A Critical Study of Agglomerated Multigrid Methods for Diffusion
NASA Technical Reports Server (NTRS)
Nishikawa, Hiroaki; Diskin, Boris; Thomas, James L.
2011-01-01
Agglomerated multigrid techniques used in unstructured-grid methods are studied critically for a model problem representative of laminar diffusion in the incompressible limit. The studied target-grid discretizations and discretizations used on agglomerated grids are typical of current node-centered formulations. Agglomerated multigrid convergence rates are presented using a range of two- and three-dimensional randomly perturbed unstructured grids for simple geometries with isotropic and stretched grids. Two agglomeration techniques are used within an overall topology-preserving agglomeration framework. The results show that multigrid with an inconsistent coarse-grid scheme using only the edge terms (also referred to in the literature as a thin-layer formulation) provides considerable speedup over single-grid methods but its convergence deteriorates on finer grids. Multigrid with a Galerkin coarse-grid discretization using piecewise-constant prolongation and a heuristic correction factor is slower and also grid-dependent. In contrast, grid-independent convergence rates are demonstrated for multigrid with consistent coarse-grid discretizations. Convergence rates of multigrid cycles are verified with quantitative analysis methods in which parts of the two-grid cycle are replaced by their idealized counterparts.
A Critical Study of Agglomerated Multigrid Methods for Diffusion
NASA Technical Reports Server (NTRS)
Thomas, James L.; Nishikawa, Hiroaki; Diskin, Boris
2009-01-01
Agglomerated multigrid techniques used in unstructured-grid methods are studied critically for a model problem representative of laminar diffusion in the incompressible limit. The studied target-grid discretizations and discretizations used on agglomerated grids are typical of current node-centered formulations. Agglomerated multigrid convergence rates are presented using a range of two- and three-dimensional randomly perturbed unstructured grids for simple geometries with isotropic and highly stretched grids. Two agglomeration techniques are used within an overall topology-preserving agglomeration framework. The results show that multigrid with an inconsistent coarse-grid scheme using only the edge terms (also referred to in the literature as a thin-layer formulation) provides considerable speedup over single-grid methods but its convergence deteriorates on finer grids. Multigrid with a Galerkin coarse-grid discretization using piecewise-constant prolongation and a heuristic correction factor is slower and also grid-dependent. In contrast, grid-independent convergence rates are demonstrated for multigrid with consistent coarse-grid discretizations. Actual cycle results are verified using quantitative analysis methods in which parts of the cycle are replaced by their idealized counterparts.
Development and Application of Agglomerated Multigrid Methods for Complex Geometries
NASA Technical Reports Server (NTRS)
Nishikawa, Hiroaki; Diskin, Boris; Thomas, James L.
2010-01-01
We report progress in the development of agglomerated multigrid techniques for fully un- structured grids in three dimensions, building upon two previous studies focused on efficiently solving a model diffusion equation. We demonstrate a robust fully-coarsened agglomerated multigrid technique for 3D complex geometries, incorporating the following key developments: consistent and stable coarse-grid discretizations, a hierarchical agglomeration scheme, and line-agglomeration/relaxation using prismatic-cell discretizations in the highly-stretched grid regions. A signi cant speed-up in computer time is demonstrated for a model diffusion problem, the Euler equations, and the Reynolds-averaged Navier-Stokes equations for 3D realistic complex geometries.
Unstructured multigrid through agglomeration
NASA Technical Reports Server (NTRS)
Venkatakrishnan, V.; Mavriplis, D. J.; Berger, M. J.
1993-01-01
In this work the compressible Euler equations are solved using finite volume techniques on unstructured grids. The spatial discretization employs a central difference approximation augmented by dissipative terms. Temporal discretization is done using a multistage Runge-Kutta scheme. A multigrid technique is used to accelerate convergence to steady state. The coarse grids are derived directly from the given fine grid through agglomeration of the control volumes. This agglomeration is accomplished by using a greedy-type algorithm and is done in such a way that the load, which is proportional to the number of edges, goes down by nearly a factor of 4 when moving from a fine to a coarse grid. The agglomeration algorithm has been implemented and the grids have been tested in a multigrid code. An area-weighted restriction is applied when moving from fine to coarse grids while a trivial injection is used for prolongation. Across a range of geometries and flows, it is shown that the agglomeration multigrid scheme compares very favorably with an unstructured multigrid algorithm that makes use of independent coarse meshes, both in terms of convergence and elapsed times.
Recent Advances in Agglomerated Multigrid
NASA Technical Reports Server (NTRS)
Nishikawa, Hiroaki; Diskin, Boris; Thomas, James L.; Hammond, Dana P.
2013-01-01
We report recent advancements of the agglomerated multigrid methodology for complex flow simulations on fully unstructured grids. An agglomerated multigrid solver is applied to a wide range of test problems from simple two-dimensional geometries to realistic three- dimensional configurations. The solver is evaluated against a single-grid solver and, in some cases, against a structured-grid multigrid solver. Grid and solver issues are identified and overcome, leading to significant improvements over single-grid solvers.
NASA Astrophysics Data System (ADS)
Langer, Stefan
2014-11-01
For unstructured finite volume methods an agglomeration multigrid with an implicit multistage Runge-Kutta method as a smoother is developed for solving the compressible Reynolds averaged Navier-Stokes (RANS) equations. The implicit Runge-Kutta method is interpreted as a preconditioned explicit Runge-Kutta method. The construction of the preconditioner is based on an approximate derivative. The linear systems are solved approximately with a symmetric Gauss-Seidel method. To significantly improve this solution method grid anisotropy is treated within the Gauss-Seidel iteration in such a way that the strong couplings in the linear system are resolved by tridiagonal systems constructed along these directions of strong coupling. The agglomeration strategy is adapted to this procedure by taking into account exactly these anisotropies in such a way that a directional coarsening is applied along these directions of strong coupling. Turbulence effects are included by a Spalart-Allmaras model, and the additional transport-type equation is approximately solved in a loosely coupled manner with the same method. For two-dimensional and three-dimensional numerical examples and a variety of differently generated meshes we show the wide range of applicability of the solution method. Finally, we exploit the GMRES method to determine approximate spectral information of the linearized RANS equations. This approximate spectral information is used to discuss and compare characteristics of multistage Runge-Kutta methods.
Agglomeration multigrid for viscous turbulent flows
NASA Technical Reports Server (NTRS)
Mavriplis, D. J.; Venkatakrishnan, V.
1994-01-01
Agglomeration multigrid, which has been demonstrated as an efficient and automatic technique for the solution of the Euler equations on unstructured meshes, is extended to viscous turbulent flows. For diffusion terms, coarse grid discretizations are not possible, and more accurate grid transfer operators are required as well. A Galerkin coarse grid operator construction and an implicit prolongation operator are proposed. Their suitability is evaluated by examining their effect on the solution of Laplace's equation. The resulting strategy is employed to solve the Reynolds-averaged Navier-Stokes equations for aerodynamic flows. Convergence rates comparable to those obtained by a previously developed non-nested mesh multigrid approach are demonstrated, and suggestions for further improvements are given.
Agglomeration multigrid for the three-dimensional Euler equations
NASA Technical Reports Server (NTRS)
Venkatakrishnan, V.; Mavriplis, D. J.
1994-01-01
A multigrid procedure that makes use of coarse grids generated by the agglomeration of control volumes is advocated as a practical approach for solving the three dimensional Euler equations on unstructured grids about complex configurations. It is shown that the agglomeration procedure can be tailored to achieve certain coarse grid properties such as the sizes of the coarse grids and aspect ratios of the coarse grid cells. The agglomeration is done as a preprocessing step and runs in linear time. The implications for multigrid of using arbitrary polyhedral coarse grids are discussed. The agglomeration multigrid technique compares very favorably with existing multigrid procedures both in terms of convergence rates and elapsed times. The main advantage of the present approach is the ease with which coarse grids of any desired degree of coarseness may be generated in three dimensions, without being constrained by considerations of geometry. Inviscid flows over a variety of complex configurations are computed using the agglomeration multigrid strategy.
