Begell House
International Journal for Multiscale Computational Engineering
International Journal for Multiscale Computational Engineering
1543-1649
6
6
2008
Preface
vii-ix
Multiscale Finite Elements for Acoustics: Continuous, Discontinuous, and Stabilized Methods
This work describes two perspectives for understanding the numerical difficulties that arise in the solution of wave problems, and various advances in the development of efficient discretization schemes for acoustics. Standard, low-order, continuous Galerkin finite element methods are unable to cope with wave phenomena at short wave lengths because the computational effort required to resolve the waves and control numerical dispersion errors becomes prohibitive. The failure to adequately represent subgrid scales misses not only the fine-scale part of the solution, but often causes severe pollution of the solution on the resolved scale as well. Since computation naturally separates the scales of a problem according to the mesh size, multi-scale considerations provide a useful framework for viewing these difficulties and developing methods to counter them. The Galerkin/least squares method arises in multiscale settings, and its stability parameter is defined by dispersion considerations. Bubble enriched methods employ auxiliary functions that are usually expressed in the form of infinite series. Dispersion analysis provides guidelines for the implementation of the series representation in practice. In the discontinuous enrichment method, the fine scales are spanned by free-space homogeneous solutions of the governing equations. These auxiliary functions may be discontinuous across element boundaries, and continuity is enforced weakly by Lagrange multipliers.
Isaac
Harari
Tel-Aviv University
511-531
A Fictitious Source Method for a Multifrequency Acoustic Source over Ground with Given Impedance
Linear multifrequency acoustics problems in the atmospheric half-space, over flat ground with given impedance, occur in various applications, for example, in environmental engineering, where the analysis of the sound pressure level (SPL) distribution near the ground due to aircraft noise is desired. Since the human hearing range is very wide, the determination of the SPL distribution for a given source spectrum is not trivial and may be regarded as a multi-scale problem. To this end, one has to solve repeatedly, for many different wave numbers, the Helmholtz equation in the upper half-space, while imposing the given impedance boundary condition. A simple computational scheme, based on the use of fictitious sources, is devised for the efficient solution of these problems, leading to an effective SPL calculation. The computational aspects of the method are discussed, and its performance is demonstrated via numerical examples.
Ido
Gur
Department of Aerospace Engineering, Technion—Israel Institute of Technology, Haifa 32000, Israel
Dan
Givoli
Department of Aerospace Engineering, Technion−Israel Institute of Technology, Haifa 32000, Israel; Faculty of Civil Engineering & Geosciences, Technical University of Delft, 2600 GA Delft, The Netherlands
533-548
Investigation of the Dynamic Behavior of Bridged Nanotube Resonators by Dissipative Particle Dynamics Simulation
Carbon nanotube (CNT)-based bridged resonators are investigated using a mesoscale dissipative particle dynamics model. Owing to their nanometer size, low mass, and ultrahigh resonance frequency, CNT-based resonators have the potential to become excellent tension, strain, or mass sensors. In this report, the resonance frequency of tubes of different lengths and in different states of tension is extracted from the numerical results and shown to fit with continuum elastic theory. Since in many cases, CNTs are produced slacked rather than taut, the effect of slackness on the resonance frequencies is presented and shown to reduce the sensitivity of the resonator considerably. According to our simulations, temperature has a major effect on the resonance frequencies and should be considered when analyzing bridged resonators. The investigation includes measurements of the vibration amplitude at different temperature, tube length, and strain. The intrinsic quality factor of carbon nanotube resonators is also discussed. Finally, the simulations presented here show that the dissipative particle dynamics model is suited to describe CNT devices such as resonator-based sensors.
Orly
Liba
School of Electrical Engineering, Department of Physical Electronics, The Iby and Aladar Fleischman Faculty of Engineering, Tel-Aviv University, Tel-Aviv 69978, Israel
Yael
Hanein
School of Electrical Engineering, Department of Physical Electronics, The Iby and Aladar Fleischman Faculty of Engineering, Tel-Aviv University, Israel
David
Kauzlaric
Laboratory for Microsystems Simulation, Department of Microsystems Engineering, University of Freiburg, Germany
Andreas
Greiner
Laboratory for Microsystems Simulation, Department of Microsystems Engineering, University of Freiburg, Germany
Jan G.
