The Experts below are selected from a list of 276 Experts worldwide ranked by ideXlab platform
S Nishimura - One of the best experts on this subject based on the ideXlab platform.
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a convergence study for the laguerre expansion in the Moment Equation method for neoclassical transport in general toroidal plasmas
Physics of Plasmas, 2010Co-Authors: S Nishimura, H Sugama, H Maassberg, C D Beidler, S Murakami, Y Nakamura, S HirookaAbstract:The dependence of neoclassical parallel flow calculations on the maximum order of Laguerre polynomial expansions is investigated in a magnetic configuration of the Large Helical Device [S. Murakami, A. Wakasa, H. Maassberg, et al., Nucl. Fusion 42, L19 (2002)] using the monoenergetic coefficient database obtained by an international collaboration. On the basis of a previous generalization (the so-called Sugama-Nishimura method [H. Sugama and S. Nishimura, Phys. Plasmas 15, 042502 (2008)]) to an arbitrary order of the expansion, the 13 M, 21 M, and 29 M approximations are compared. In a previous comparison, only the ion distribution function in the banana collisionality regime of single-ion-species plasmas in tokamak configurations was investigated. In this paper, the dependence of the problems including electrons and impurities in the general collisionality regime in an actual nonsymmetric toroidal configuration is reported. In particular, qualities of approximations for the electron distribution function are investigated in detail.
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Moment Equation methods for calculating neoclassical transport coefficients in general toroidal plasmas
Physics of Plasmas, 2008Co-Authors: H Sugama, S NishimuraAbstract:A detailed comparison is made between Moment-Equation methods presented by H. Sugama and S. Nishimura [Phys. Plasmas 9, 4637 (2002)] and by M. Taguchi [Phys. Fluids B 4, 3638 (1992)] for calculating neoclassical transport coefficients in general toroidal plasmas including nonsymmetric systems. It is shown that these methods can be derived from the drift kinetic Equation with the same collision model used for correctly taking account of collisional Momentum conservation. In both methods, the Laguerre polynomials of the energy variable are employed to expand the guiding-center distribution function and to obtain the Moment Equations, by which the radial neoclassical transport fluxes and the parallel flows are related to the thermodynamic forces. The methods are given here in the forms applicable for an arbitrary truncation number of the Laguerre-polynomial expansion so that their accuracies can be improved by increasing the truncation number. Differences between results from the two methods appear when the ...
Jens Osterhoff - One of the best experts on this subject based on the ideXlab platform.
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phase space Moment Equation model of highly relativistic electron beams in plasma wakefield accelerators
Annals of Physics, 2015Co-Authors: R E Robson, Timon Mehrling, Jens OsterhoffAbstract:We formulate a new procedure for modelling the transverse dynamics of relativistic electron beams with significant energy spread when injected into plasma-based accelerators operated in the blow-out regime. Quantities of physical interest, such as the emittance, are furnished directly from solution of phase space Moment Equations formed from the relativistic Vlasov Equation. The Moment Equations are closed by an Ansatz, and solved analytically for prescribed wakefields. The accuracy of the analytic formulas is established by benchmarking against the results of a semi-analytic/numerical procedure which is described within the scope of this work, and results from a simulation with the 3D quasi-static PIC code HiPACE.
H Sugama - One of the best experts on this subject based on the ideXlab platform.
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a convergence study for the laguerre expansion in the Moment Equation method for neoclassical transport in general toroidal plasmas
Physics of Plasmas, 2010Co-Authors: S Nishimura, H Sugama, H Maassberg, C D Beidler, S Murakami, Y Nakamura, S HirookaAbstract:The dependence of neoclassical parallel flow calculations on the maximum order of Laguerre polynomial expansions is investigated in a magnetic configuration of the Large Helical Device [S. Murakami, A. Wakasa, H. Maassberg, et al., Nucl. Fusion 42, L19 (2002)] using the monoenergetic coefficient database obtained by an international collaboration. On the basis of a previous generalization (the so-called Sugama-Nishimura method [H. Sugama and S. Nishimura, Phys. Plasmas 15, 042502 (2008)]) to an arbitrary order of the expansion, the 13 M, 21 M, and 29 M approximations are compared. In a previous comparison, only the ion distribution function in the banana collisionality regime of single-ion-species plasmas in tokamak configurations was investigated. In this paper, the dependence of the problems including electrons and impurities in the general collisionality regime in an actual nonsymmetric toroidal configuration is reported. In particular, qualities of approximations for the electron distribution function are investigated in detail.