Introduction to multigrid methods
NASA Technical Reports Server (NTRS)
Wesseling, P.
1995-01-01
These notes were written for an introductory course on the application of multigrid methods to elliptic and hyperbolic partial differential equations for engineers, physicists and applied mathematicians. The use of more advanced mathematical tools, such as functional analysis, is avoided. The course is intended to be accessible to a wide audience of users of computational methods. We restrict ourselves to finite volume and finite difference discretization. The basic principles are given. Smoothing methods and Fourier smoothing analysis are reviewed. The fundamental multigrid algorithm is studied. The smoothing and coarse grid approximation properties are discussed. Multigrid schedules and structured programming of multigrid algorithms are treated. Robustness and efficiency are considered.
Adaptive Algebraic Multigrid Methods
Brezina, M; Falgout, R; MacLachlan, S; Manteuffel, T; McCormick, S; Ruge, J
2004-04-09
Our ability to simulate physical processes numerically is constrained by our ability to solve the resulting linear systems, prompting substantial research into the development of multiscale iterative methods capable of solving these linear systems with an optimal amount of effort. Overcoming the limitations of geometric multigrid methods to simple geometries and differential equations, algebraic multigrid methods construct the multigrid hierarchy based only on the given matrix. While this allows for efficient black-box solution of the linear systems associated with discretizations of many elliptic differential equations, it also results in a lack of robustness due to assumptions made on the near-null spaces of these matrices. This paper introduces an extension to algebraic multigrid methods that removes the need to make such assumptions by utilizing an adaptive process. The principles which guide the adaptivity are highlighted, as well as their application to algebraic multigrid solution of certain symmetric positive-definite linear systems.
Agglomeration Multigrid for an Unstructured-Grid Flow Solver
NASA Technical Reports Server (NTRS)
Frink, Neal; Pandya, Mohagna J.
2004-01-01
An agglomeration multigrid scheme has been implemented into the sequential version of the NASA code USM3Dns, tetrahedral cell-centered finite volume Euler/Navier-Stokes flow solver. Efficiency and robustness of the multigrid-enhanced flow solver have been assessed for three configurations assuming an inviscid flow and one configuration assuming a viscous fully turbulent flow. The inviscid studies include a transonic flow over the ONERA M6 wing and a generic business jet with flow-through nacelles and a low subsonic flow over a high-lift trapezoidal wing. The viscous case includes a fully turbulent flow over the RAE 2822 rectangular wing. The multigrid solutions converged with 12%-33% of the Central Processing Unit (CPU) time required by the solutions obtained without multigrid. For all of the inviscid cases, multigrid in conjunction with an explicit time-stepping scheme performed the best with regard to the run time memory and CPU time requirements. However, for the viscous case multigrid had to be used with an implicit backward Euler time-stepping scheme that increased the run time memory requirement by 22% as compared to the run made without multigrid.
NASA Technical Reports Server (NTRS)
Marvriplis, D. J.; Venkatakrishnan, V.
1995-01-01
An agglomeration multigrid strategy is developed and implemented for the solution of three-dimensional steady viscous flows. The method enables convergence acceleration with minimal additional memory overheads, and is completely automated, in that it can deal with grids of arbitrary construction. The multigrid technique is validated by comparing the delivered convergence rates with those obtained by a previously developed overset-mesh multigrid approach, and by demonstrating grid independent convergence rates for aerodynamic problems on very large grids. Prospects for further increases in multigrid efficiency for high-Reynolds number viscous flows on highly stretched meshes are discussed.
NASA Technical Reports Server (NTRS)
Schaffer, Steve; Stenger, Frank
1986-01-01
A Galerkin method using Whittaker cardinal or 'sinc' functions as basis functions is described for the solution of boundary-value problems. When the solution is analytic in the interior of the domain, the error of approximation using 2N + 1 points is O(e exp /-gamma sq rt N/) even if derivatives of the solution are singular at the boundaries. A multigrid method with overall complexity O(N log N) is used to solve the discrete equations. This paper contains a description of the multigrid-sinc algorithm along with some preliminary numerical results for two-point boundary-value problems.
Multigrid contact detection method
NASA Astrophysics Data System (ADS)
He, Kejing; Dong, Shoubin; Zhou, Zhaoyao
2007-03-01
Contact detection is a general problem of many physical simulations. This work presents a O(N) multigrid method for general contact detection problems (MGCD). The multigrid idea is integrated with contact detection problems. Both the time complexity and memory consumption of the MGCD are O(N) . Unlike other methods, whose efficiencies are influenced strongly by the object size distribution, the performance of MGCD is insensitive to the object size distribution. We compare the MGCD with the no binary search (NBS) method and the multilevel boxing method in three dimensions for both time complexity and memory consumption. For objects with similar size, the MGCD is as good as the NBS method, both of which outperform the multilevel boxing method regarding memory consumption. For objects with diverse size, the MGCD outperform both the NBS method and the multilevel boxing method. We use the MGCD to solve the contact detection problem for a granular simulation system based on the discrete element method. From this granular simulation, we get the density property of monosize packing and binary packing with size ratio equal to 10. The packing density for monosize particles is 0.636. For binary packing with size ratio equal to 10, when the number of small particles is 300 times as the number of big particles, the maximal packing density 0.824 is achieved.
Unstructured multigrid methods
NASA Technical Reports Server (NTRS)
Loehner, R.; Morgan, K.
1987-01-01
The use of the multigrid procedure with a sequence of unnested coarser grids is discussed. Validity of the procedure is assessed by considering the solution of a single linear elliptic equation. It is demonstrated how a scheme with the optimum order of operations can be constructed. Application to the solution of the Euler equations is considered.
Directional Agglomeration Multigrid Techniques for High Reynolds Number Viscous Flow Solvers
NASA Technical Reports Server (NTRS)
1998-01-01
A preconditioned directional-implicit agglomeration algorithm is developed for solving two- and three-dimensional viscous flows on highly anisotropic unstructured meshes of mixed-element types. The multigrid smoother consists of a pre-conditioned point- or line-implicit solver which operates on lines constructed in the unstructured mesh using a weighted graph algorithm. Directional coarsening or agglomeration is achieved using a similar weighted graph algorithm. A tight coupling of the line construction and directional agglomeration algorithms enables the use of aggressive coarsening ratios in the multigrid algorithm, which in turn reduces the cost of a multigrid cycle. Convergence rates which are independent of the degree of grid stretching are demonstrated in both two and three dimensions. Further improvement of the three-dimensional convergence rates through a GMRES technique is also demonstrated.
Some Aspects of Multigrid Methods on Non-Structured Meshes
NASA Technical Reports Server (NTRS)
Guillard, H.; Marco, N.
1996-01-01
To solve a given fine mesh problem, the design of a multigrid method requires the definition of coarse levels, associated coarse grid operators and inter-grid transfer operators. For non-structured simplified meshes, these definitions can rely on the use of non-nested triangulations. These definitions can also be founded on agglomeration/aggregation techniques in a purely algebraic manner. This paper analyzes these two options, shows the connections of the volume-agglomeration method with algebraic methods and proposes a new definition of prolongation operator suitable for the application of the volume-agglomeration method to elliptic problems.
Parallel Element Agglomeration Algebraic Multigrid and Upscaling Library
2015-02-19
ParFELAG is a parallel distributed memory C++ library for numerical upscaling of finite element discretizations. It provides optimal complesity algorithms ro build multilevel hierarchies and solvers that can be used for solving a wide class of partial differential equations (elliptic, hyperbolic, saddle point problems) on general unstructured mesh (under the assumption that the topology of the agglomerated entities is correct). Additionally, a novel multilevel solver for saddle point problems with divergence constraint is implemented.
