Begell House Inc.
International Journal for Multiscale Computational Engineering
JMC
1543-1649
3
1
2005
Preface to Special Issue on Multiscale Transport Phenomena
1-4
Andrei G.
Fedorov
Georgia Institute of Technology, George W. Woodruff School of Mechanical Engineering, Parker H. Petit Inst. for Bioengineering and Bioscience, USA
Review of Multiscale Simulation in Submicron Heat Transfer
5-32
Jayathi Y.
Murthy
School of Mechanical Engineering Purdue University, West Lafayette, IN 47907; Department of Mechanical Engineering, University of Texas at Austin, Austin, TX, USA
Sreekant V. J.
Narumanchi
National Renewable Energy Laboratory MC 1633,1617 Cole Boulevard, Golden, CO 80401-3393
Jose' A.
Pascual-Gutierrez
School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907
Tianjiao
Wang
School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907
Chunjian
Ni
School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907
Sanjay R.
Mathur
Fluent Inc. 10 Cavendish Court, Lebanon, NH 03766, USA
Over the last decade, interest in the simulation of micro- and nanoscale heat transfer has lead to the development of a variety of models and numerical methods for phonon transport in semiconductors and dielectrics. These models span direct simulation using molecular dynamics, a range of models of varying fidelity based on the Boltzmann transport equation, as well as simpler hyperbolic extensions to the classical Fourier heat conduction equation. The paper reviews the basics of phonon transport in crystals, available models for phonon transport, as well as numerical methods for solving the equations resulting from these models. Recommendations are made for future work.
Multiscale Electrochemistry Modeling of Solid Oxide Fuel Cells
33-48
M. A.
Khaleel
Computational Science and Mathematics Division, Pacific Northwest National Laboratory, P.O. Box 999, Richland, WA 99352
D. R.
Rector
Computational Science and Mathematics Division, Pacific Northwest National Laboratory, P.O. Box 999, Richland, WA 99352
Z.
Lin
Computational Science and Mathematics Division, Pacific Northwest National Laboratory, P.O. Box 999, Richland, WA 99352
K.
Johnson
Computational Science and Mathematics Division, Pacific Northwest National Laboratory, P.O. Box 999, Richland, WA 99352
K.
Recknagle
Computational Science and Mathematics Division, Pacific Northwest National Laboratory, P.O. Box 999, Richland, WA 99352
In this paper, we present two levels of electrochemical modeling for solid oxide fuel cells: cell continuum and microscale electrochemistry. The microscale electrochemistry model simulates the performance of porous electrode materials based on the microstructure of the material, the distribution of reaction surfaces, and the transport of oxygen ions through the material. The overall fuel cell current-voltage relations are obtained using the microscale electrochemistry modeling and form the basic input to the continuum level electrochemistry model. The continuum electrochemistry model calculates the current electrical density, cell voltage, and heat production in fuel cell stacks with H2 or other fuels, taking into account as inputs local values of the gas partial pressures and temperatures. This approach is based on a parameterized current-voltage (I-V) relation and includes the heat generation from both Joule heating and chemical reactions. It also accounts for species production and destruction via mass balance. The continuum electrochemistry model is then coupled with a flow-thermal-mechanical simulation framework for fuel cell stack design and optimizing operating conditions.
Implicit Hybrid Simulation Framework for Steady-State Dilute Gas Flows
49-58
Nicolas G.
Hadjiconstantinou
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Lowell
Baker
Mechanical Engineering Department Massachusetts Institute of Technology, Cambridge, MA 02139
We present a hybrid simulation framework for steady-state dilute gas flows. The ingredients of this hybrid formulation are the Navier-Stokes description on the continuum side and the Boltzmann description on the atomistic side. Steady-state numerical solutions of the Boltzmann equation are obtained via an iterative finite difference formulation; these are coupled to the Navier-Stokes solution using the Schwarz alternating method, an iterative domain decomposition framework for steady-state problems. The Schwarz method is well suited for molecular-continuum hybrid methods because it provides time scale decoupling. It also enables the use of an iterative method for obtaining steady solutions in the Boltzmann domain leading to a fully implicit hybrid formulation with no time scale limitations. We show that interleaving the outer (Schwarz) iteration with the inner (Boltzmann) iteration leads to additional computational savings.
