Numerical-Value Perturbation Method with Application of Solving Convective-Diffusion Integral Equation

The convective--diffusion equation is of primary importance in such fields as fluid dynamics and heat transfer hi the numerical methods solving the convective-diffusion equation, the finite volume method can use conveniently diversified grids (structured and unstructured grids) and is suitable for very complex geometry The disadvantage of FV methods compared to the finite difference method is that FV-methods of order higher than second are more difficult to develop in three-dimensional cases. The second-order central scheme (2cs) offers a good compromise among accuracy, simplicity and efficiency, however, it will produce oscillatory solutions when the grid Reynolds numbers are large and then very fine grids are required to obtain accurate solution. The simplest first-order upwind (IUW) scheme satisfies the convective boundedness criteria, however. Its numerical diffusion is large. The power-law scheme, QMCK and second-order upwind (2UW) schemes are also often used in some commercial codes. Their numerical accurate are roughly consistent with that of ZCS. Therefore, it is meaningful to offer higher-accurate three point FV scheme. In this paper, the numerical-value perturbational method suggested by Zhi Gao is used to develop an upwind and mixed FV scheme using any higher-order interpolation and second-order integration approximations, which is called perturbational finite volume (PFV) scheme. The PFV scheme uses the least nodes similar to the standard three-point schemes, namely, the number of the nodes needed equals to unity plus the face-number of the control volume. For instanc6, in the two-dimensional (2-D) case, only four nodes for the triangle grids and five nodes for the Cartesian grids are utilized, respectively. The PFV scheme is applied on a number of 1-D problems, 2~Dand 3-D flow model equations. Comparing with other standard three-point schemes, The PFV scheme has much smaller numerical diffusion than the first-order upwind (IUW) scheme, its numerical accuracy are also higher than the second-order central scheme (2CS), the power-law scheme (PLS), the QUICK scheme and the second-order upwind(ZUW) scheme.

Development of a Cell Size Relaxed Scheme for the Direct Simulation Monte Carlo Method

The conventional direct simulation Monte Carlo (DSMC) method has a strong restriction on the cell size because simulated particles are selected randomly within the cell for collisions. Cells with size larger than the molecular mean free path are generally not allowed in correct DSMC simulations. However, the cell-size induced numerical error can be controlled if the gradients of flow properties are properly involved during collisions. In this study, a large cell DSMC scheme is proposed to relax the cell size restriction. The scheme is applied to simulate several test problems and promising results are obtained even when the cell size is greater than 10 mean free paths of gas molecules. However, it is still necessary, of course, that the cell size be small with respect to the flow field structures that must be resolved.

Size-dependent elastic properties of Ni nanofilms by molecular dynamics simulation

Size-dependent elastic properties of Ni nanofilms are investigated by molecular dynamics ( MD) simulations with embedded atom method (EAM). The surface effects are considered by calculating the surface relaxation, surface energy, and surface stress. The Young's modulus and yield stress are obtained as functions of thickness and crystallographic orientation. It is shown that the surface relaxation has important effects on the the elastic properties at nanoscale. When the surface relaxation is outward, the Young's modulus decreases with the film thickness decreasing, and vice versa. The results also show that the yield stresses of the films increase with the films becoming thinner. With the thickness of the nanofilms decreasing, the surface effects on the elastic properties become dominant.

Rarefied gas dynamics: fundamentals, simulations and micro flows

Population dynamics of the anchoveta, Cetengraulis mysticetus, in the Gulf of Panama, as determined by tagging experiments