Report on the Copper Mountain Conference on Multigrid Methods
2001-04-06
OAK B188 Report on the Copper Mountain Conference on Multigrid Methods. The Copper Mountain Conference on Multigrid Methods was held on April 11-16, 1999. Over 100 mathematicians from all over the world attended the meeting. The conference had two major themes: algebraic multigrid and parallel multigrid. During the five day meeting 69 talks on current research topics were presented as well as 3 tutorials. Talks with similar content were organized into sessions. Session topics included: Fluids; Multigrid and Multilevel Methods; Applications; PDE Reformulation; Inverse Problems; Special Methods; Decomposition Methods; Student Paper Winners; Parallel Multigrid; Parallel Algebraic Multigrid; and FOSLS.
Extending the applicability of multigrid methods
Brannick, J; Brezina, M; Falgout, R; Manteuffel, T; McCormick, S; Ruge, J; Sheehan, B; Xu, J; Zikatanov, L
2006-09-25
Multigrid methods are ideal for solving the increasingly large-scale problems that arise in numerical simulations of physical phenomena because of their potential for computational costs and memory requirements that scale linearly with the degrees of freedom. Unfortunately, they have been historically limited by their applicability to elliptic-type problems and the need for special handling in their implementation. In this paper, we present an overview of several recent theoretical and algorithmic advances made by the TOPS multigrid partners and their collaborators in extending applicability of multigrid methods. Specific examples that are presented include quantum chromodynamics, radiation transport, and electromagnetics.
A multigrid method for the Euler equations
NASA Technical Reports Server (NTRS)
Jespersen, D. C.
1983-01-01
A multigrid algorithm has been developed for the numerical solution of the steady two-dimensional Euler equations. Flux vector splitting and one-sided differencing are employed to define the spatial discretization. Newton's method is used to solve the nonlinear equations, and a multigrid solver is used on each linear problem. The relaxation scheme for the linear problems is symmetric Gauss-Seidel. Standard restriction and interpolation operators are employed. Local mode analysis is used to predict the convergence rate of the multigrid process on the linear problems. Computed results for transonic flows over airfoils are presented.
Multigrid Methods for EHL Problems
NASA Technical Reports Server (NTRS)
Nurgat, Elyas; Berzins, Martin
1996-01-01
In many bearings and contacts, forces are transmitted through thin continuous fluid films which separate two contacting elements. Objects in contact are normally subjected to friction and wear which can be reduced effectively by using lubricants. If the lubricant film is sufficiently thin to prevent the opposing solids from coming into contact and carries the entire load, then we have hydrodynamic lubrication, where the lubricant film is determined by the motion and geometry of the solids. However, for loaded contacts of low geometrical conformity, such as gears, rolling contact bearings and cams, this is not the case due to high pressures and this is referred to as Elasto-Hydrodynamic Lubrication (EHL) In EHL, elastic deformation of the contacting elements and the increase in fluid viscosity with pressure are very significant and cannot be ignored. Since the deformation results in changing the geometry of the lubricating film, which in turn determines the pressure distribution, an EHL mathematical model must simultaneously satisfy the complex elasticity (integral) and the Reynolds lubrication (differential) equations. The nonlinear and coupled nature of the two equations makes numerical calculations computationally intensive. This is especially true for highly loaded problems found in practice. One novel feature of these problems is that the solution may exhibit sharp pressure spikes in the outlet region. To this date both finite element and finite difference methods have been used to solve EHL problems with perhaps greater emphasis on the use of the finite difference approach. In both cases, a major computational difficulty is ensuring convergence of the nonlinear equations solver to a steady state solution. Two successful methods for achieving this are direct iteration and multigrid methods. Direct iteration methods (e.g Gauss Seidel) have long been used in conjunction with finite difference discretizations on regular meshes. Perhaps one of the best examples of
A full multigrid method for eigenvalue problems
NASA Astrophysics Data System (ADS)
Chen, Hongtao; Xie, Hehu; Xu, Fei
2016-10-01
In this paper, a full (nested) multigrid scheme is proposed to solve eigenvalue problems. The idea here is to use a correction method to transform the eigenvalue problem solving to a series of corresponding boundary value problem solving and eigenvalue problems defined on a very low-dimensional finite element space. The boundary value problems which are defined on a sequence of multilevel finite element spaces can be solved by some multigrid iteration steps. The computational work of this new scheme can reach the same optimal order as solving the corresponding boundary value problem by the full multigrid method. Therefore, this type of full multigrid method improves the overfull efficiency of the eigenvalue problem solving.
A multigrid method for variational inequalities
Oliveira, S.; Stewart, D.E.; Wu, W.
1996-12-31
Multigrid methods have been used with great success for solving elliptic partial differential equations. Penalty methods have been successful in solving finite-dimensional quadratic programs. In this paper these two techniques are combined to give a fast method for solving obstacle problems. A nonlinear penalized problem is solved using Newton`s method for large values of a penalty parameter. Multigrid methods are used to solve the linear systems in Newton`s method. The overall numerical method developed is based on an exterior penalty function, and numerical results showing the performance of the method have been obtained.
Multigrid methods with applications to reservoir simulation
Xiao, Shengyou
1994-05-01
Multigrid methods are studied for solving elliptic partial differential equations. Focus is on parallel multigrid methods and their use for reservoir simulation. Multicolor Fourier analysis is used to analyze the behavior of standard multigrid methods for problems in one and two dimensions. Relation between multicolor and standard Fourier analysis is established. Multiple coarse grid methods for solving model problems in 1 and 2 dimensions are considered; at each coarse grid level we use more than one coarse grid to improve convergence. For a given Dirichlet problem, a related extended problem is first constructed; a purification procedure can be used to obtain Moore-Penrose solutions of the singular systems encountered. For solving anisotropic equations, semicoarsening and line smoothing techniques are used with multiple coarse grid methods to improve convergence. Two-level convergence factors are estimated using multicolor. In the case where each operator has the same stencil on each grid point on one level, exact multilevel convergence factors can be obtained. For solving partial differential equations with discontinuous coefficients, interpolation and restriction operators should include information about the equation coefficients. Matrix-dependent interpolation and restriction operators based on the Schur complement can be used in nonsymmetric cases. A semicoarsening multigrid solver with these operators is used in UTCOMP, a 3-D, multiphase, multicomponent, compositional reservoir simulator. The numerical experiments are carried out on different computing systems. Results indicate that the multigrid methods are promising.
Spectral multigrid methods for elliptic equations
NASA Technical Reports Server (NTRS)
Zang, T. A.; Wong, Y. S.; Hussaini, M. Y.
1981-01-01
An alternative approach which employs multigrid concepts in the iterative solution of spectral equations was examined. Spectral multigrid methods are described for self adjoint elliptic equations with either periodic or Dirichlet boundary conditions. For realistic fluid calculations the relevant boundary conditions are periodic in at least one (angular) coordinate and Dirichlet (or Neumann) in the remaining coordinates. Spectral methods are always effective for flows in strictly rectangular geometries since corners generally introduce singularities into the solution. If the boundary is smooth, then mapping techniques are used to transform the problem into one with a combination of periodic and Dirichlet boundary conditions. It is suggested that spectral multigrid methods in these geometries can be devised by combining the techniques.
Relaxation schemes for Chebyshev spectral multigrid methods
NASA Technical Reports Server (NTRS)
Kang, Yimin; Fulton, Scott R.
1993-01-01
Two relaxation schemes for Chebyshev spectral multigrid methods are presented for elliptic equations with Dirichlet boundary conditions. The first scheme is a pointwise-preconditioned Richardson relaxation scheme and the second is a line relaxation scheme. The line relaxation scheme provides an efficient and relatively simple approach for solving two-dimensional spectral equations. Numerical examples and comparisons with other methods are given.
Spectral multigrid methods for elliptic equations II
NASA Technical Reports Server (NTRS)
Zang, T. A.; Wong, Y. S.; Hussaini, M. Y.
