J.M. McDonough

An alternative discretization and solution procedure for the dual phase-lag equation

We describe an alternative numerical treatment of the dual phase-lag equation often used to account for microscale, short-time heat transport. The approach consists of an undecomposed formulation of the partial differential equation resulting from Taylor expansion with respect to lag times of the original delay partial differential equation. Trapezoidal integration in time and centered differencing in space provide an accurate discretization, as demonstrated by comparisons with analytical and experimental results in one dimension, and via grid-function convergence tests in three dimensions. For relatively fine 3-D grids the approach is approximately six times faster than a standard explicit scheme and nearly three times faster than an implicit method employing conjugate gradient iteration at each time step.

Fractal Analysis of Eye Movements during Reading

We present a new method for the analysis of reading eye movements based on the methods of nonlinear dynamics. In this preliminary study, the eye movements of normal and abnormal readers were analyzed for evidence of chaotic, nonlinear dynamical behavior. Both power spectral density analysis and fractal dimension determination showed evidence of nonlinearity as manifest in chaotic behavior. The computed fractal dimension of the system’s presumed attractor seemed directly related to qualitative assessment of reading ability. Representative subjects did not differ in a similar analysis of pursuit movements. Although fractal analysis did not distinguish unconditionally between normal and abnormal reading in this preliminary study, it nevertheless offers a promising hitherto unused approach to the analysis of eye movements and the modeling of oculomotor behavior.

A numerical procedure for solving 2D phase-field model problems

We present a general 2D phase-field model, but without anisotropy, applied to freezing into a supercooled melt of pure nickel. The complete numerical procedure and details of assigning the numerical parameters are provided; convergence of the numerical method is demonstrated by conducting grid function convergence tests. The physics of solidification problems such as conditions for nucleation and crystal growth rate are discussed theoretically and shown to display at least qualitative agreement numerically. In particular, comparison of the computed critical radius with the theoretical one and the consistency of the computational dendrite structure for different Stefan numbers, the relationship between the growth rate and the Stefan number, etc., with the theoretical and experimental evidence indicate that phase-field models are able to capture the physics of supercooled solidification.

Simulation of Vorticity-Buoyancy Interactions in Fire-Whirl-Like Phenomena

In this study the commercial flow code STAR-CD has been used to simulate a laboratory experiment involving a so-called fire whirl. Such phenomena are typically characterized as exhibiting significantly enhanced mixing and consequently higher combustion rates due to an interaction of buoyancy and vorticity, but the details of this are only beginning to be understood. The present study focuses attention on this interaction in the absence of combustion, thus removing significant complications and allowing a clearer view of the vorticity-buoyancy interaction itself.© 2003 ASME

An Efficient Numerical Procedure for Solving Microscale Heat Transport Equation During Femtosecond Laser Heating of Nanoscale Metal Films

An alternative discretization and solution procedure is developed for implicitly solving a microscale heat transport equation during femtosecond laser heating of nanoscale metal films. The proposed numerical technique directly solves a single partial differential equation, unlike other techniques available in the literature which split the equation into a system of two equations and then apply discretization. It is shown by von Neumann stability analysis that the proposed numerical method is unconditionally stable. The numerical technique is then extended to three space dimensions, and an overall procedure for computing the transient temperature distribution during short-pulse laser heating of thin metal films is presented. Douglas-Gunn time-splitting and delta-form Douglas-Gunn time-splitting methods are employed to solve the discretized 3-D equations; a simple argument for stability is given for the split equation. The performance of the proposed numerical scheme will be compared with the numerical techniques available in the literature and it is shown that the new formulation is comparably accurate and significantly more efficient. Finally, it is shown that numerical predictions agree with available experimental data during sub-picosecond laser heating.Copyright

Parallelization of a Modern CFD Incompressible Turbulent Flow Code

Publisher Summary This chapter outlines the numerical analysis and turbulence modeling of a new large-eddy simulation technique for incompressible flows. It is shown that many opportunities for parallelization occur for the chosen algorithmic structure, and reasonably good speedups with increasing number of processors is observed through 32 processors for a message passing interface (MPI) implementation on a HP SuperDome, even with only partial parallelization. In particular most (but not all) commercial CFD software is based on one form or another of the SIMPLE algorithm. These basic approaches are not efficient for time-dependent simulations that are becoming increasingly more widely performed as computing power continues to improve. The parallelization of these commercial codes in almost all cases has been done long after the codes were originally constructed—that is, they were not designed to be parallelized at the time they were initially coded.