ENGLISH: The anchoveta is the major constituent of the important bait and reduction fisheries of the Gulf of Panama. It is a short-lived species, the great majority of the catch consisting of fish in their first year of life. Fish for reduction are caught chiefly in the Isla Verde area, between Punta Chame and the entrance of the Panama Canal. In 1960 and 1961 anchovetas were tagged with metal internal tags and released in the major areas of occurrence of this species. The tags were recovered from the meal in the reduction plants with magnets. From the 53,380 fish tagged in 1960, 745 tags were returned during the 1960 season, 246 during the 1961 season, and 8 during the 1962 season. From the 113,202 tagged in 1961, 373 tags were returned during the 1961 season and 48 during the 1962 season. Complete catch statistics are available, and length-frequency and length-weight data were used to convert these from pounds to numbers of fish of each year class. The annual survival rate for the fish of the 1959 year class in the Isla Verde area was estimated to be 0.086 by the Chapman-Robson method, 0.102 by the year-class method, and 0.088 by the Jackson positive method. The first method is considered to give the best estimate. Six estimates of the population of fish of the 1959 year class in the Isla Verde area were obtained from the sample tag ratios of six experiments conducted in that area in 1960. The estimates differed due to the temporal decrease in the population, but the downward trend corresponded fairly well to what was expected from the total annual mortality rate. It was estimated that the population of 1959-year class fish was about 818 million on March 8, 1960, and about 70 million on March 8, 1961. As the population of anchovetas decreases during the season the effort increases sufficiently that the catch remains roughly constant. This is described as the "constant absolute catch" type fishery. Of the original population of fish in the Isla Verde area at the beginning of the 1960 season, about 11 per cent were caught and 81 per cent died of natural causes. Evaluation of growth and mortality data demonstrated that beginning the fishery for the youngest age group later than March 8 (the date it began in 1960) would reduce the yield per recruit, while increasing the fishing effort would greatly increase it. Further, it is believed unlikely that increases in the catch in the Isla Verde area alone would noticeably decrease the number of recruits to that area. Therefore there is no foreseeable need for regulation of the fishery. SPANISH: El principal constituyente de la importante pesquería para carnada y para reducción en el Golfo de Panamá es la anchoveta. Es una especie de vida corta cuya pesca, en su mayor parte, está constituida por peces que se encuentran en su primer año de vida. Para la industria de reducción los peces son capturados principalmente en el área de Isla Verde, entre Punta Chame y la entrada del Canal de Panamá. En 1960 y 1961 las anchovetas fueron marcadas con marcas metálicas internas y liberadas en las áreas más importantes en que se encuentra esta especie. Las marcas fueron recobradas de la harina en las plantas de reducción por medio de magnetos. De los 53,380 peces marcados en 1960, fueron devueltas 745 marcas durante la temporada pesquera de 1960, 246 durante la de 1961, y 8 durante la de 1962. De los 113,202 marcados en 1961, 373 marcas fueron devueltas durante la temporada pesquera de 1961 y 48 durante la de 1962. Se dispone de estadísticas completas de captura, y los datos de frecuencia-longitud y de longitud-peso fueron usados para convertir éstos de libras a números de peces de cada clase anual. La tasa anual de supervivencia correspondiente a la clase anual de 1959 en el área de Isla Verde estimó en 0.086 por medio del método Chapman-Robson; en 0.102 por método de la clase anual; y en 0.088 por el método positivo de Jackson. Se considera que el primer método dé la mejor estimación. Seis estimaciones de la población de peces de la clase anual 1959 en el área de Isla Verde fueron obtenidas según la proporción de marcas halladas en las muestras correspondientes a seis experimentos efectuados en aquella área en 1960. Las estimaciones variaron debido a la disminución temporal de la población, pero esta tendencia descendente correspondió bastante bien a lo que se esperaba según la tasa total de mortalidad anual. Se estimó que la población de peces de la clase anual de 1959 era de unos 818 millones el 8 de marzo de 1960, y aproximadamente de unos 70 millones el 8 de marzo de 1961. Conforme a que la población de anchovetas disminuye durante la temporada pesquera, el esfuerzo aumenta lo suficientemente como para que la pesca se mantenga más o menos constante. Este es el tipo de pesquería descrito como de "captura absoluta constante". De la población original de peces en el área de Isla Verde al comienzo de la temporada pesquera de 1960, cerca del 11 por ciento fue capturada y el 81 por ciento murió por causas naturales. La evaluación de los datos del crecimiento mortalidad demostraron que al comenzar la pesquería a explotar grupo de edad más joven en una fecha posterior al 8 de marzo (la fecha en que comenzó en 1960) se reduciría el rendimiento por recluta, mientras que al aumentar el esfuerzo de pesca lo aumentaría considerablemente. Más aún, se cree improbable que el aumento en la pesca en el área de Isla Verde de por sí disminuyera perceptiblemente el número de reclutas en esa área. En consecuencia no se prevé la necesidad de una reglamentación de la pesquería. (PDF contains 172 pages.)