1984-01-01
A detailed description of spectral multigrid methods is provided. This includes the interpolation and coarse-grid operators for both periodic and Dirichlet problems. The spectral methods for periodic problems use Fourier series and those for Dirichlet problems are based upon Chebyshev polynomials. An improved preconditioning for Dirichlet problems is given. Numerical examples and practical advice are included.
Spectral multigrid methods for elliptic equations 2
NASA Technical Reports Server (NTRS)
Zang, T. A.; Wong, Y. S.; Hussaini, M. Y.
1983-01-01
A detailed description of spectral multigrid methods is provided. This includes the interpolation and coarse-grid operators for both periodic and Dirichlet problems. The spectral methods for periodic problems use Fourier series and those for Dirichlet problems are based upon Chebyshev polynomials. An improved preconditioning for Dirichlet problems is given. Numerical examples and practical advice are included.
Multigrid Methods in Electronic Structure Calculations
NASA Astrophysics Data System (ADS)
Briggs, Emil
1996-03-01
Multigrid techniques have become the method of choice for a broad range of computational problems. Their use in electronic structure calculations introduces a new set of issues when compared to traditional plane wave approaches. We have developed a set of techniques that address these issues and permit multigrid algorithms to be applied to the electronic structure problem in an efficient manner. In our approach the Kohn-Sham equations are discretized on a real-space mesh using a compact representation of the Hamiltonian. The resulting equations are solved directly on the mesh using multigrid iterations. This produces rapid convergence rates even for ill-conditioned systems with large length and/or energy scales. The method has been applied to both periodic and non-periodic systems containing over 400 atoms and the results are in very good agreement with both theory and experiment. Example applications include a vacancy in diamond, an isolated C60 molecule, and a 64-atom cell of GaN with the Ga d-electrons in valence which required a 250 Ry cutoff. A particular strength of a real-space multigrid approach is its ready adaptability to massively parallel computer architectures. The compact representation of the Hamiltonian is especially well suited to such machines. Tests on the Cray-T3D have shown nearly linear scaling of the execution time up to the maximum number of processors (512). The MPP implementation has been used for studies of a large Amyloid Beta Peptide (C_146O_45N_42H_210) found in the brains of Alzheimers disease patients. Further applications of the multigrid method will also be described. (in collaboration D. J. Sullivan and J. Bernholc)
Grandchild of the frequency: Decomposition multigrid method
Dendy, J.E. Jr.; Tazartes, C.C.
1994-12-31
Previously the authors considered the frequency decomposition multigrid method and rejected it because it was not robust for problems with discontinuous coefficients. In this paper they show how to modify the method so as to obtain such robustness while retaining robustness for problems with anisotropic coefficients. They also discuss application of this method to a problem arising in global ocean modeling on the CM-5.
On Some Versions of the Element Agglomeration AMGe Method
Lashuk, I; Vassilevski, P
2007-08-09
The present paper deals with element-based AMG methods that target linear systems of equations coming from finite element discretizations of elliptic PDEs. The individual element information (element matrices and element topology) is the main input to construct the AMG hierarchy. We study a number of variants of the spectral agglomerate element based AMG method. The core of the algorithms relies on element agglomeration utilizing the element topology (built recursively from fine to coarse levels). The actual selection of the coarse degrees of freedom (dofs) is based on solving large number of local eigenvalue problems. Additionally, we investigate strategies for adaptive AMG as well as multigrid cycles that are more expensive than the V-cycle utilizing simple interpolation matrices and nested conjugate gradient (CG) based recursive calls between the levels. The presented algorithms are illustrated with an extensive set of experiments based on a matlab implementation of the methods.
Implementing abstract multigrid or multilevel methods
NASA Technical Reports Server (NTRS)
Douglas, Craig C.
1993-01-01
Multigrid methods can be formulated as an algorithm for an abstract problem that is independent of the partial differential equation, domain, and discretization method. In such an abstract setting, problems not arising from partial differential equations can be treated. A general theory exists for linear problems. The general theory was motivated by a series of abstract solvers (Madpack). The latest version was motivated by the theory. Madpack now allows for a wide variety of iterative and direct solvers, preconditioners, and interpolation and projection schemes, including user callback ones. It allows for sparse, dense, and stencil matrices. Mildly nonlinear problems can be handled. Also, there is a fast, multigrid Poisson solver (two and three dimensions). The type of solvers and design decisions (including language, data structures, external library support, and callbacks) are discussed. Based on the author's experiences with two versions of Madpack, a better approach is proposed. This is based on a mixed language formulation (C and FORTRAN + preprocessor). Reasons for not using FORTRAN, C, or C++ (individually) are given. Implementing the proposed strategy is not difficult.
Lecture Notes on Multigrid Methods
Vassilevski, P S
2010-06-28
The Lecture Notes are primarily based on a sequence of lectures given by the author while been a Fulbright scholar at 'St. Kliment Ohridski' University of Sofia, Sofia, Bulgaria during the winter semester of 2009-2010 academic year. The notes are somewhat expanded version of the actual one semester class he taught there. The material covered is slightly modified and adapted version of similar topics covered in the author's monograph 'Multilevel Block-Factorization Preconditioners' published in 2008 by Springer. The author tried to keep the notes as self-contained as possible. That is why the lecture notes begin with some basic introductory matrix-vector linear algebra, numerical PDEs (finite element) facts emphasizing the relations between functions in finite dimensional spaces and their coefficient vectors and respective norms. Then, some additional facts on the implementation of finite elements based on relation tables using the popular compressed sparse row (CSR) format are given. Also, typical condition number estimates of stiffness and mass matrices, the global matrix assembly from local element matrices are given as well. Finally, some basic introductory facts about stationary iterative methods, such as Gauss-Seidel and its symmetrized version are presented. The introductory material ends up with the smoothing property of the classical iterative methods and the main definition of two-grid iterative methods. From here on, the second part of the notes begins which deals with the various aspects of the principal TG and the numerous versions of the MG cycles. At the end, in part III, we briefly introduce algebraic versions of MG referred to as AMG, focusing on classes of AMG specialized for finite element matrices.
Vandewalle, S.
1994-12-31
Time-stepping methods for parabolic partial differential equations are essentially sequential. This prohibits the use of massively parallel computers unless the problem on each time-level is very large. This observation has led to the development of algorithms that operate on more than one time-level simultaneously; that is to say, on grids extending in space and in time. The so-called parabolic multigrid methods solve the time-dependent parabolic PDE as if it were a stationary PDE discretized on a space-time grid. The author has investigated the use of multigrid waveform relaxation, an algorithm developed by Lubich and Ostermann. The algorithm is based on a multigrid acceleration of waveform relaxation, a highly concurrent technique for solving large systems of ordinary differential equations. Another method of this class is the time-parallel multigrid method. This method was developed by Hackbusch and was recently subject of further study by Horton. It extends the elliptic multigrid idea to the set of equations that is derived by discretizing a parabolic problem in space and in time.
Semi-coarsening multigrid methods for parallel computing
Jones, J.E.
1996-12-31
Standard multigrid methods are not well suited for problems with anisotropic coefficients which can occur, for example, on grids that are stretched to resolve a boundary layer. There are several different modifications of the standard multigrid algorithm that yield efficient methods for anisotropic problems. In the paper, we investigate the parallel performance of these multigrid algorithms. Multigrid algorithms which work well for anisotropic problems are based on line relaxation and/or semi-coarsening. In semi-coarsening multigrid algorithms a grid is coarsened in only one of the coordinate directions unlike standard or full-coarsening multigrid algorithms where a grid is coarsened in each of the coordinate directions. When both semi-coarsening and line relaxation are used, the resulting multigrid algorithm is robust and automatic in that it requires no knowledge of the nature of the anisotropy. This is the basic multigrid algorithm whose parallel performance we investigate in the paper. The algorithm is currently being implemented on an IBM SP2 and its performance is being analyzed. In addition to looking at the parallel performance of the basic semi-coarsening algorithm, we present algorithmic modifications with potentially better parallel efficiency. One modification reduces the amount of computational work done in relaxation at the expense of using multiple coarse grids. This modification is also being implemented with the aim of comparing its performance to that of the basic semi-coarsening algorithm.
