The Experts below are selected from a list of 197580 Experts worldwide ranked by ideXlab platform
Jianzhong Lin - One of the best experts on this subject based on the ideXlab platform.
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the verification of the taylor expansion Moment Method for the nanoparticle coagulation in the entire size regime due to brownian motion
Journal of Nanoparticle Research, 2011Co-Authors: Jianzhong Lin, Hanhui Jin, Ying JiangAbstract:The closure of Moment equations for nanoparticle coagulation due to Brownian motion in the entire size regime is performed using a newly proposed Method of Moments. The equations in the free molecular size regime and the continuum plus near-continuum regime are derived separately in which the fractal Moments are approximated by three-order Taylor-expansion series. The Moment equations for coagulation in the entire size regime are achieved by the harmonic mean solution and the Dahneke’s solution. The results produced by the quadrature Method of Moments (QMOM), the Pratsinis’s log-normal Moment Method (PMM), the sectional Method (SM), and the newly derived Taylor-expansion Moment Method (TEMOM) are presented and compared in accuracy and efficiency. The TEMOM Method with Dahneke’s solution produces the most accurate results with a high efficiency than other existing Moment models in the entire size regime, and thus it is recommended to be used in the following studies on nanoparticle dynamics due to Brownian motion.
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solution of the agglomerate brownian coagulation using taylor expansion Moment Method
Journal of Colloid and Interface Science, 2009Co-Authors: Jianzhong LinAbstract:The newly proposed Taylor-expansion Moment Method (TEMOM) is extended to solve agglomerate coagulation in the free-molecule regime and in the continuum regime, respectively. The Moment equations with respect to fractal dimension are derived based on 3rd Taylor-series expansion technique. The validation of this Method is done by comparing its result with the published data at each limited size regime. By comparing with analytical Method, sectional Method (SM) and quadrature Method of Moments (QMOMs), this new approach is shown to produce the most efficiency without losing much accuracy. At each limited size regime, the effect of fractal dimension on the decay of particle number and particle size growth is mainly investigated, and especially in the continuum regime the relation of mean diameters of size distributions with different fractal dimensions is first proposed. The agglomerate size distribution is found to be sensitive to the fractal dimension and the initial geometric mean deviation before the self-preserving size distribution is achieved in the continuum regime.
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taylor expansion Moment Method for agglomerate coagulation due to brownian motion in the entire size regime
Journal of Aerosol Science, 2009Co-Authors: Jianzhong LinAbstract:Abstract Through applying the Taylor-expansion technique to the particle general dynamic equation, the newly proposed Taylor-expansion Moment Method (TEMOM) is extended to solve agglomerate coagulation due to Brownian motion in the entire size regime. The TEMOM model disposed by Dahneke's solution (TEMOM–Dahneke) is proved to be more accurate than by harmonic mean solution (TEMOM–harmonic) through comparing their results with the reference sectional model (SM) for different fractal dimensions. In the transition regime, the TEMOM–Dahneke gives the more accurate results than the quadrature Method of Moments with three nodes (QMOM3). The mass fractal dimension is found to play an important role in determining the decay of agglomerate number and the spectrum of agglomerate size distribution, but the effect decreases with decreasing agglomerate Knudsen number. The self-preserving size distribution (SPSD) theory and linear decay law for agglomerate number are only applicable to be in the free molecular regime and continuum plus near-continuum regime, but not perfectly in the transition regime.
E H Van Brummelen - One of the best experts on this subject based on the ideXlab platform.
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an entropy stable discontinuous galerkin finite element Moment Method for the boltzmann equation
Computers & Mathematics With Applications, 2016Co-Authors: M R A Abdelmalik, E H Van BrummelenAbstract:This paper presents a numerical approximation technique for the Boltzmann equation based on a Moment-system approximation in velocity dependence and a discontinuous Galerkin finite-element approximation in position dependence. The closure relation for the Moment systems derives from minimization of a suitable -divergence. This divergence-based closure yields a hierarchy of tractable symmetric hyperbolic Moment systems that retain the fundamental structural properties of the Boltzmann equation. The approximation in position dependence is based on the discontinuous Galerkin finite-element Method. The resulting combined discontinuous Galerkin Moment Method corresponds to a Galerkin approximation of the Boltzmann equation in renormalized form. The new Momentclosure formulation engenders a new upwind numerical flux function, based on half-space integrals of the approximate distribution. We establish that the proposed upwind flux ensures entropy dissipation of the discontinuous Galerkin finite-element approximation. Numerical results are presented for a one-dimensional test case.
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an entropy stable discontinuous galerkin finite element Moment Method for the boltzmann equation
arXiv: Computational Physics, 2016Co-Authors: M R A Abdelmalik, E H Van BrummelenAbstract:This paper presents a numerical approximation technique for the Boltzmann equation based on a Moment system approximation in velocity dependence and a discontinuous Galerkin finite-element approximation in position dependence. The closure relation for the Moment systems derives from minimization of a suitable {\phi}-divergence. This divergence-based closure yields a hierarchy of tractable symmetric hyperbolic Moment systems that retain the fundamental structural properties of the Boltzmann equation. The resulting combined discontinuous Galerkin Moment Method corresponds to a Galerkin approximation of the Boltzmann equation in renormalized form. We present a new class of numerical flux functions, based on the underlying renormalized Boltzmann equation, that ensure entropy dissipation of the approximation scheme. Numerical results are presented for a one-dimensional test case.