Using the system dynamics paradigm in teaching and learning technological university subjets

2nd International Conference on Education and New Learning Technologies

Numerical study on heavy rigid particle motion in a plane wake flow by spectral element method

Experimental particle dispersion patterns in a plane wake flow at a high Reynolds number have been predicted numerically by discrete vortex method (Phys. Fluids A 1992; 4:2244-2251; Int. J. Multiphase Flow 2000; 26:1583-1607). To address the particle motion at a moderate Reynolds number, spectral element method is employed to provide an instantaneous wake flow field for particle dynamics equations, which are solved to make a detail classification of the patterns in relation to the Stokes and Froude numbers. It is found that particle motion features only depend on the Stokes number at a high Froude number and depend on both numbers at a low Froude number. A ratio of the Stokes number to squared Froude number is introduced and threshold values of this parameter are evaluated that delineate the different regions of particle behavior. The parameter describes approximately the gravitational settling velocity divided by the characteristic velocity of wake flow. In order to present effects of particle density but preserve rigid sphere, hollow sphere particle dynamics in the plane wake flow is investigated. The evolution of hollow particle motion patterns for the increase of equivalent particle density corresponds to that of solid particle motion patterns for the decrease of particle size. Although the thresholds change a little, the parameter can still make a good qualitative classification of particle motion patterns as the inner diameter changes.

Large-eddy simulation of flows past a flapping airfoil using immersed boundary method

The numerical simulation of flows past flapping foils at moderate Reynolds numbers presents two challenges to computational fluid dynamics: turbulent flows and moving boundaries. The direct forcing immersed boundary (IB) method has been devel- oped to simulate laminar flows. However, its performance in simulating turbulent flows and transitional flows with moving boundaries has not been fully evaluated. In the present work, we use the IB method to simulate fully developed turbulent channel flows and transitional flows past a stationary/plunging SD7003 airfoil. To suppress the non-physical force oscillations in the plunging case, we use the smoothed discrete delta function for interpolation in the IB method. The results of the present work demonstrate that the IB method can be used to simulate turbulent flows and transitional flows with moving boundaries.

Splitting the fast and slow motions in molecular dynamics simulations based on the change of cold potential well bottom

Abstract. The atomic motion is coupled by the fast and slow components due to the high frequency vibration of atoms and the low frequency deformation of atomic lattice, respectively. A two-step approximate method was presented to determine the atomic slow motion. The first step is based on the change of the location of the cold potential well bottom and the second step is based on the average of the appropriate slow velocities of the surrounding atoms. The simple tensions of one-dimensional atoms and two-dimensional atoms were performed with the full molecular dynamics simulations. The conjugate gradient method was employed to determine the corresponding location of cold potential well bottom. Results show that our two-step approximate method is appropriate to determine the atomic slow motion under the low strain rate loading. This splitting method may be helpful to develop more efficient molecular modeling methods and simulations pertinent to realistic loading conditions of materials.

Dissipative particle dynamics simulation of wettability alternation phenomena in the chemical flooding process

Wettability alternation phenomena is considered one of the most important enhanced oil recovery (EOR) mechanisms in the chemical flooding process and induced by the adsorption of surfactant on the rock surface. These phenomena are studied by a mesoscopic method named as dissipative particle dynamics (DPD). Both the alteration phenomena of water-wet to oil-wet and that of oil-wet to water-wet are simulated based on reasonable definition of interaction parameters between beads. The wetting hysteresis phenomenon and the process of oil-drops detachment from rock surfaces with different wettability are simulated by adding long-range external forces on the fluid particles. The simulation results show that, the oil drop is liable to spread on the oil-wetting surface and move in the form of liquid film flow, whereas it is likely to move as a whole on the water-wetting surface. There are the same phenomena occuring in wettability-alternated cases. The results also show that DPD method provides a feasible approach to the problems of seepage flow with physicochemical phenomena and can be used to study the mechanism of EOR of chemical flooding.

Periodic solutions of integro-differential equations which arise in population dynamics

The problem of the existence and stability of periodic solutions of infinite-lag integra-differential equations is considered. Specifically, the integrals involved are of the convolution type with the dependent variable being integrated over the range (- ∞,t), as occur in models of population growth. It is shown that Hopf bifurcation of periodic solutions from a steady state can occur, when a pair of eigenvalues crosses the imaginary axis. Also considered is the existence of traveling wave solutions of a model population equation allowing spatial diffusion in addition to the usual temporal variation. Lastly, the stability of the periodic solutions resulting from Hopf bifurcation is determined with aid of a Floquet theory.