Preconditioners for the spectral multigrid method
NASA Technical Reports Server (NTRS)
Phillips, T. N.; Zang, T. A.; Hussaini, M. Y.
1983-01-01
The systems of algebraic equations which arise from spectral discretizations of elliptic equations are full and direct solutions of them are rarely feasible. Iterative methods are an attractive alternative because Fourier transform techniques enable the discrete matrix-vector products to be computed with nearly the same efficiency as is possible for corresponding but sparse finite difference discretizations. For realistic Dirichlet problems preconditioning is essential for acceptable convergence rates. A brief description of Chebyshev spectral approximations and spectral multigrid methods for elliptic problems is given. A survey of preconditioners for Dirichlet problems based on second-order finite difference methods is made. New preconditioning techniques based on higher order finite differences and on the spectral matrix itself are presented. The preconditioners are analyzed in terms of their spectra and numerical examples are presented.
Preconditioners for the spectral multigrid method
NASA Technical Reports Server (NTRS)
Phillips, T. N.; Hussaini, M. Y.; Zang, T. A.
1986-01-01
The systems of algebraic equations which arise from spectral discretizations of elliptic equations are full and direct solutions of them are rarely feasible. Iterative methods are an attractive alternative because Fourier transform techniques enable the discrete matrix-vector products to be computed with nearly the same efficiency as is possible for corresponding but sparse finite difference discretizations. For realistic Dirichlet problem preconditioning is essential for acceptable convergence rates. A brief description of Chebyshev spectral approximations and spectral multigrid methods for elliptic problems is given. A survey of preconditioners for Dirichlet problems based on second-order finite difference methods is made. New preconditioning techniques based on higher order finite differences and on the spectral matrix itself are presented. The preconditioners are analyzed in terms of their spectra and numerical examples are presented.
Layout optimization with algebraic multigrid methods
NASA Technical Reports Server (NTRS)
Regler, Hans; Ruede, Ulrich
1993-01-01
Finding the optimal position for the individual cells (also called functional modules) on the chip surface is an important and difficult step in the design of integrated circuits. This paper deals with the problem of relative placement, that is the minimization of a quadratic functional with a large, sparse, positive definite system matrix. The basic optimization problem must be augmented by constraints to inhibit solutions where cells overlap. Besides classical iterative methods, based on conjugate gradients (CG), we show that algebraic multigrid methods (AMG) provide an interesting alternative. For moderately sized examples with about 10000 cells, AMG is already competitive with CG and is expected to be superior for larger problems. Besides the classical 'multiplicative' AMG algorithm where the levels are visited sequentially, we propose an 'additive' variant of AMG where levels may be treated in parallel and that is suitable as a preconditioner in the CG algorithm.
Convergence acceleration of the Proteus computer code with multigrid methods
NASA Technical Reports Server (NTRS)
Demuren, A. O.; Ibraheem, S. O.
1995-01-01
This report presents the results of a study to implement convergence acceleration techniques based on the multigrid concept in the two-dimensional and three-dimensional versions of the Proteus computer code. The first section presents a review of the relevant literature on the implementation of the multigrid methods in computer codes for compressible flow analysis. The next two sections present detailed stability analysis of numerical schemes for solving the Euler and Navier-Stokes equations, based on conventional von Neumann analysis and the bi-grid analysis, respectively. The next section presents details of the computational method used in the Proteus computer code. Finally, the multigrid implementation and applications to several two-dimensional and three-dimensional test problems are presented. The results of the present study show that the multigrid method always leads to a reduction in the number of iterations (or time steps) required for convergence. However, there is an overhead associated with the use of multigrid acceleration. The overhead is higher in 2-D problems than in 3-D problems, thus overall multigrid savings in CPU time are in general better in the latter. Savings of about 40-50 percent are typical in 3-D problems, but they are about 20-30 percent in large 2-D problems. The present multigrid method is applicable to steady-state problems and is therefore ineffective in problems with inherently unstable solutions.
Convergence acceleration of the Proteus computer code with multigrid methods
NASA Technical Reports Server (NTRS)
Demuren, A. O.; Ibraheem, S. O.
1992-01-01
Presented here is the first part of a study to implement convergence acceleration techniques based on the multigrid concept in the Proteus computer code. A review is given of previous studies on the implementation of multigrid methods in computer codes for compressible flow analysis. Also presented is a detailed stability analysis of upwind and central-difference based numerical schemes for solving the Euler and Navier-Stokes equations. Results are given of a convergence study of the Proteus code on computational grids of different sizes. The results presented here form the foundation for the implementation of multigrid methods in the Proteus code.
Multiple Coarse Grid Multigrid Methods for Solving Elliptic Problems
NASA Technical Reports Server (NTRS)
Xiao, Shengyou; Young, David
1996-01-01
In this paper we describe some classes of multigrid methods for solving large linear systems arising in the solution by finite difference methods of certain boundary value problems involving Poisson's equation on rectangular regions. If parallel computing systems are used, then with standard multigrid methods many of the processors will be idle when one is working at the coarsest grid levels. We describe the use of Multiple Coarse Grid MultiGrid (MCGMG) methods. Here one first constructs a periodic set of equations corresponding to the given system. One then constructs a set of coarse grids such that for each grid corresponding to the grid size h there are four grids corresponding to the grid size 2*h. Multigrid operations such as restriction of residuals and interpolation of corrections are done in parallel at each grid level. For suitable choices of the multigrid operators the MCGMG method is equivalent to the Parallel Superconvergent MultiGrid (PSMG) method of Frederickson and McBryan. The convergence properties of MCGMG methods can be accurately analyzed using spectral methods.
Multigrid Methods for Fully Implicit Oil Reservoir Simulation
NASA Technical Reports Server (NTRS)
Molenaar, J.
1996-01-01
In this paper we consider the simultaneous flow of oil and water in reservoir rock. This displacement process is modeled by two basic equations: the material balance or continuity equations and the equation of motion (Darcy's law). For the numerical solution of this system of nonlinear partial differential equations there are two approaches: the fully implicit or simultaneous solution method and the sequential solution method. In the sequential solution method the system of partial differential equations is manipulated to give an elliptic pressure equation and a hyperbolic (or parabolic) saturation equation. In the IMPES approach the pressure equation is first solved, using values for the saturation from the previous time level. Next the saturations are updated by some explicit time stepping method; this implies that the method is only conditionally stable. For the numerical solution of the linear, elliptic pressure equation multigrid methods have become an accepted technique. On the other hand, the fully implicit method is unconditionally stable, but it has the disadvantage that in every time step a large system of nonlinear algebraic equations has to be solved. The most time-consuming part of any fully implicit reservoir simulator is the solution of this large system of equations. Usually this is done by Newton's method. The resulting systems of linear equations are then either solved by a direct method or by some conjugate gradient type method. In this paper we consider the possibility of applying multigrid methods for the iterative solution of the systems of nonlinear equations. There are two ways of using multigrid for this job: either we use a nonlinear multigrid method or we use a linear multigrid method to deal with the linear systems that arise in Newton's method. So far only a few authors have reported on the use of multigrid methods for fully implicit simulations. Two-level FAS algorithm is presented for the black-oil equations, and linear multigrid for
Multigrid Methods for Aerodynamic Problems in Complex Geometries
NASA Technical Reports Server (NTRS)
Caughey, David A.