Macole Sabat - One of the best experts on this subject based on the ideXlab platform.
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statistical description of turbulent particle laden flows in the very dilute regime using the anisotropic gaussian Moment Method
International Journal of Multiphase Flow, 2019Co-Authors: Macole Sabat, Aymeric Vie, Adam Larat, Marc MassotAbstract:Abstract The present work aims at investigating the ability of a Kinetic-Based Moment Method (KBMM) to reproduce the statistics of turbulent particle-laden flows using the Anisotropic Gaussian (AG) closure. This Method is the simplest KBMM member that can account for Particle Trajectory Crossing (PTC) properly with a well-posed mathematical structure Vie et al. (2015). In order to validate this model further, we investigate here 3D turbulent flows that are more representative of the mixing processes, which occurs in realistic applications. The chosen configuration is a 3D statistically-stationary Homogeneous Isotropic Turbulence (HIT) loaded with particles in a very dilute regime. The analysis focuses on the description of the first three lowest order Moments of the particulate flow: the number density, the Eulerian velocity and the internal energy. A thorough numerical study on a large range of particle inertia allows us to show that the AG closure extends the ability of the Eulerian models to correctly reproduce the particle dynamics up to a Stokes number based on the Eulerian turbulence macro-scale equal to one, but also highlights the necessity of high-order numerical schemes to reach mesh convergence, especially for the number density field.
Guangwu Yan - One of the best experts on this subject based on the ideXlab platform.
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a higher order Moment Method of the lattice boltzmann model for the conservation law equation
Applied Mathematical Modelling, 2010Co-Authors: Yinfeng Dong, Jianying Zhang, Guangwu YanAbstract:Abstract In this paper, we proposed a higher-order Moment Method in the lattice Boltzmann model for the conservation law equation. In contrast to the lattice Bhatnagar–Gross–Krook (BGK) model, the higher-order Moment Method has a wide flexibility to select equilibrium distribution function. This Method is based on so-called a series of partial differential equations obtained by using multi-scale technique and Chapman–Enskog expansion. According to Hirt’s heuristic stability theory, the stability of the scheme can be controlled by modulating some special Moments to design the third-order dispersion term and the fourth-order dissipation term. As results, the conservation law equation is recovered with higher-order truncation error. The numerical examples show the higher-order Moment Method can be used to raise the accuracy of the truncation error of the lattice Boltzmann scheme for the conservation law equation.
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a higher order Moment Method of the lattice boltzmann model for the korteweg de vries equation
Mathematics and Computers in Simulation, 2009Co-Authors: Guangwu Yan, Jianying ZhangAbstract:In this paper, a lattice Boltzmann model for the Korteweg-de Vries (KdV) equation with higher-order accuracy of truncation error is presented by using the higher-order Moment Method. In contrast to the previous lattice Boltzmann model, our Method has a wide flexibility to select equilibrium distribution function. The higher-order Moment Method bases on so-called a series of lattice Boltzmann equation obtained by using multi-scale technique and Chapman-Enskog expansion. We can also control the stability of the scheme by modulating some special Moments to design the dispersion term and the dissipation term. The numerical example shows the higher-order Moment Method can be used to raise the accuracy of truncation error of the lattice Boltzmann scheme.
M R A Abdelmalik - One of the best experts on this subject based on the ideXlab platform.
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an entropy stable discontinuous galerkin finite element Moment Method for the boltzmann equation
Computers & Mathematics With Applications, 2016Co-Authors: M R A Abdelmalik, E H Van BrummelenAbstract:This paper presents a numerical approximation technique for the Boltzmann equation based on a Moment-system approximation in velocity dependence and a discontinuous Galerkin finite-element approximation in position dependence. The closure relation for the Moment systems derives from minimization of a suitable -divergence. This divergence-based closure yields a hierarchy of tractable symmetric hyperbolic Moment systems that retain the fundamental structural properties of the Boltzmann equation. The approximation in position dependence is based on the discontinuous Galerkin finite-element Method. The resulting combined discontinuous Galerkin Moment Method corresponds to a Galerkin approximation of the Boltzmann equation in renormalized form. The new Momentclosure formulation engenders a new upwind numerical flux function, based on half-space integrals of the approximate distribution. We establish that the proposed upwind flux ensures entropy dissipation of the discontinuous Galerkin finite-element approximation. Numerical results are presented for a one-dimensional test case.
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an entropy stable discontinuous galerkin finite element Moment Method for the boltzmann equation
arXiv: Computational Physics, 2016Co-Authors: M R A Abdelmalik, E H Van BrummelenAbstract:This paper presents a numerical approximation technique for the Boltzmann equation based on a Moment system approximation in velocity dependence and a discontinuous Galerkin finite-element approximation in position dependence. The closure relation for the Moment systems derives from minimization of a suitable {\phi}-divergence. This divergence-based closure yields a hierarchy of tractable symmetric hyperbolic Moment systems that retain the fundamental structural properties of the Boltzmann equation. The resulting combined discontinuous Galerkin Moment Method corresponds to a Galerkin approximation of the Boltzmann equation in renormalized form. We present a new class of numerical flux functions, based on the underlying renormalized Boltzmann equation, that ensure entropy dissipation of the approximation scheme. Numerical results are presented for a one-dimensional test case.