Numerical Assessment of Theoretical Error Estimates in Coarse-Grained Kinetic Monte Carlo Simulations: Application to Surface Diffusion
59-70
Abhijit
Chatterjee
Department of Chemical Engineering Center for Catalytic Science and Technology (CCST), University of Delaware, Newark, DE 19716
Dionisios G.
Vlachos
Department of Chemical Engineering Center for Catalytic Science and Technology (CCST), University of Delaware, Newark, DE 19716-3110
Markos A.
Katsoulakis
Department of Mathematics and Statistics University of Massachusetts, Amherst, MA 01003
A coarse-grained kinetic Monte Carlo (CG-KMC) method was recently introduced as a hierarchical multiscale modeling tool for extending the length scales reached by stochastic simulations. Coarse-graining causes errors due to loss of degrees of freedom. To quantify these errors, theoretical error estimates derived using information loss theory are first presented. Simulations are subsequently carried out in the canonical ensemble for various combinations of key parameters suggested by theoretical estimates. Numerically evaluated errors are compared to theoretical error estimates to assess whether the latter can qualitatively capture the loss of information during coarse-graining. Finally, a standing wave example is presented to illustrate how these error estimates can be used to control accuracy in CG-KMC by employing adaptive meshes.
Micromorphic Fluid in an Elastic Porous Body: Blood Flow in Tissues with Microcirculation
71-84
Natalie K.
Axtell
Department of Mathematics Purdue University, West Lafayette, IN 47907
Moongyu
Park
Department of Mathematics, Purdue University, West Lafayette, IN 47907
John H.
Cushman
Purdue University West Lafayette Indiana UNITED STATES
The circulation of blood in tissues is a multiscale, multiphase porous media problem with a unique characteristic that the fluid phase is a micromorphic continuum, i.e., the fluid phase contains deformable particles that affect its flow. Fluid continuum particles possess three translational degrees of freedom and nine additional degrees for microrotation, microshear, and microstretch. These latter nine degrees of freedom are required to model the behavior of the red blood cells in small capillaries. The tissue phase is assumed to be an elastic porous body. The micromorphic fluid and the porous solid are homogenized to obtain balance and conservation equations. The entropy inequality for the mixture is employed to obtain thermodynamically consistent constitutive equations that are subsequently linearized. The resultant system has 28 equations with a like number of unknowns.
Multiscale Modeling of Turbulence, Radiation, and Combustion Interactions in Turbulent Flames
85-106
Traditional modeling of radiative transfer in reacting flows has ignored turbulence-radiation interactions, due to difficulties caused by their inherent nonlinearities and their vast range of length scales and time scales. The state-of-the-art of modeling TRI is reviewed, and some results are presented, in which TRI are calculated from basic principles from the composition probability density function method and from direct numerical simulation calculations. The results show that in turbulent jet flames TRI are always of great importance, and that they are dominated by the correlation between the absorption coefficient and the radiative Planck function.
Review: Multiscale Thermal Modeling in Nanoelectronics
107-133
Sanjiv
Sinha
Thermosciences Division, Department of Mechanical Engineering, Stanford University, Stanford, CA 94305-3030, USA
Kenneth E.
Goodson
Thermosciences Division, Mechanical Engineering Department, Stanford University Bldg. 530, 440 Escondido Mall, Stanford, CA 94305-3030, USA
Subcontinuum phonon conduction phenomena impede the cooling of field-effect transistors with gate lengths less than 100 nm, which degrades their performance and reliability. Thermal modeling of these nanodevices requires attention to a broad range of length scales and physical phenomena, ranging from continuum heat diffusion to atomic-scale interactions and phonon confinement. This review describes the state of the art in subcontinuum thermal modeling. Although the focus is on the silicon field-effect transistor, the models are general enough to apply to other semiconductor devices as well. Special attention is given to the recent advances in applying statistical and atomistic simulation methods to thermal transport.