1995-01-01
Work has been directed at the development of efficient multigrid methods for the solution of aerodynamic problems involving complex geometries, including the development of computational methods for the solution of both inviscid and viscous transonic flow problems. The emphasis is on problems of complex, three-dimensional geometry. The methods developed are based upon finite-volume approximations to both the Euler and the Reynolds-Averaged Navier-Stokes equations. The methods are developed for use on multi-block grids using diagonalized implicit multigrid methods to achieve computational efficiency. The work is focused upon aerodynamic problems involving complex geometries, including advanced engine inlets.
Final report on the Copper Mountain conference on multigrid methods
1997-10-01
The Copper Mountain Conference on Multigrid Methods was held on April 6-11, 1997. It took the same format used in the previous Copper Mountain Conferences on Multigrid Method conferences. Over 87 mathematicians from all over the world attended the meeting. 56 half-hour talks on current research topics were presented. Talks with similar content were organized into sessions. Session topics included: fluids; domain decomposition; iterative methods; basics; adaptive methods; non-linear filtering; CFD; applications; transport; algebraic solvers; supercomputing; and student paper winners.
Parallel Algebraic Multigrid Methods - High Performance Preconditioners
Yang, U M
2004-11-11
The development of high performance, massively parallel computers and the increasing demands of computationally challenging applications have necessitated the development of scalable solvers and preconditioners. One of the most effective ways to achieve scalability is the use of multigrid or multilevel techniques. Algebraic multigrid (AMG) is a very efficient algorithm for solving large problems on unstructured grids. While much of it can be parallelized in a straightforward way, some components of the classical algorithm, particularly the coarsening process and some of the most efficient smoothers, are highly sequential, and require new parallel approaches. This chapter presents the basic principles of AMG and gives an overview of various parallel implementations of AMG, including descriptions of parallel coarsening schemes and smoothers, some numerical results as well as references to existing software packages.
A multigrid solution method for mixed hybrid finite elements
Schmid, W.
1996-12-31
We consider the multigrid solution of linear equations arising within the discretization of elliptic second order boundary value problems of the form by mixed hybrid finite elements. Using the equivalence of mixed hybrid finite elements and non-conforming nodal finite elements, we construct a multigrid scheme for the corresponding non-conforming finite elements, and, by this equivalence, for the mixed hybrid finite elements, following guidelines from Arbogast/Chen. For a rectangular triangulation of the computational domain, this non-conforming schemes are the so-called nodal finite elements. We explicitly construct prolongation and restriction operators for this type of non-conforming finite elements. We discuss the use of plain multigrid and the multilevel-preconditioned cg-method and compare their efficiency in numerical tests.
Seventh Copper Mountain Conference on Multigrid Methods. Part 2
NASA Technical Reports Server (NTRS)
Melson, N. Duane (Editor); Manteuffel, Tom A. (Editor); McCormick, Steve F. (Editor); Douglas, Craig C. (Editor)
1996-01-01
The Seventh Copper Mountain Conference on Multigrid Methods was held on April 2-7, 1995 at Copper Mountain, Colorado. This book is a collection of many of the papers presented at the conference and so represents the conference proceedings. NASA Langley graciously provided printing of this document so that all of the papers could be presented in a single forum. Each paper was reviewed by a member of the conference organizing committee under the coordination of the editors. The vibrancy and diversity in this field are amply expressed in these important papers, and the collection clearly shows the continuing rapid growth of the use of multigrid acceleration techniques.
Geometric multigrid for an implicit-time immersed boundary method
Guy, Robert D.; Philip, Bobby; Griffith, Boyce E.
2014-10-12
The immersed boundary (IB) method is an approach to fluid-structure interaction that uses Lagrangian variables to describe the deformations and resulting forces of the structure and Eulerian variables to describe the motion and forces of the fluid. Explicit time stepping schemes for the IB method require solvers only for Eulerian equations, for which fast Cartesian grid solution methods are available. Such methods are relatively straightforward to develop and are widely used in practice but often require very small time steps to maintain stability. Implicit-time IB methods permit the stable use of large time steps, but efficient implementations of such methods require significantly more complex solvers that effectively treat both Lagrangian and Eulerian variables simultaneously. Moreover, several different approaches to solving the coupled Lagrangian-Eulerian equations have been proposed, but a complete understanding of this problem is still emerging. This paper presents a geometric multigrid method for an implicit-time discretization of the IB equations. This multigrid scheme uses a generalization of box relaxation that is shown to handle problems in which the physical stiffness of the structure is very large. Numerical examples are provided to illustrate the effectiveness and efficiency of the algorithms described herein. Finally, these tests show that using multigrid as a preconditioner for a Krylov method yields improvements in both robustness and efficiency as compared to using multigrid as a solver. They also demonstrate that with a time step 100–1000 times larger than that permitted by an explicit IB method, the multigrid-preconditioned implicit IB method is approximately 50–200 times more efficient than the explicit method.
NASA Technical Reports Server (NTRS)
Dinar, N.
1978-01-01
Several aspects of multigrid methods are briefly described. The main subjects include the development of very efficient multigrid algorithms for systems of elliptic equations (Cauchy-Riemann, Stokes, Navier-Stokes), as well as the development of control and prediction tools (based on local mode Fourier analysis), used to analyze, check and improve these algorithms. Preliminary research on multigrid algorithms for time dependent parabolic equations is also described. Improvements in existing multigrid processes and algorithms for elliptic equations were studied.
Multigrid methods for bifurcation problems: The self adjoint case
NASA Technical Reports Server (NTRS)
Taasan, Shlomo
1987-01-01
This paper deals with multigrid methods for computational problems that arise in the theory of bifurcation and is restricted to the self adjoint case. The basic problem is to solve for arcs of solutions, a task that is done successfully with an arc length continuation method. Other important issues are, for example, detecting and locating singular points as part of the continuation process, switching branches at bifurcation points, etc. Multigrid methods have been applied to continuation problems. These methods work well at regular points and at limit points, while they may encounter difficulties in the vicinity of bifurcation points. A new continuation method that is very efficient also near bifurcation points is presented here. The other issues mentioned above are also treated very efficiently with appropriate multigrid algorithms. For example, it is shown that limit points and bifurcation points can be solved for directly by a multigrid algorithm. Moreover, the algorithms presented here solve the corresponding problems in just a few work units (about 10 or less), where a work unit is the work involved in one local relaxation on the finest grid.
Geometric multigrid for an implicit-time immersed boundary method
Guy, Robert D.; Philip, Bobby; Griffith, Boyce E.
2014-10-12
The immersed boundary (IB) method is an approach to fluid-structure interaction that uses Lagrangian variables to describe the deformations and resulting forces of the structure and Eulerian variables to describe the motion and forces of the fluid. Explicit time stepping schemes for the IB method require solvers only for Eulerian equations, for which fast Cartesian grid solution methods are available. Such methods are relatively straightforward to develop and are widely used in practice but often require very small time steps to maintain stability. Implicit-time IB methods permit the stable use of large time steps, but efficient implementations of such methodsmore » require significantly more complex solvers that effectively treat both Lagrangian and Eulerian variables simultaneously. Moreover, several different approaches to solving the coupled Lagrangian-Eulerian equations have been proposed, but a complete understanding of this problem is still emerging. This paper presents a geometric multigrid method for an implicit-time discretization of the IB equations. This multigrid scheme uses a generalization of box relaxation that is shown to handle problems in which the physical stiffness of the structure is very large. Numerical examples are provided to illustrate the effectiveness and efficiency of the algorithms described herein. Finally, these tests show that using multigrid as a preconditioner for a Krylov method yields improvements in both robustness and efficiency as compared to using multigrid as a solver. They also demonstrate that with a time step 100–1000 times larger than that permitted by an explicit IB method, the multigrid-preconditioned implicit IB method is approximately 50–200 times more efficient than the explicit method.« less
Multigrid methods for numerical simulation of laminar diffusion flames
NASA Technical Reports Server (NTRS)
Liu, C.; Liu, Z.; Mccormick, S.
