to develop simplified methods for predicting the outcome of physical processes. These simplified analytic techniques have the virtue of calculational efficiency and are, therefore, preferable to numerical simulations for parameter sensitivity studies. Typically, rather restrictive assumptions are made on the bounds of material response in order to simplify the problem and make it tractable to analytic methods of solution. Thus, analytic methods lack the generality of numerical simulations and care must be taken to apply them only to problems where the assumptions on which they are based will be valid. [Pg.324]

Although direct numerical simulations under limited circumstances have been carried out to determine (unaveraged) fluctuating velocity fields, in general the solution of the equations of motion for turbulent flow is based on the time-averaged equations. This requires semi- [Pg.671]

Zannetti, Paolo, Numerical Simulation Modeling of Air Pollution An Oveiview, Ecological Physical Chemistiy, 2d International Workshop, May 1992. [Pg.2184]

Mitsoulis, E., 1990. Numerical Simulation of Viscoelastic Fluids. In Encyclopaedia of Fluid Mechanics, Vol. 9, Chapter 21, Gulf Publishers, Houston. [Pg.15]

Crochet, M. J., 1982, Numerical simulation of die-entry and die-exit flow of a viscoelastic fluid. In Numerical Methods in Forming Processes, Pineridge Press, Swansea. [Pg.108]

Mitsoulis, E., 1986. The numerical simulation of Boger fluids a viscometric approximation approach. Polym. Eng. Sci. 26, 1552-1562. [Pg.15]

The MathWorks Inc. (1993) SIMULINK Numerical Simulation Software - Reference Guide, The MathWorks Inc., Natick, Mass. [Pg.432]

Beaulne, M. and Milsoulis, E. 1999. Numerical simulation of the fihn casting process. Int. Poly. Proce.ss. XfV, 261-275. [Pg.188]

In the context of molecular simulation, particularly biomolecular modelling, a critical aspect for numerical simulation is the presence of long-range Coulombic forces which render the force computations much more costly [Pg.349]

The flow processes are described as Marangoni convections and up to now they were determined by several research centers through numeric simulation works [9]. Due to the [Pg.547]

The methods discussed in the technical hterature are not exact. Numerical simulations of plant performance show that gross errors frequently remain undetected when they are present, or measurements are isolated as containing gross errors when they do not contain any. [Pg.2571]

B. Engquist and A. Majda, Absorbing Boundary Conditions for the Numerical Simulation of Waves, Math. Comput. 31, No. 139 (1977). [Pg.351]

The development of Remote Field Eddy Current probes requires experience and expensive experiments. The numerical simulation of electromagnetic fields can be used not only for a better understanding of the Remote Field effect but also for the probe lay out. Geometrical parameters of the prohe can be derived from calculation results as well as inspection parameters. An important requirement for a realistic prediction of the probe performance is the consideration of material properties of the tube for which the probe is designed. The experimental determination of magnetization curves is necessary and can be satisfactory done with a simple experimental setup. [Pg.317]

Recently, Langer (1999) has joined the debate. He at first sounds a distinct note of scepticism ... the term numerical simulation makes many of us uncomfortable. It is easy to build models on computers and watch what they do, but it is often unjustified to claim that we learn anything from such exercises. He continues by examining a number of actual simulations and points out, first, the value of [Pg.467]

Figure A3.14.17. Self-replicating spots in the FIS reaction in a CFUR, comparing an experimental time sequence with numerical simulation based on a simple autocatalytic scheme. (Reprmted with pennission from Lee etal [M], Macmillan Magazines Ltd. 1994.) |

Straub J E and Berne B J 1986 Energy diffusion in many dimensional Markovian systems the consequences of the competition between inter- and intra-molecular vibrational energy transfer J. Chem. Phys. 85 2999 Straub J E, Borkovec M and Berne B J 1987 Numerical simulation of rate constants for a two degree of freedom system in the weak collision limit J. Chem. Phys. 86 4296 [Pg.897]

The present book, with contributions from a group of very knowledgable scientists in the field, is an attempt to provide a basis for addressing Bridgman s concerns. The response requires multidisciplinary contributions from solid mechanics, solid-state physics, materials science, and solid-state chemistry. Certainly, advances in theory, experimentation, and numerical simulation are impressive, and many aspects of shock-compressed solids have been studied in detail. At the fundamental level, however, it is certainly appropriate to question how well shock-compression processes are understood. [Pg.2]

As these examples have demonstrated, in particular for fast reactions, chemical kinetics can only be appropriately described if one takes into account dynamic effects, though in practice it may prove extremely difficult to separate and identify different phenomena. It seems that more experiments under systematically controlled variation of solvent enviromnent parameters are needed, in conjunction with numerical simulations that as closely as possible mimic the experimental conditions to improve our understanding of condensed-phase reaction kmetics. The theoretical tools that are available to do so are covered in more depth in other chapters of this encyclopedia and also in comprehensive reviews [6, 118. 119], [Pg.863]

Caustics The above formulae can only be valid as long as Eq. (9) describes a unique map in position space. Indeed, the underlying Hamilton-Jacobi theory is only valid for the time interval [0,T] if at all instances t [0, T] the map (QOi4o) —> Q t, qo,qo) is one-to-one, [6, 19, 1], i.e., as long as trajectories with different initial data do not cross each other in position space (cf. Fig. 1). Consequently, the detection of any caustics in a numerical simulation is only possible if we propagate a trajectory bundle with different initial values. Thus, in pure QCMD, Eq. (11), caustics cannot be detected. [Pg.384]

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