Behavioral, Parameterized, and Broadband Modeling of Wired Interconnects with Internal Discontinuities

We present a complete workflow for the extraction of behavioral reduced-order models of wired interconnect links, including an explicit dependence on geometrical or material parameters describing internal discontinuities that may affect the quality of signal transmission. Thanks to the adopted structure, the models are easily identified from sampled frequency responses at discrete points in the parameter space. Such responses are obtained from off-the-shelf full-wave solvers. A novel algorithm is used for checking and enforcing model stability and passivity, two fundamental requirements for reliably running stable transient simulations. Finally, an ad hoc procedure is devised to synthesize the models as parameterized circuit equivalents, compatible with any SPICE solver. Several examples illustrate and validate the workflow, confirming the suitability of the proposed approach for what-if, parameter sweep, design centering, and optimization through time-domain simulations, possibly including nonlinear devices and terminations

Complex Eigenvalue Analysis for Structures with Viscoelastic Behavior

This document deals with a method for eigenvalue extraction for the analysis of structures with viscoelastic materials. A generalized Maxwell model is used to model linear viscoelasticity. Such kind of model necessitates a state-space formulation to perform eigenvalue analysis with standard solvers. This formulation is very close to ADF formulation. The use of several materials on the same structure and during the same analysis may lead to a large number of internal states. This article purpose is to identify simultaneously all the viscoelastic materials and to constrain them to have the same time-constants. As it is usually possible, the size of the state-space problem is therefore widely reduced. Moreover, an accurate method for reducing mass and stiffness operators is proposed; The enhancement of the modal basis allows to obtain good results with large reduction. As the length of the paper is limited, only theoretical development are presented in the present paper while numerical results will be presented in the conference.Comment: ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC/CIE2011), Washington : France (2011

The effects of large and small-scale topography upon internal waves and implications for tidally induced mixing in sill regions

A free surface non-hydrostatic model in cross-sectional form namely two dimensional in the vertical is used to examine the role of larger scale topography, namely sill width and smaller scale topography namely ripples on the sill upon internal wave generation and mixing in sill regions. The present work is set in the context of earlier work, and the wider literature in order to emphasis the problems of simulating mixing in hydrographic models. Highlights from previous calculations, and references to the literature for detail together with new results presented here with smooth and “ripple” topography are used to show that an idealised cross sectional model can reproduce the dominant features found in observations at the Loch Etive sill. Calculations show that on both the short and long time scales the presence of small scale “ripple” topography influence the mixing and associated Richardson number distribution in the sill region. Subsequent calculations in which the position and form of the small scale sill topography is varied, show for the first time that it is the small scale topography near the sill crest that is particularly important in enhancing mid-water mixing on the lee side of the sill. Both short term and longer term calculations with a reduced sill width, and associated time series, show that as the sill width is reduced the non-linear response of the system increases. In addition Richardson number plots show that the region of critical Richardson number, and hence enhanced mixing increases with time and a reduction in sill width. Calculations in which buoyancy frequency N varies through the vertical show that buoyancy frequency close to the top of the sill is primarily controlling mixing rather than its mean value. Hence a Froude number based on sill depth and local N is the critical parameter, rather than one based on total depth and mean N

Order Out of Chaos: Slowly Reversing Mean Flows Emerge from Turbulently Generated Internal Waves

We demonstrate via direct numerical simulations that a periodic, oscillating mean flow spontaneously develops from turbulently generated internal waves. We consider a minimal physical model where the fluid self-organizes in a convective layer adjacent to a stably stratified one. Internal waves are excited by turbulent convective motions, then nonlinearly interact to produce a mean flow reversing on timescales much longer than the waves' period. Our results demonstrate for the first time that the three-scale dynamics due to convection, waves, and mean flow is generic and hence can occur in many astrophysical and geophysical fluids. We discuss efforts to reproduce the mean flow in reduced models, where the turbulence is bypassed. We demonstrate that wave intermittency, resulting from the chaotic nature of convection, plays a key role in the mean-flow dynamics, which thus cannot be captured using only second-order statistics of the turbulent motions