1993-01-01
This paper documents the result of a computational study of multigrid methods for numerical simulation of 2D diffusion flames. The focus is on a simplified combustion model, which is assumed to be a single step, infinitely fast and irreversible chemical reaction with five species (C3H8, O2, N2, CO2 and H2O). A fully-implicit second-order hybrid scheme is developed on a staggered grid, which is stretched in the streamwise coordinate direction. A full approximation multigrid scheme (FAS) based on line distributive relaxation is developed as a fast solver for the algebraic equations arising at each time step. Convergence of the process for the simplified model problem is more than two-orders of magnitude faster than other iterative methods, and the computational results show good grid convergence, with second-order accuracy, as well as qualitatively agreement with the results of other researchers.
Monolithic multigrid methods for two-dimensional resistive magnetohydrodynamics
Adler, James H.; Benson, Thomas R.; Cyr, Eric C.; MacLachlan, Scott P.; Tuminaro, Raymond S.
2016-01-06
Magnetohydrodynamic (MHD) representations are used to model a wide range of plasma physics applications and are characterized by a nonlinear system of partial differential equations that strongly couples a charged fluid with the evolution of electromagnetic fields. The resulting linear systems that arise from discretization and linearization of the nonlinear problem are generally difficult to solve. In this paper, we investigate multigrid preconditioners for this system. We consider two well-known multigrid relaxation methods for incompressible fluid dynamics: Braess--Sarazin relaxation and Vanka relaxation. We first extend these to the context of steady-state one-fluid viscoresistive MHD. Then we compare the two relaxationmore » procedures within a multigrid-preconditioned GMRES method employed within Newton's method. To isolate the effects of the different relaxation methods, we use structured grids, inf-sup stable finite elements, and geometric interpolation. Furthermore, we present convergence and timing results for a two-dimensional, steady-state test problem.« less
The Sixth Copper Mountain Conference on Multigrid Methods, part 2
NASA Technical Reports Server (NTRS)
Melson, N. Duane (Editor); Mccormick, Steve F. (Editor); Manteuffel, Thomas A. (Editor)
1993-01-01
The Sixth Copper Mountain Conference on Multigrid Methods was held on April 4-9, 1993, at Copper Mountain, Colorado. This book is a collection of many of the papers presented at the conference and so represents the conference proceedings. NASA Langley graciously provided printing of this document so that all of the papers could be presented in a single forum. Each paper was reviewed by a member of the conference organizing committee under the coordination of the editors. The multigrid discipline continues to expand and mature, as is evident from these proceedings. The vibrancy in this field is amply expressed in these important papers, and the collection clearly shows its rapid trend to further diversity and depth.
Seventh Copper Mountain Conference on Multigrid Methods. Part 1
NASA Technical Reports Server (NTRS)
Melson, N. Duane; Manteuffel, Tom A.; McCormick, Steve F.; Douglas, Craig C.
1996-01-01
The Seventh Copper Mountain Conference on Multigrid Methods was held on 2-7 Apr. 1995 at Copper Mountain, Colorado. This book is a collection of many of the papers presented at the conference and so represents the conference proceedings. NASA Langley graciously provided printing of this document so that all of the papers could be presented in a single forum. Each paper was reviewed by a member of the conference organizing committee under the coordination of the editors. The multigrid discipline continues to expand and mature, as is evident from these proceedings. The vibrancy in this field is amply expressed in these important papers, and the collection shows its rapid trend to further diversity and depth.
The Sixth Copper Mountain Conference on Multigrid Methods, part 1
NASA Technical Reports Server (NTRS)
Melson, N. Duane (Editor); Manteuffel, T. A. (Editor); Mccormick, S. F. (Editor)
1993-01-01
The Sixth Copper Mountain Conference on Multigrid Methods was held on 4-9 Apr. 1993, at Copper Mountain, CO. This book is a collection of many of the papers presented at the conference and as such represents the conference proceedings. NASA LaRC graciously provided printing of this document so that all of the papers could be presented in a single forum. Each paper was reviewed by a member of the conference organizing committee under the coordination of the editors. The multigrid discipline continues to expand and mature, as is evident from these proceedings. The vibrancy in this field is amply expressed in these important papers, and the collection clearly shows its rapid trend to further diversity and depth.
Multigrid methods and the surface consistent equations of Geophysics
NASA Astrophysics Data System (ADS)
Millar, John
The surface consistent equations are a large linear system that is frequently used in signal enhancement for land seismic surveys. Different signatures may be consistent with a particular dynamite (or other) source. Each receiver and the conditions around the receiver will have different impact on the signal. Seismic deconvolution operators, amplitude corrections and static shifts of traces are calculated using the surface consistent equations, both in commercial and scientific seismic processing software. The system of equations is singular, making direct methods such as Gaussian elimination impossible to implement. Iterative methods such as Gauss-Seidel and conjugate gradient are frequently used. A limitation in the nature of the methods leave the long wavelengths of the solution poorly resolved. To reduce the limitations of traditional iterative methods, we employ a multigrid method. Multigrid methods re-sample the entire system of equations on a more coarse grid. An iterative method is employed on the coarse grid. The long wavelengths of the solutions that traditional iterative methods were unable to resolve are calculated on the reduced system of equations. The coarse estimate can be interpolated back up to the original sample rate, and refined using a standard iterative procedure. Multigrid methods provide more accurate solutions to the surface consistent equations, with the largest improvement concentrated in the long wavelengths. Synthetic models and tests on field data show that multigrid solutions to the system of equations can significantly increase the resolution of the seismic data, when used to correct both static time shifts and in calculating deconvolution operators. The first chapter of this thesis is a description of the physical model we are addressing. It reviews some of the literature concerning the surface consistent equations, and provides background on the nature of the problem. Chapter 2 contains a review of iterative and multigrid methods
Algebraic multigrid methods applied to problems in computational structural mechanics
NASA Technical Reports Server (NTRS)
Mccormick, Steve; Ruge, John
1989-01-01
The development of algebraic multigrid (AMG) methods and their application to certain problems in structural mechanics are described with emphasis on two- and three-dimensional linear elasticity equations and the 'jacket problems' (three-dimensional beam structures). Various possible extensions of AMG are also described. The basic idea of AMG is to develop the discretization sequence based on the target matrix and not the differential equation. Therefore, the matrix is analyzed for certain dependencies that permit the proper construction of coarser matrices and attendant transfer operators. In this manner, AMG appears to be adaptable to structural analysis applications.
Multigrid method for the equilibrium equations of elasticity using a compact scheme
NASA Technical Reports Server (NTRS)
Taasan, S.
1986-01-01
A compact difference scheme is derived for treating the equilibrium equations of elasticity. The scheme is inconsistent and unstable. A multigrid method which takes into account these properties is described. The solution of the discrete equations, up to the level of discretization errors, is obtained by this method in just two multigrid cycles.
Method for producing ceramic particles and agglomerates
Phillips, Jonathan; Gleiman, Seth S.; Chen, Chun-Ku
2001-01-01
A method for generating spherical and irregularly shaped dense particles of ceramic oxides having a controlled particle size and particle size distribution. An aerosol containing precursor particles of oxide ceramics is directed into a plasma. As the particles flow through the hot zone of the plasma, they melt, collide, and join to form larger particles. If these larger particles remain in the hot zone, they continue melting and acquire a spherical shape that is retained after they exit the hot zone, cool down, and solidify. If they exit the hot zone before melting completely, their irregular shape persists and agglomerates are produced. The size and size distribution of the dense product particles can be controlled by adjusting several parameters, the most important in the case of powder precursors appears to be the density of powder in the aerosol stream that enters the plasma hot zone. This suggests that particle collision rate is responsible for determining ultimate size of the resulting sphere or agglomerate. Other parameters, particularly the gas flow rates and the microwave power, are also adjusted to control the particle size distribution.
Application of multi-grid methods for solving the Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Demuren, A. O.