The first chapter is devoted to linear integro-differential equations with constant coefficients utilizing the method of semi-groups of operators. The second chapter analyzes the Hopf bifurcation providing an existence theorem. Also, the two-timing perturbation procedure is applied to construct the periodic solutions. The third chapter uses two-timing to obtain traveling wave solutions of the diffusive model, as well as providing an existence theorem. The fourth chapter develops a Floquet theory for linear integro-differential equations with periodic coefficients again using the semi-group approach. The fifth chapter gives sufficient conditions for the stability or instability of a periodic solution in terms of the linearization of the equations. These results are then applied to the Hopf bifurcation problem and to a certain population equation modeling periodically fluctuating environments to deduce the stability of the corresponding periodic solutions.

A perturbation procedure for nonlinear oscillations (The dynamics of two oscillators with weak nonlinear coupling)

This thesis considers in detail the dynamics of two oscillators with weak nonlinear coupling. There are three classes of such problems: non-resonant, where the Poincaré procedure is valid to the order considered; weakly resonant, where the Poincaré procedure breaks down because small divisors appear (but do not affect the O(1) term) and strongly resonant, where small divisors appear and lead to O(1) corrections. A perturbation method based on Cole's two-timing procedure is introduced. It avoids the small divisor problem in a straightforward manner, gives accurate answers which are valid for long times, and appears capable of handling all three types of problems with no change in the basic approach.

One example of each type is studied with the aid of this procedure: for the nonresonant case the answer is equivalent to the Poincaré result; for the weakly resonant case the analytic form of the answer is found to depend (smoothly) on the difference between the initial energies of the two oscillators; for the strongly resonant case we find that the amplitudes of the two oscillators vary slowly with time as elliptic functions of ϵ t, where ϵ is the (small) coupling parameter.

Our results suggest that, as one might expect, the dynamical behavior of such systems varies smoothly with changes in the ratio of the fundamental frequencies of the two oscillators. Thus the pathological behavior of Whittaker's adelphic integrals as the frequency ratio is varied appears to be due to the fact that Whittaker ignored the small divisor problem. The energy sharing properties of these systems appear to depend strongly on the initial conditions, so that the systems not ergodic.

The perturbation procedure appears to be applicable to a wide variety of other problems in addition to those considered here.

Application of the Schwinger multichannel method to multichannel studies of electronically inelastic electron-molecule collisions

We have applied the Schwinger Multichannel Method(SMC) to the study of electronically inelastic, low energy electron-molecule collisions. The focus of these studies has been the assessment of the importance of multichannel coupling to the dynamics of these excitation processes. It has transpired that the promising quality of results realized in early SMC work on such inelastic scattering processes has been far more difficult to obtain in these more sophisticated studies.

We have attempted to understand the sources of instability of the SMC method which are evident in these multichannel studies. Particular instances of such instability have been considered in detail, which indicate that linear dependence, failure of the separable potential approximation, and difficulties in converging matrix elements involving recorrelation or Q-space terms all conspire to complicate application of the SMC method to these studies. A method involving singular value decomposition(SVD) has been developed to, if not resolve these problems, at least mitigate their deleterious effects on the computation of electronically inelastic cross sections.

In conjunction with this SVD procedure, the SMC method has been applied to the study of the H_2 , H_2O, and N_2 molecules. Rydberg excitations of the first two molecules were found to be most sensitive to multichannel coupling near threshold. The (3σ_g → 1π_g ) and (1π_u → 1π_g) valence excitations of the N_2 molecule were found to be strongly influenced by the choice of channel coupling scheme at all collision energies considered in these studies.

Ablation and ultrafast dynamics of zinc selenide under femtosecond laser irradiation

The ablation in zinc selenide (ZnSe) crystal is studied by using 150-fs, 800-nm laser system. The images of the ablation pit measured by scanning electronic microscope (SEM) show no thermal stress and melting dynamics. The threshold fluence is measured to be 0.7 J/cm2. The ultrafast ablation dynamics is studied by using pump and probe method. The result suggests that optical breakdown and ultrafast melting take place in ZnSe irradiated under femtosecond laser pulses.