Finite Difference

Imaging techniques for geophysic prospection of sea bottom are extremely demanding in terms of mathematical methods and computational resources (8). This is because the measurements are going deeper than before, thus making the structures identification a hard task, a nd the datasets to be com- puted huge. Besides, the current trend is to analyze the images in three dimensions (3D) (4), adding an extra difficulty to the process. Currently, the prospection process is h ighly automatized by computer programs, where these programs not only implement and solve the mathematical model, but also carry the burden of the datasets manipulation, particularly in pre and post proces sing. All of these demands (complex mathematical models to be solved and huge datasets to be manipulated) lead us to high per- formance computing (HPC) environments, which are mainly available by supercomputers composed by thousands of computational nodes, thus efficient parallelization of those c omputer programs is...

Although several models have been developed to describe the evaporative casting of dense polymer films, none of them has included the convective transport terms which arise owing to the densification which occurs. In this paper we first describe a new finite element solution to the binary nonisothermal evaporative casting process which is used to confirm the predictions of the finite

A theoretical investigation on the performance prediction of solar still is presented in this paper. A solar still of conventional type is considered. The mathematical model is based on time-averaged Navier-Stokes equations. The effect of the variable fluid properties is taken into consideration by using a mixture of air and vapour in the still. A steady state twodimensional approach with constant temperature boundaries is considered. A discretization schema with finite-difference technique is adapted. The SIMPLER (Semi-Implicit Method for Pressure-Linked Equations Revised) methodology is used. The grid size independence solution is checked for convergence. The numerical results show clearly different zones of circulation with reverse velocity on the inside still glass cover. The numerical results prove the necessity to undertake a numerical investigation before the sizing of solar still. The objective of the present investigation is to present a mathematical model in order to impro...

A hybrid in situ bioremediation/pulsed pumping strategy has been developed to cost effectively remediate a carbon tetrachloride plume in Schoolcraft, Michigan. The pulsed pumping system uses a line of alternating injection and extraction wells perpendicular to the direction of natural groundwater flow. The wells pump periodically to clean the recirculation zone between adjacent wells. During the pump-off phase, natural groundwater flow brings new contaminant into the recirculation zone. The wells are pumped again prior to breakthrough of contaminant from the recirculation zone.A computationally efficient reactor model has been developed, which conceptually divides the aquifer into injection, extraction, and recirculation zones, which are represented by a network of chemical reactors. Solute concentration histories from three-dimensional finite difference simulations and from field data confirm the reactor model predictions. The reactor model is used to investigate the optimal well c...

A hybrid method, coupling a ray tracing method and a finite difference approach, is proposed for modelling T-wave propagation from an underwater source to an on-land seismic station. The long-range hydroacoustic wavefield, estimated in the SOFAR channel by the Maslov approach, shows many triplications of propagation with an increasing number of caustics as the range increases. Ray tracing approaches lead to a straightforward analysis of the SOFAR propagation: we find that the duration and the amplitude of the hydroacoustic T waves generated by a source close to the SOFAR axis may be respectively eight times longer and almost seven times higher than the duration and the amplitude of hydroacoustic T waves generated by a source close to the SOFAR limits. The finite difference modelling handles the complex hydroacoustic–seismi c T-wave conversion on atoll shores with an illustration of seismic T waves recorded during the Midplate experiment in 1989. Two different seismic stations, FGA on the Fangataufa Atoll and DIN on the Mururoa Atoll, both in French Polynesia, have recorded the seismic T waves due to an underwater chemical blast at a distance greater than 900 km. Synthetic seismograms computed by our proposed hybrid method are close enough to the real data for quantitative interpretation. We believe that the input model structure is accurate enough to allow such analysis of the seismic T waves. The numerical simulation shows that the seismic T waves recorded at both stations are mainly composed of P phases and Rayleigh phases. The simulation shows that the seismic T-wave duration is often linked to the source depth, although other factors (the continental slope or the distance between the top of the continental slope and the seismic station) may also affect the signal duration.

As far as we are concerned, the implementation of the finite differences in the time domain (FDTD) method requires, for the solutions of several practical problems in electromagnetism, a long process time and a large amount of memory, what makes it impracticable in various cases, principally when the serial process is used. The current work deals with the conception of a Beowulf cluster and it aims to implement the FDTD method using parallel process for the study of antennas. The obtained system efficiency is then tested in the analysis of a monopole antenna, what is done by comparing the time spent in the parallel and serial processing.