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Moment Equation methods for calculating neoclassical transport coefficients in general toroidal plasmas
Physics of Plasmas, 2008Co-Authors: H Sugama, S NishimuraAbstract:A detailed comparison is made between Moment-Equation methods presented by H. Sugama and S. Nishimura [Phys. Plasmas 9, 4637 (2002)] and by M. Taguchi [Phys. Fluids B 4, 3638 (1992)] for calculating neoclassical transport coefficients in general toroidal plasmas including nonsymmetric systems. It is shown that these methods can be derived from the drift kinetic Equation with the same collision model used for correctly taking account of collisional Momentum conservation. In both methods, the Laguerre polynomials of the energy variable are employed to expand the guiding-center distribution function and to obtain the Moment Equations, by which the radial neoclassical transport fluxes and the parallel flows are related to the thermodynamic forces. The methods are given here in the forms applicable for an arbitrary truncation number of the Laguerre-polynomial expansion so that their accuracies can be improved by increasing the truncation number. Differences between results from the two methods appear when the ...
S Hirooka - One of the best experts on this subject based on the ideXlab platform.
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a convergence study for the laguerre expansion in the Moment Equation method for neoclassical transport in general toroidal plasmas
Physics of Plasmas, 2010Co-Authors: S Nishimura, H Sugama, H Maassberg, C D Beidler, S Murakami, Y Nakamura, S HirookaAbstract:The dependence of neoclassical parallel flow calculations on the maximum order of Laguerre polynomial expansions is investigated in a magnetic configuration of the Large Helical Device [S. Murakami, A. Wakasa, H. Maassberg, et al., Nucl. Fusion 42, L19 (2002)] using the monoenergetic coefficient database obtained by an international collaboration. On the basis of a previous generalization (the so-called Sugama-Nishimura method [H. Sugama and S. Nishimura, Phys. Plasmas 15, 042502 (2008)]) to an arbitrary order of the expansion, the 13 M, 21 M, and 29 M approximations are compared. In a previous comparison, only the ion distribution function in the banana collisionality regime of single-ion-species plasmas in tokamak configurations was investigated. In this paper, the dependence of the problems including electrons and impurities in the general collisionality regime in an actual nonsymmetric toroidal configuration is reported. In particular, qualities of approximations for the electron distribution function are investigated in detail.
Dongxiao Zhang - One of the best experts on this subject based on the ideXlab platform.
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stochastic uncertainty analysis for solute transport in randomly heterogeneous media using a karhunen loeve based Moment Equation approach
Water Resources Research, 2007Co-Authors: Gaisheng Liu, Dongxiao ZhangAbstract:[1] A new approach has been developed for solving solute transport problems in randomly heterogeneous media using the Karhunen-Loeve-based Moment Equation (KLME) technique proposed by Zhang and Lu (2004). The KLME approach combines the Karhunen-Loeve decomposition of the underlying random conductivity field and the perturbative and polynomial expansions of dependent variables including the hydraulic head, flow velocity, dispersion coefficient, and solute concentration. The Equations obtained in this approach are sequential, and their structure is formulated in the same form as the original governing Equations such that any existing simulator, such as Modular Three-Dimensional Multispecies Transport Model for Simulation of Advection, Dispersion, and Chemical Reactions of Contaminants in Groundwater Systems (MT3DMS), can be directly applied as the solver. Through a series of two-dimensional examples, the validity of the KLME approach is evaluated against the classical Monte Carlo simulations. Results indicate that under the flow and transport conditions examined in this work, the KLME approach provides an accurate representation of the mean concentration. For the concentration variance, the accuracy of the KLME approach is good when the conductivity variance is 0.5. As the conductivity variance increases up to 1.0, the mismatch on the concentration variance becomes large, although the mean concentration can still be accurately reproduced by the KLME approach. Our results also indicate that when the conductivity variance is relatively large, neglecting the effects of the cross terms between velocity fluctuations and local dispersivities, as done in some previous studies, can produce noticeable errors, and a rigorous treatment of the dispersion terms becomes more appropriate.
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stochastic simulations for flow in nonstationary randomly heterogeneous porous media using a kl based Moment Equation approach
Multiscale Modeling & Simulation, 2007Co-Authors: Dongxiao ZhangAbstract:In this study, we extend the Karhunen–Loeve Moment Equation (KLME) approach, an approach based on KL decomposition, to efficiently and accurately quantify uncertainty for flow in nonstationary heterogeneous porous media that include a number of zones with different statistics of the hydraulic conductivity. We first decompose the log hydraulic conductivity $Y = {\rm ln}\, K_s$ for each zone by the KL decomposition, which is related to a set of eigenvalues and their corresponding orthogonal deterministic eigenfunctions. Based on the decomposition for all individual zones, we develop an algorithm to find the eigenvalues and eigenfunctions for the entire domain. Following the methodology proposed by Zhang and Lu [J. Comput. Phys., 194 (2004), pp. 773–794], we solve the head variability up to second order in terms of $\sigma_Y^2$ and compare the results with those obtained from Monte Carlo (MC) simulations. It is evident that the results from the KLME approach with higher‐order corrections are close to those f...