A reduced-order model of diffusive effects on the dynamics of bubbles

We propose a new reduced-order model for spherical bubble dynamics that accurately captures the effects of heat and mass diffusion. The objective is to reduce the full system of partial differential equations to a set of coupled ordinary differential equations that are efficient enough to implement into complex bubbly flow computations. Comparisons to computations of the full partial differential equations and of other reduced-order models are used to validate the model and establish its range of validity

Reduced-Order Modeling of Diffusive Effects on the Dynamics of Bubbles

The Rayleigh-Plesset equation and its extensions have been used extensively to model spherical bubble dynamics, yet radial diffusion equations must be solved to correctly capture damping effects due to mass and thermal diffusion. The latter are too computationally intensive to implement into a continuum model for bubbly cavitating flows, since the diffusion equations must be solved at each position in the flow. The goal of the present research is to derive a reduced-order model that accounts for thermal and mass diffusion. Motivated by results of applying the Proper Orthogonal Decomposition to data from full radial computations, we derive a model based upon estimates of the average heat transfer coefficients. The model captures the damping effects of the diffusion processes in two ordinary differential equations, and gives better results than previous models

Order Reduction of the Radiative Heat Transfer Model for the Simulation of Plasma Arcs

An approach to derive low-complexity models describing thermal radiation for the sake of simulating the behavior of electric arcs in switchgear systems is presented. The idea is to approximate the (high dimensional) full-order equations, modeling the propagation of the radiated intensity in space, with a model of much lower dimension, whose parameters are identified by means of nonlinear system identification techniques. The low-order model preserves the main structural aspects of the full-order one, and its parameters can be straightforwardly used in arc simulation tools based on computational fluid dynamics. In particular, the model parameters can be used together with the common approaches to resolve radiation in magnetohydrodynamic simulations, including the discrete-ordinate method, the P-N methods and photohydrodynamics. The proposed order reduction approach is able to systematically compute the partitioning of the electromagnetic spectrum in frequency bands, and the related absorption coefficients, that yield the best matching with respect to the finely resolved absorption spectrum of the considered gaseous medium. It is shown how the problem's structure can be exploited to improve the computational efficiency when solving the resulting nonlinear optimization problem. In addition to the order reduction approach and the related computational aspects, an analysis by means of Laplace transform is presented, providing a justification to the use of very low orders in the reduction procedure as compared with the full-order model. Finally, comparisons between the full-order model and the reduced-order ones are presented

Physics-based passivity-preserving parameterized model order reduction for PEEC circuit analysis

The decrease of integrated circuit feature size and the increase of operating frequencies require 3-D electromagnetic methods, such as the partial element equivalent circuit (PEEC) method, for the analysis and design of high-speed circuits. Very large systems of equations are often produced by 3-D electromagnetic methods, and model order reduction (MOR) methods have proven to be very effective in combating such high complexity. During the circuit synthesis of large-scale digital or analog applications, it is important to predict the response of the circuit under study as a function of design parameters such as geometrical and substrate features. Traditional MOR techniques perform order reduction only with respect to frequency, and therefore the computation of a new electromagnetic model and the corresponding reduced model are needed each time a design parameter is modified, reducing the CPU efficiency. Parameterized model order reduction (PMOR) methods become necessary to reduce large systems of equations with respect to frequency and other design parameters of the circuit, such as geometrical layout or substrate characteristics. We propose a novel PMOR technique applicable to PEEC analysis which is based on a parameterization process of matrices generated by the PEEC method and the projection subspace generated by a passivity-preserving MOR method. The proposed PMOR technique guarantees overall stability and passivity of parameterized reduced order models over a user-defined range of design parameter values. Pertinent numerical examples validate the proposed PMOR approach