Begell House Inc.
International Journal for Multiscale Computational Engineering
JMC
1543-1649
3
3
2005
A Coupled Discrete/Continuum Model for Multiscale Diffusion
257-266
J. S.
Tello
Division of Engineering, Brown University Providence, RI02912
William A.
Curtin
Brown University; École Polytechnique Fédérale de Lausanne
(EPFL), Mechanical Engineering
1015 Lausanne, Switzerland
A method is developed to model continuum (finite element) and discrete [kinetic Monte Carlo (kMC)] diffusion occurring simultaneously in connected regions of space. The two regions are coupled across an interface using an iterative domain-decomposition approach in which time-dependent boundary conditions are applied on the kMC region (concentration) and on the continuum region (flux). Evolving forward in small time increments permits iterations in the kMC region to be performed only in a narrow band near the interface. An on-the-fly convergence criterion based on the inherent fluctuations in the discrete problem is developed. Application to the decay of a Gaussian concentration profile demonstrates the accuracy and efficiency of the method. Generalizations to more complex problems in two and three dimensions, and with spatially varying diffusivity due to interactions or applied stress fields, are straightforward.
Turbulent Structures in a Slightly Compressible Mixing Layer
267-284
Mohamed
Si-Ameur
LESEI Laboratory, Department of Mechanical Engineering, Technology Faculty, University of Batna 2, Algeria
The configuration of a compressible mixing layer confined between rigid walls at high Reynolds number is studied at convective Mach number Mc=0.64, using the monotonically integrated large eddy simulation approach. The purpose is to analyze the flow configuration with attention to the turbulent mixing linked to large scales in the transition and turbulent zones. The full Navier-Stokes equations are solved with a high-order Godunov's scheme piecewise parabolic method with the approximate Riemann solver of Roe. On the basis of flow visualization, highly three-dimensional vortex lattices undergoing helical pairing of oblique structures are observed in the transition zone. A particular structure of mixing in sublayers is detected qualitatively and through probability density function analysis. Computed statistics are in good agreement with experimental measurements.
The Leading-Order Term in the Asymptotic Expansion of the Scattering Amplitude of a Collection of Finite Number of Dielectric Inhomogeneities of Small Diameter
285-296
Habib
Ammari
Centre de Mathematiques Appliquees, CNRS UMR 7641 & Ecole Polytechnique, 91128 Palaiseau Cedex, France
Darko
Volkov
Mathematical Sciences Department, Worcester Polytechnic Institute, 100 Institute Road Worcester, MA 01609
We rigorously derive the leading-order term in the asymptotic expansion of the scattering amplitude for a collection of a finite number of dielectric inhomogeneities of small diameter. The asymptotic formula derived in this paper provides the basis for the numerical reconstruction of dielectric scatterers of small diameter, as demonstrated by Volkov.
Multiscale and Residual-Free Bubble Functions for Reaction-Advection-Diffusion Problems
297-312
Leo
Franca
University of Colorado at Denver
J. V. A.
Ramalho
Instituto de Fısica e Matematica, Universidade Federal de Pelotas Pelotas, Brazil, Campus Capao do Leao s/n, 96.160-000
F.
Valentin
Laboratorio Nacional de Computacao Cientifica - LNCC, Av. Getulio Vargas 333, Quitandinha, Petropolis, RJ, 25651-070, Brazil
We propose a finite element method based on enriching the Galerkin approximation spaces with a combination of multiscale functions and residual-free bubbles (RFB). This approach is presented as a Petrov-Galerkin method and applied to the singularly perturbed reaction-advection-diffusion model. Numerical tests confirm that switching RFB by suitable multiscale functions in the elements connected to the outflow boundaries of the domain improves the accuracy of the solution in this region.
Membrane-Bending Coupling in Laminated Shells: Asymptotics and Implementation
313-336
H.
Ranarivelo
Laboratoire de Mecanique, Modelisation Mathematique et numerique, Universite de Caen, BP 5186,14032 Caen, France
J.