There has been a rapid development of electronic devices and competition among the elec-tronic companies to produce smaller and lighter devices with high performance, reliability and multi-functionality. This results in the adjustment of increasing number of electronic compo-nents called chips. The demand of small shape and size of the devices needs micro analysis in this field. To adjust maximum number of chips, the space among them should be minimized. But the problem is that each of the chips can generate a significant amount of heat which can degrade the performance of the device and some of the chips could be completely damaged be-cause of high temperature. Each of the components has its own maximum tolerate temperature and if this temperature exceeds, the component may not function properly or could be dam-aged completely. Thus the thermal management is an important issue for both in electronic components and the board (Printed Circuit Board) where they will be placed. This pa...

A finite difference technique is developed to predict the second stage creep displacement rates and stress analysis of a short fiber metal matrix composite subjecting to a constant axial load through a micromechanical approach. The technique is capable to take into account the presence of interfacial debonding as one of the main factors affecting the creep performance of short fiber composites. The exponential law is adopted to describe the matrix creep behavior. Also, a model for prediction of interfacial debonding at fiber/matrix interface is developed using a stress based method. The obtained results could greatly help to better understand the flow pattern of matrix material and the load transfer mechanism between fiber and matrix with and without the presence of interfacial debond. The predicted strain rate by the proposed approach exhibits good agreement with the experimental results.

Brizolis asked the question: does every prime p have a pair (g,h) such that h is a fixed point for the discrete logarithm with base g? The first author previously extended this question to ask about not only fixed points but also two-cycles, and gave heuristics (building on work of Zhang, Cobeli, Zaharescu, Campbell, and Pomerance) for estimating the number of such pairs given certain conditions on g and h. In this paper we extend these heuristics and prove results for some of them, building again on the aforementioned work. We also make some new conjectures and prove some average versions of the results.

Numerical simulation of fluid flow and transport processes in the subsurface must account for the presence of wells. The pressure at a gridblock that contains a well is different from the average pressure in that block and different from the flowing bottom hole pressure for the well (17). Various finite difference well models have been developed to account for the difference. This paper presents a systematical derivation of well models for other numerical methods such as standard finite element, control volume finite element, and mixed finite element methods. Numerical results for a simple well example illustrating local grid refinement effects are given to validate these well models. The well models have particular applications to groundwater hydrology and petroleum reservoirs. Numerical simulation of fluid flow and transport processes in the subsurface must account for the presence of wells. The pressure at a gridblock that contains a well is different from the average pressure in...

Numerical simulation based on finite numerical methods is used to predict the production process by injection molding of two polymers parts used in low cost domestic refrigerators. The Hele-Shaw fluid mechanics model along with the volume of fluid method are used to calculate velocity and pressure for non- newtonian polymer flows during the injection process using finite elements. The energy equation, with transient, convective, diffusive and viscous dissipation terms, describing the cooling process of the heated polymer while being injected in the cold mold, is solved by the finite difference method. Results for the time evolution of polymer front, pressure and temperature distributions during injection of Polystrol 495F in the mould cavity to produce the freezer door, obtained from two different non-newtonian fluid models, three mold temperatures and two thickness are presented. The effects of the location of the injection point and heat transfer coefficient between polymer flow a...

Résumé -On propose une étude numérique, par différences finies, du transfert de chaleur dans un mur multicouche (à deux ou trois couches) soumis à une condition de rayonnement solaire sur le côté extérieur et prenant en compte les échanges de chaleur par convection sur ses deux faces. L'exploitation du code numérique est développée sur des cas relatifs au problème posé dans l'habitat. Les résultats numériques sont présentés sur des exemples de matériaux utilisés dans le domaine du bâtiment dans des conditions réelles de fonctionnement (flux solaire, pertes convectives, etc…). On analyse également, l'influence, sur le transfert de chaleur, de quelques paramètres clés du système comme le choix des matériaux, l'optimisation de leur épaisseur et également la nature variable du flux solaire. Une proposition optimale sera dégagée de cette étude en fonction des objectifs recherchés. Abstract -We propose a numerical study by finite differences, of the heat transfer in a mult...