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A reduced-order model for heat transfer in multiphase flow and practical aspects of the proper orthogonal decomposition

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COMPUTERS & CHEMICAL ENGINEERING 2012年 43卷 68-80页

作者： Brenner, Thomas A. Fontenot, Raymond L. Cizmas, Paul G. A. O'Brien, Thomas J. Breault, Ronald W. Texas A&M Univ Dept Aerosp Engn College Stn TX 77843 USA Dept Energy Natl Energy Technol Lab Morgantown WV 26507 USA

This paper discusses two practical aspects of reduced-order models (ROMs) based on proper orthogonal decomposition (POD) and presents the derivation and implementation of a ROM for non-isothermal multiphase flow. The POD method calculates basis functions for a reduced-order representation of two-phase flow by calculating the eigenvectors of an autocorrelation matrix composed of snapshots of the flow. The flow is divided into transient and quasi-steady regions and two methods are shown for clustering snapshots in the transient region. Both methods reduce error as compared to the constant sampling case. The ROM for non-isothermal flow was developed using numerical results from a full-order computational fluid dynamics model for a two-dimensional non-isothermal fluidized bed. Excellent agreement is shown between the reduced- and full-order models. The composition of the autocorrelation matrix is also considered for an isothermal case. An approach treating field variables separately is shown to produce less error than a coupled approach. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Proper orthogonal decomposition Reduced-order modeling Multiphase flow computational methods in fluid dynamics

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Flow simulations with multi-particle collision dynamics

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MECCANICA 2012年第8期47卷 2069-2077页

作者： De Angelis, E. Chinappi, M. Graziani, G. Univ Roma La Sapienza Dipartimento Ingn Meccan & Aerosp I-00184 Rome Italy Univ Bologna DIEM I-47100 Forli Italy Univ Roma La Sapienza Dipartimento Fis I-001185 Rome Italy

Multi-particle collision dynamics (MPCD) is a particle based Navier-Stokes solver and in the last ten years it has been largely used to analyze mesoscopic systems where both hydrodynamics and thermal effects have to be taken into account, typical examples being colloidal suspensions and polymer solutions. Though the soundness of this approach is well documented, only a few studies present a systematic validation of the method as a Navier-Stokes solver for relatively complex flows (e.g. unsteady, non-uniform). In this study we use MPCD to simulate an unsteady periodic flow (second Stokes' problem) and a two dimensional flow (lid-driven cavity). Quantitative comparisons with analytical and finite difference results show that MPCD is able to correctly reproduce the hydrodynamics of these systems in a wide range of numerical parameter values, allowing the applications of MPCD to the analysis of complex fluids in confined geometries such as in Lab-On-a-Chip microfluidic devices. Discrepancies for certain parameter ranges and in specific flow conditions are singled out and discussed.

关键词： computational methods in fluid dynamics Multi-particle collision dynamics

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On the microscopic foundation of dissipative particle dynamics

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EPL 2009年第4期86卷 44001 (6pp-44001 (6pp页

作者： Eriksson, A. Jacobi, M. Nilsson Nystrom, J. Tunstrom, K. Univ Gothenburg Dept Phys SE-41296 Gothenburg Sweden Chalmers Univ Technol Environm & Energy Dept Complex Syst Grp SE-41296 Gothenburg Sweden

Mesoscopic-particle-based fluid models, such as dissipative particle dynamics, are usually assumed to be coarse-grained representations of an underlying microscopic fluid. A fundamental question is whether there exists a map from microscopic particles in these systems to the corresponding coarse-grained particles, such that the coarse-grained system has the same bulk and transport properties as the underlying system. In this letter, we investigate the coarse-graining of microscopic fluids using a Voronoi-type projection that has been suggested in several studies. The simulations show that the projection fails in de. ning coarse-grained particles that have a physically meaningful connection to the microscopic fluid. In particular, the Voronoi projection produces identical coarse-grained equilibrium properties when applied to systems with different microscopic interactions and different bulk properties. Copyright (C) EPLA, 2009

关键词： computational methods in fluid dynamics Multi-scale methods Complex fluids and colloidal systems

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Continuum free-energy formulation for a class of lattice Boltzmann multiphase models