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a comparative study on uncertainty quantification for flow in randomly heterogeneous media using monte carlo simulations and conventional and kl based Moment Equation approaches
Computational Science and Engineering, 2005Co-Authors: Dongxiao ZhangAbstract:Geological formations are ubiquitously heterogeneous, and the Equations that govern flow and transport in such formations can be treated as stochastic partial differential Equations. The Monte Carlo method is a straightforward approach for simulating flow in heterogeneous porous media; an alternative based on the Moment-Equation approach has been developed in the last two decades to reduce the high computational expense required by the Monte Carlo method. However, the computational cost of the Moment-Equation approach is still high. For example, to solve head covariance up to first order in terms of $\sigma_Y^2$, the variance of log hydraulic conductivity Y = ln Ks, it is required to solve sets of linear algebraic Equations with N unknowns for 2N times (N being the number of grid nodes). The cost is even higher if higher-order approximations are needed. Zhang and Lu [J. Comput. Phys., 194 (2004), pp. 773--794] developed a new approach to evaluate high-order Moments (fourth order for mean head in terms of $\sigma_Y$, and third order for head variances in terms of $\sigma_Y^2$) of flow quantities based on the combination of Karhunen--Loeve decomposition and perturbation methods. In this study, we systematically investigate the computational efficiency and solution accuracy of three approaches: Monte Carlo simulations, the conventional Moment-Equation (CME) approach, and the Moment-Equation approach based on Karhunen--Loeve decomposition (KLME). It is evident that the computational cost for the KLME approach is significantly lower than those required by the Monte Carlo and CME approaches. More importantly, while the computational costs (in terms of the number of times for solving linear algebraic Equations with N unknowns) for the CME approach depend on the number of grid nodes, the cost for the KLME approach is independent of the number of grid nodes. This makes it possible to apply the KLME method to solve more realistic large-scale flow problems.
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conditional simulations of flow in randomly heterogeneous porous media using a kl based Moment Equation approach
Advances in Water Resources, 2004Co-Authors: Zhiming Lu, Dongxiao ZhangAbstract:Abstract In this study, we extend the KLME approach, a Moment-Equation approach based on the Karhunen–Loeve decomposition (KL), developed by Zhang and Lu [An efficient, higher-order perturbation approach for flow in randomly heterogeneous porous media via Karhunen–Loeve decomposition. J Comput Phys 2004;194(2):773–94] to efficiently incorporate existing direct measurements of the log hydraulic conductivity. We first decompose the conditional log hydraulic conductivity Y = lnKs as an infinite series on the basis of a set of orthogonal Gaussian standard random variables {ξi}. The coefficients of this series are related to eigenvalues and eigenfunctions of the conditional covariance function of the log hydraulic conductivity. We then write head as an infinite series whose terms h(n) represent the head contribution at the nth order in terms of σY, the standard deviation of Y, and derive a set of recursive Equations for h(n). We assume that h(n) can be expressed as infinite series in terms of the products of n Gaussian random variables. The coefficients in these series are determined by substituting decompositions of Y and h(m), m σ Y 2 . The higher-order corrections for the conditional mean flux and flux covariance can be determined directly from the higher-order Moments of the head, using Darcy’s law. We compare the results from the KLME approach against those from Monte Carlo (MC) simulations and the conventional first-order Moment method. It is evident that the KLME approach with higher-order corrections is superior to the conventional first-order approximations and is computationally more efficient than both the Monte Carlo simulations and the conventional first-order Moment method.
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Higher-Order Approximations for Saturated Flow in Randomly Heterogeneous Media via Karhunen-Loéve Decomposition
World Water & Environmental Resources Congress 2003, 2003Co-Authors: Zhiming Lu, Dongxiao ZhangAbstract:In this study, we consider transient saturated flow in randomly heterogeneous porous media and try to obtain higher-order solutions of mean head and mean flux, as well as their associated uncertainties based on the combination of Karhunen-Loeve decomposition and perturbation methods. We first decompose the log hydraulic conductivity Y = lnKs as an infinite series on the basis of a set of orthogonal Gaussian standard random variables. The coefficients of the series are related to eigenvalues and eigenfunctions of the covariance function of the log hydraulic conductivity. We then write head as an infinite series whose terms h (n) represent the hydraulic head of n th order in terms of σY, the standard deviation of Y, and derive a set of recursive Equations for h (n) . We assume that h (n) can be expressed as infinite series in terms of products of n Gaussian random variables. The coefficients in these series are determined by substituting decompositions of Ya nd h (n) into those recursive Equations. We solve the mean head (and mean flux) up to fourth order in σY and the head (and flux) variances up to third order in σY 2 . We conduct Monte Carlo simulations (MC) and compare MC results against approximations of various orders from our Moment-Equation approach on the basis of Karhunen-Loeve decomposition (KLME). We also compare our results with those from first-order conventional Moment-Equation approach (CME). It is evident that the KLME approach with higher-order corrections is superior to firstorder approximations and is computationally more efficient than Monte Carlo simulations and the conventional Moment-Equation approach.