Time-Dependent Model of Forest Fire Spread in Turbulent Gusting Winds

In this paper we describe a model for simulating the spread of large-scale forest fires based on three novel concepts related, respectively to the three main features of the forest-fire problem that make it essentially intractable to simulate from first principles-namely, i) inhomogeneity and irregularity of forest fuel materials, ii) chemistry and radiation, and iii) turbulence. In particular, the complex structural features of the forest are treated as an inhomogeneous, very permeable porous medium; effects of chemistry and radiation are included as a source term in the thermal energy equation, and turbulence is modeled via the standard k-e model. Firebrand trajectories are computed at the end of any given flowfield calculation to estimate maximum spotting distances.

Two-Dimensional Phase-Field Model Applied to Freezing into Supercooled Melt

Cryopreservation of living cells is a necessary part of many medical procedures such as organ transplants and preservation of sperm and oocytes of endangered species. However, there is at least one apparent contradiction between the concept of cryopreservation and experimental findings that cells and tissues can be damaged by the cryopreservation process itself. Successful cryopreservation was made possible by the addition of glycerol as a cryoprotective agent (CPA). A major portion of the damage is due to and occurs during the supercooling of tissues and cells and their environment. Therefore, a detailed understanding of how supercooling impacts biological environments is important to preventing damage to cells and tissues during cryopreservation. Studies of supercooling are complicated due to the inherent instability associated with supercooling and the influence of surface tension as a stabilizing factor and other parameters associated with the liquid-solid phase-change front. The only method that effe...

Local Discrete-Operator Interpolation Solution of the Phase-Field Model

This paper reports continuing work on application of discrete-operator interpolation (DOI) in solving the one-dimensional phase-field model applied to melt-front tracking. DOI is a numerical technique for computing function values not computed at the original grid points of a finite-difference (or finite element) scheme so as to satisfy the discrete governing equations at the new points. The previous study showed that the DOI technique works quite well for the phase-field model problem. The shortcoming of earlier work was global (in space) application of DOI. Due to the fact that at any instant in time, the melt-front of the phase-field model exists within only a small region of space, it is more efficient to employ a local DOI technique. Local DOI interpolates the numerical solutions only in the melt-front region while a standard numerical method is applied in other regions. In this paper, we describe the phase-field model together with the details of the local DOI method and their numerical implementations. The results of the phase-field model are obtained using a Crank-Nicolson finite-difference scheme. The local DOI results are compared with direct numerical simulation results obtained on a very fine grid to demonstrate the advantages of this method.Copyright

Turbulence-radiation interactions in flames: A chaotic-map based formulation

In this paper we report initial efforts in developing large-eddy simulation (LES) subgrid-scale (SGS) models capable of treating turbulence-radiation interactions in sufficient detail to permit calculation of radiation intensity fluctuations on small scales. These models are constructed with a fluctuating component consisting of a discrete dynamical system (chaotic map) and are thus completely deterministic. We present an outline of the development of this formulation and then employ experimental data to generate large-scale behavior permitting what might be viewed as part of an a priori test of the SGS model. We display spatially extensive instantaneous fluctuating temperatures produced by the model as well as time series of fluctuating intensity calculated from the radiative transfer equation at several heights in a pool fire. We conclude that such results are physically realistic (and very efficiently computed) and warrant continued investigations, but we have at this time not yet completely validated the approach due to lack of detailed laboratory data.Copyright