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EPL 2009年第2期86卷 24005 (6pp-24005 (6pp页

作者： Sbragaglia, M. Chen, H. Shan, X. Succi, S. Univ Roma Tor Vergata Dept Phys I-00133 Rome Italy Univ Roma Tor Vergata Ist Nazl Fis Nucl I-00133 Rome Italy EXA Corp Burlington MA 01803 USA CNR Ist Applicaz Calcolo I-00161 Rome Italy

It is shown that the Shan-Chen (SC) model for non-ideal lattice fluids can be made compliant with a pseudo-free-energy principle by simple addition of a gradient force, whose expression is uniquely specified in terms of the fluid density. This additional term is numerically simulated and shown to provide fairly negligible effects on the system evolution during phase-separation. To the best of our knowledge, these important properties of the SC model were not noted before. The approach developed in the present work is based on a continuum analysis: Further extensions, more in line with a discrete lattice theory (SHAN X., Phys. Rev. E, 77 (2008) 066702), can be envisaged for the future. Copyright (C) EPLA, 2009

关键词： computational methods in fluid dynamics Rarefied gas dynamics computational techniques, simulations

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Acceleration techniques for reduced-order models based on proper orthogonal decomposition

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JOURNAL OF computational PHYSICS 2008年第16期227卷 7791-7812页

作者： Cizmas, Paul G. A. Richardson, Brian R. Brenner, Thomas A. O'Brien, Thomas J. Breault, Ronald W. Texas A&M Univ Dept Aerosp Engn College Stn TX 77843 USA Dept Energy Natl Energy Technol Lab Morgantown WV 26507 USA

This paper presents several acceleration techniques for reduced-order models based on the proper orthogonal decomposition (POD) method. The techniques proposed herein are: (i) an algorithm for splitting the database of snapshots generated by the full-order model;(ii) a method for solving quasi-symmetrical matrices;(iii) a strategy for reducing the frequency of the projection. The acceleration techniques were applied to a POD-based reduced-order model of the two-phase flows in fluidized beds. This reduced-order model was developed using numerical results from a full-order computational fluid dynamics model of a two-dimensional fluidized bed. Using these acceleration techniques the computational time of the POD model was two orders of magnitude shorter than the full-order model. (C) 2008 Elsevier Inc. All rights reserved.

关键词： proper orthogonal decomposition multiphase flow computational methods in fluid dynamics nonlinear dynamics

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Lattice Boltzmann across scales: from turbulence to DNA translocation

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EUROPEAN PHYSICAL JOURNAL B 2008年第3-4期64卷 471-479页

作者： Succi, S. CNR Ist Applicaz Calcolo I-00161 Rome Italy

The capability of the lattice Boltzmann (LB) method to describe complex flow behaviour across a wide range of scales of motion is discussed. This capability is illustrated by means of three examples, straddling across over ten decades of fluid motion, from macroscopic turbulence, to microfluidics, all the way down to nanoscopic flows of biological interest. It is pointed out that each of these applications requires extensions of the original LB scheme, beyond the realm of Navier-Stokes hydrodynamics for which the method was originally designed. The main qualitative ideas behind such extensions are discussed and commented on, with special emphasis on their direct ties with modern non-equilibrium statistical mechanics.

关键词： Kinetic theory computational methods in fluid dynamics Statistical physics and nonlinear dynamics

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Galilean invariance of lattice Boltzmann models

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EPL 2008年第3期81卷

作者： Nie, X. B. Shan, X. Chen, H. Exa Corp Burlington MA 01803 USA

It is well known that the original lattice Boltzmann (LB) equation deviates from the Navier-Stokes equations due to an unphysical velocity-dependent viscosity. This unphysical dependence violates the Galilean invariance and limits the validation domain of the LB method to near incompressible flows. As previously shown, recovery of correct transport phenomena in kinetic equations depends on the higher hydrodynamic moments. In this letter, we give specific criteria for recovery of various transport coefficients. The Galilean invariance of a general class of LB models is demonstrated via numerical experiments. Copyright (C) EPLA, 2008.