Korvink
Laboratory for Microsystems Simulation, Department of Microsystems Engineering, University of Freiburg, Germany
549-562
Parametric Excitation and Stabilization of Electrostatically Actuated Microstructures
The parametric instability of double-clamped microscale beams actuated by a time-varying distributed electrostatic force provided by two electrodes symmetrically located at two sides of the beam and subjected to nonlinear squeeze film damping is investigated. A reduced-order model is built using the Galerkin decomposition with undamped linear modes as base functions. The stability analysis is performed by evaluating the sign of the largest Lyapunov exponent, which defines the character of the response. It is shown that this approach provides an efficient quantitative criterion for the evaluation of parametric instability, especially when combined with compact reduced-order models. Based on the Lyapunov exponent criterion, the influence of various parameters on the beam dynamic stability is investigated. We show that application of a time-dependent (ac) voltage in addition to a steady (dc) voltage exceeding the static stability limit may have a stabilizing influence while the structure, in accordance with the Lyapunov exponent criterion, remains stable. Parametric stabilization considered in this work represents an example of the strong influence of the fast-scale excitation on the slow-scale behavior.
Slava
Krylov
School of Mechanical Engineering, Tel Aviv University, Israel
563-584
Modeling the Impact of Flow Modulation on Surface Structure during the Growth of Potassium Dihydrogen Phosphate Single Crystals from Solution
We study the influence of liquid-phase flow on a potassium dihydrogen phosphate (KDP) crystal growing from solution. In particular, we focus on the effect of modulated flow on the structure of the crystalline surface both from microscopic and from macroscopic viewpoints. Our microscopic model, based on a phase-field representation of steps, correctly predicts the appearance of step bunching due to (destabilizing) solution flow in the direction of step motion; suppression of step bunches by modulating the direction of flow above the crystal surface is analyzed with this model. At the same time, our macroscopic model uncovers complications associated with flow modulation. Resultant spatiotemporal changes in the supersaturation field along the crystal surface may lead to time-dependent rates of step generation at active step sources, causing variations in the crystal slope (i.e., weak step bunching), as well as promoting periodic reversal of the step flow direction along portions of the surface. Revisiting the microscopic model, with boundary conditions modified to account for these macroscopic observations, reveals more clearly the possible impact of these complications on crystalline quality. Our microscopic and macroscopic observations suggest the need for nontrivial multi-scale analyses for the investigation of modulation or even more complex time-dependent flows as possible tools for effectively controlling flow-driven step bunching during crystal growth from solution.
Igal
Rasin
Department of Chemical Engineering, Technion-Israel Institute of Technology Haifa 32000, Israel
Simon
Brandon
Department of Chemical Engineering, Technion-Israel Institute of Technology, Israel
Oleg
Weinstein
Institute for Crystal Growth (IKZ), Max-Born-Str.2,12489 Berlin, Germany
585-601
Multistep One-Way Nesting Scaling Approach to the Numerical Solution of Pedestrian Comfort-Related Wind Effects around a Tall Building
This work describes the application of a one-way nesting numerical method aimed at analyzing the pedestrian-level wind distribution around a tall building in addition to proposing and evaluating wind-mitigating barrier configurations. The implemented nesting procedure is termed "one-way" because it is assumed that the far-field boundary condition is dictated by the regional winds, regardless of the geometry of the site and its influence on the local fluid flow field. A consistent domain-reducing technique is used in order to achieve adequate domain discretization resolution without exceeding limited memory resources. The evaluation of the existing configuration and the consolidation of different mitigation configurations are accomplished through numerical experimentation before actual wind tunnel tests are carried out. The number of configurations to be tested in the wind tunnel is therefore reduced. Expected mitigation results for some of the areas under analysis are presented in detail.
Amiel
Herszage
Israel Electric Corporation Ltd.; and Technion-Israel Institute of Technology
603-615
A Scale-Consistent Approach to Image Completion
Most patch based algorithms for completing missing parts of images fill in the absent regions by copying patches from the known part of the image into the unknown part, somewhat like plastic surgery. The criterion for deciding which patch to copy is compatibility of the copied patch with the vicinity of the region being completed. In this article we propose introducing a new dimension to this compatibility criterion, namely, scale. The patch is thus chosen by evaluating its consistency with respect to a hierarchy of smoothed (less detailed) versions of the image as well as its surroundings in the current version. Applied recursively, this approach results in a multiscale framework that is shown to yield a dramatic improvement in the robustness of patch-based image completion.
Irad
Yavneh
Technion-Israel Institute of Technology
Michal
Holtzman-Gazit
CS Department, Technion-Israeli Institute of Technology, Haifa 32000, Israel
617-628