Sanchez-Hubert
Laboratoire de Modelisation en Mecanique, Universite Pierre et Marie Curie (Paris VI), 4 place Jussieu, 75252 Paris, France
Generalized elasticity coefficients including membrane-bending coupling terms appear in thin (i.e., with very small relative thickness) shell theory when the material is heterogeneous. In this paper, we give a method to compute coefficients in the case of multilayered shells. A new program is implemented in the finite element code Modulef The numerical experiments are concerned with inhibited (i.e., such that the middle surface S with kinematic boundary conditions is geometrically rigid or, equivalently, that the boundary conditions are such that S does not admit “pure bending,” i.e., displacements keeping the length invariant on S) multilayered thin shells with hyperbolic middle surface involving a composite material with unidirectional fibers. The model considered here is that deduced from asymptotic theory. Two different cases of loading are considered. We observe that the presence of anisotropy modifies the quantitative results obtained for an isotropic homogeneous material, but not the qualitative trends of the solutions.
Order Reduction for Large-Scale Finite Element Models: A Systems Perspective
337-362
William
Gressick
Rensselaer Polytechnic Institute, Troy, NY 12180
John T.
Wen
Rensselaer Polytechnic Institute, Troy, NY 12180
Jacob
Fish
Civil Engineering and Engineering Mechanics, Columbia University, New York, New York
10027, USA
Large-scale finite element models are routinely used in design and optimization for complex engineering systems. However, the high model order prevents efficient exploration of the design space. Many model reduction methods have been proposed in the literature on approximating the high-dimensional model with a lower-order model. These methods typically replace a fine-scale model with a coarser-scale model in schemes, such as coarse graining, macromodeling, domain decomposition, and homogenization. This paper takes a systems perspective by stating the model reduction objective in terms of the approximation of the mapping between specified input and output variables. Methods from linear systems theory, including balance truncation and optimal Hankel norm approximation, are reviewed and compared to the standard modal truncation. For high-order systems, computational load, numerical stability, and memory storage become key considerations. We discuss several computationally more attractive iterative schemes that generate the approximate Gramian matrices needed in the model reduction procedure. A numerical example is also included to illustrate the model reduction algorithms discussed in the paper. We envision that these systems-oriented model reduction methods complementing the existing methods to produce low-order models suitable for design, optimization, and control.
Calibration of a Nonlinear Elastic Composite With Goal-Oriented Error Control
363-378
Hakan
Johansson
Department of Applied Mechanics, Chalmers University of Technology S-412 96 Goteborg, Sweden
Kenneth
Runesson
Department of Structural Mechanics Chalmers, University of Technology
S-41296 Goteborg, Sweden
Fredrik
Larsson
Department of Applied Mechanics, Chalmers University of Technology, S-412 96 Gothenburg
In order to determine the parameter values for the constituents of a nonlinear elastic composite on the mesoscale, while experimental data are available on the macroscale only, a meso-macro-transition approach is adopted. A representative volume element (RVE) with piecewise linear Dirichlet boundary conditions, is analyzed using a recently proposed technique for the calibration of constitutive models. The strategy is based on an optimization problem expressed such that the state equation is incorporated via an additional costate field, which has the distinct advantage that error control in an arbitrary “goal” quantity is formally straightforward. The practical solution of the optimization problem is essentially based on Newton's method, which is feasible since it is possible to decompose each Newton step in a number of linear problems using the conventional finite element structure for the RVE problem. The same problem character is pertinent to the solution of the dual problem for a given choice of error measure, which is the key ingredient in the a posteriori error computation. The numerical results show the effectivity of the error prediction for the special case when the material parameters are constant within the subdomains of mesostructural constituents.
Comparison of CH4 and 2 Transport Through Opened Carbon Nanotubes: Predictions from Molecular Dynamics Simulations
379-391
Ki-Ho
Lee
Department of Materials Science and Engineering, University of Florida, Gainesville, FL 32611-6400
Susan B.
Sinnott
Department of Materials Science and Engineering, University of Florida, Gainesville, FL 32611-6400
Computational studies of the properties of molecules confined in nanoporous materials have been undertaken by many research groups to predict their behavior for such applications as molecular sieves and hydrogen storage. Carbon nanotubes have especially high potential to be used for environmental and pharmaceutical applications because of their uniform, cylindrical channel structures and propensity to close-pack into ordered arrays. This paper summarizes the results of classical, nonequilibrium molecular dynamics simulations that are used to predict the dynamic transport behavior of methane and oxygen molecules through opened, single-walled carbon nanotubes. Empirical potentials are used to calculate the forces in the simulations. For nanotubes with diameters below about 20 Å, the gas molecules move via normal-mode, single-file, and superdiffusion modes depending on the properties of the nanotubes. Within individual nanotubes, molecular transport can transition from one diffusion mode to another and the mass transport system changes from nonequilibrium to near equilibrium behavior over the course of the simulations.