关键词： computational methods in fluid dynamics Kinetic theory Compressible flows, shock waves

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Lattice Boltzmann method for inhomogeneous fluids

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EPL 2008年第3期81卷

作者： Melchionna, S. Marconi, U. Marini Bettolo Univ Rome Dipartimento Fis INFM SOFT I-00185 Rome Italy Ist Nazl Fis Mat I-00185 Rome Italy Univ Camerino Dipartimento Fis INFM SOFT I-62032 Camerino Italy Ist Nazl Fis Mat I-62032 Camerino Italy

We present a lattice-based numerical method to describe the non-equilibrium behavior of a simple fluid under non-uniform spatial conditions. The evolution equation for the one-particle phase-space distribution function is derived starting from a microscopic description of the system. It involves a series of approximations which are similar to those employed in theories of inhomogeneous fluids, such as the density functional theory. Among the merits of the present approach: the possibility to determine the equation of state of the model, the transport coefficients and to provide an efficient method of numerical solution under non-uniform conditions. The algorithm is tested in a particular non-equilibrium situation, namely the steady flow of a hardsphere fluid across a narrow slit. Pronounced non-hydrodynamic oscillations in the density and velocity profiles are found. Copyright (C) EPLA, 2008.

关键词： computational methods in fluid dynamics Micro- and nano- scale flow phenomena Structure of liquids

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Quasi-equilibrium lattice Boltzmann method

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EUROPEAN PHYSICAL JOURNAL B 2007年第2期56卷 135-139页

作者： Ansumali, S. Arcidiacono, S. Chikatamarla, S. S. Prasianakis, N. I. Gorban, A. N. Karlin, I. V. Nanyang Technol Univ CBE Singapore 639798 Singapore Paul Scherrer Inst Combust Res Unit CH-5232 Villigen Switzerland ETH Aerothermochem & Combust Syst Lab CH-8092 Zurich Switzerland Univ Leicester Dept Math Leicester LE1 7RH Leics England

A general lattice Boltzmann method for simulation of fluids with tailored transport coefficients is presented. It is based on the recently introduced quasi-equilibrium kinetic models, and a general lattice Boltzmann implementation is developed. Lattice Boltzmann models for isothermal binary mixtures with a given Schmidt number, and for a weakly compressible flow with a given Prandtl number are derived and validated.

关键词： computational methods in fluid dynamics Kinetic theory

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Numerical simulations of the aspherical collapse of laser and acoustically generated bubbles

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ULTRASONICS SONOCHEMISTRY 2007年第4期14卷 456-469页

作者： Tsiglifis, Kostas Pelekasis, Nikos A. Univ Thessaly Dept Mech & Ind Engn Volos 38334 Greece

The details of nonlinear axisymmetric oscillations and collapse of bubbles subject to large internal or external pressure disturbances, are studied via a boundary integral method. Weak viscous effects on the liquid side are accounted for by integrating the equations of motion across the boundary layer that is formed adjacent to the interface. Simulations of single-cavitation bubble luminescence (SCBL) and single-bubble sonoluminescence (SBSL) are performed under conditions similar to reported experimental observations, aiming at capturing the details of bubble collapse. It is shown that any small initial deviation from sphericity, modeled through a small initial elongation along the axis of symmetry, may result in the formation and impact of two counter-propagating jets during collapse of the bubble, provided the amplitude of the initial disturbance is large enough and the viscosity of the surrounding fluid is small enough. Comparison between simulations and experimental observations show that this is the case for bubbles induced via a nano-second laser pulse (SCBL) during a luminescence event. In a similar fashion, simulations show that loss of sphericity accompanied with jet formation and impact during collapse is also possible with acoustically trapped bubbles in a standing pressure wave (SBSL), due to the many afterbounces of the bubble during its collapse phase. In both cases jet impact occurs as a result Of P-2 growth in the form of an afterbounce instability. When the sound amplitude is decreased or liquid viscosity is increased the intensity of the afterbounce is decreased and jet impact is suppressed. When the sound amplitude is increased jet formation is superceded by Rayleigh-Taylor instability. In the same context stable luminescence is quenched in experimental observations. In both SCBL and SBSL simulations the severity of jet impact during collapse is quite large, and its local nature quite distinct. This attests to the fact that it is an energy focusi

关键词： nonlinear acoustics sonoluminescence computational methods in fluid dynamics jets bubble dynamics weak viscous effects collapse laser bubbles

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