1989-01-01
The application of a class of multi-grid methods to the solution of the Navier-Stokes equations for two-dimensional laminar flow problems is discussed. The methods consist of combining the full approximation scheme-full multi-grid technique (FAS-FMG) with point-, line-, or plane-relaxation routines for solving the Navier-Stokes equations in primitive variables. The performance of the multi-grid methods is compared to that of several single-grid methods. The results show that much faster convergence can be procured through the use of the multi-grid approach than through the various suggestions for improving single-grid methods. The importance of the choice of relaxation scheme for the multi-grid method is illustrated.
Application of multi-grid methods for solving the Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Demuren, A. O.
1989-01-01
This paper presents the application of a class of multi-grid methods to the solution of the Navier-Stokes equations for two-dimensional laminar flow problems. The methods consists of combining the full approximation scheme-full multi-grid technique (FAS-FMG) with point-, line- or plane-relaxation routines for solving the Navier-Stokes equations in primitive variables. The performance of the multi-grid methods is compared to those of several single-grid methods. The results show that much faster convergence can be procured through the use of the multi-grid approach than through the various suggestions for improving single-grid methods. The importance of the choice of relaxation scheme for the multi-grid method is illustrated.
A generalized BPX multigrid framework covering nonnested V-cycle methods
NASA Astrophysics Data System (ADS)
Duan, Huo-Yuan; Gao, Shao-Qin; Tan, Roger C. E.; Zhang, Shangyou
2007-03-01
More than a decade ago, Bramble, Pasciak and Xu developed a framework in analyzing the multigrid methods with nonnested spaces or noninherited quadratic forms. It was subsequently known as the BPX multigrid framework, which was widely used in the analysis of multigrid and domain decomposition methods. However, the framework has an apparent limit in the analysis of nonnested V-cycle methods, and it produces a variable V-cycle, or nonuniform convergence rate V-cycle methods, or other nonoptimal results in analysis thus far. This paper completes a long-time effort in extending the BPX multigrid framework so that it truly covers the nonnested V-cycle. We will apply the extended BPX framework to the analysis of many V-cycle nonnested multigrid methods. Some of them were proven previously only for two-level and W-cycle iterations. Some numerical results are presented to support the theoretical analysis of this paper.
Relaxation schemes for spectral multigrid methods
NASA Technical Reports Server (NTRS)
Phillips, Timothy N.
1987-01-01
The effectiveness of relaxation schemes for solving the systems of algebraic equations which arise from spectral discretizations of elliptic equations is examined. Iterative methods are an attractive alternative to direct methods because Fourier transform techniques enable the discrete matrix-vector products to be computed almost as efficiently as for corresponding but sparse finite difference discretizations. Preconditioning is found to be essential for acceptable rates of convergence. Preconditioners based on second-order finite difference methods are used. A comparison is made of the performance of different relaxation methods on model problems with a variety of conditions specified around the boundary. The investigations show that iterations based on incomplete LU decompositions provide the most efficient methods for solving these algebraic systems.
Constructive interference II: Semi-chaotic multigrid methods
Douglas, C.C.
1994-12-31
Parallel computer vendors have mostly decided to move towards multi-user, multi-tasking per node machines. A number of these machines already exist today. Self load balancing on these machines is not an option to the users except when the user can convince someone to boot the entire machine in single user mode, which may have to be done node by node. Chaotic relaxation schemes were considered for situations like this as far back as the middle 1960`s. However, very little convergence theory exists. Further, what exists indicates that this is not really a good method. Besides chaotic relaxation, chaotic conjugate direction and minimum residual methods are explored as smoothers for symmetric and nonsymmetric problems. While having each processor potentially going off in a different direction from the rest is not what one would strive for in a unigrid situation, the change of grid procedures in multigrid provide a natural way of aiming all of the processors in the right direction. The author presents some new results for multigrid methods in which synchronization of the calculations on one or more levels is not assumed. However, he assumes that he knows how far out of synch neighboring subdomains are with respect to each other. Thus the author can show that the combination of a limited chaotic smoother and coarse level corrections produces a better algorithm than would be expected.
A multigrid method for variable coefficient Maxwell's equations
Jones, J E; Lee, B
2004-05-13
This paper presents a multigrid method for solving variable coefficient Maxwell's equations. The novelty in this method is the use of interpolation operators that do not produce multilevel commutativity complexes that lead to multilevel exactness. Rather, the effects of multilevel exactness are built into the level equations themselves--on the finest level using a discrete T-V formulation, and on the coarser grids through the Galerkin coarsening procedure of a T-V formulation. These built-in structures permit the levelwise use of an effective hybrid smoother on the curl-free near-nullspace components, and these structures permit the development of interpolation operators for handling the curl-free and divergence-free error components separately, with the resulting block diagonal interpolation operator not satisfying multilevel commutativity but having good approximation properties for both of these error components. Applying operator-dependent interpolation for each of these error components leads to an effective multigrid scheme for variable coefficient Maxwell's equations, where multilevel commutativity-based methods can degrade. Numerical results are presented to verify the effectiveness of this new scheme.
Large-Eddy Simulation and Multigrid Methods
Falgout,R D; Naegle,S; Wittum,G
2001-06-18
A method to simulate turbulent flows with Large-Eddy Simulation on unstructured grids is presented. Two kinds of dynamic models are used to model the unresolved scales of motion and are compared with each other on different grids. Thereby the behavior of the models is shown and additionally the feature of adaptive grid refinement is investigated. Furthermore the parallelization aspect is addressed.
Multigrid hierarchical simulated annealing method for reconstructing heterogeneous media
NASA Astrophysics Data System (ADS)
Pant, Lalit M.; Mitra, Sushanta K.; Secanell, Marc
2015-12-01
A reconstruction methodology based on different-phase-neighbor (DPN) pixel swapping and multigrid hierarchical annealing is presented. The method performs reconstructions by starting at a coarse image and successively refining it. The DPN information is used at each refinement stage to freeze interior pixels of preformed structures. This preserves the large-scale structures in refined images and also reduces the number of pixels to be swapped, thereby resulting in a decrease in the necessary computational time to reach a solution. Compared to conventional single-grid simulated annealing, this method was found to reduce the required computation time to achieve a reconstruction by around a factor of 70-90, with the potential of even higher speedups for larger reconstructions. The method is able to perform medium sized (up to 3003 voxels) three-dimensional reconstructions with multiple correlation functions in 36-47 h.
Revenge of the Semicoarsening Frequency Decomposition Multigrid Method
NASA Technical Reports Server (NTRS)
Dendy, J. E., Jr.
1996-01-01
The frequency decomposition multigrid method was previously considered and modified so as to obtain robustness for problems with discontinuous coefficients while retaining robustness for problems with anisotropic coefficients. The application of this modified method to a problem arising in global ocean modeling was also considered. For this problem it was shown that the discretization employed gives rise to an operator for which point relaxation is not robust. In fact, alternating line relaxation is required for robustness, negating the main advantage of the frequency decomposition method: robustness for anisotropic operators using only point relaxation. In this paper a semicoarsening variant, which requires line relaxation in one direction only is considered, and it is shown that this variant works well for the global ocean modeling problem.
Apparatus and method for compacting, degassing and carbonizing carbonaceous agglomerates
Theodore, F.W.
1980-08-19
An apparatus for compacting, degassing and carbonizing carbonaceous agglomerates is described. The apparatus comprises a rotary kiln having an agglomerate inlet means for introducing green agglomerates into the kiln near the inlet of the kiln and a heating medium inlet for introducing a heating medium comprising a finely divided solid into the kiln at a preselected location intermediate the inlet end of the kiln and the outlet end of the kiln to produce a mixture at a temperature above the carbonizing temperature of the agglomerates and a sieve positioned to receive the products from the rotary kiln and separate the heating medium and the compacted, degassed, carbonized agglomerate product. A method for producing compacted, degassed, carbonized carbonaceous agglomerates by the use of the apparatus is also disclosed.
Method for recovering light hydrocarbons from coal agglomerates
Huettenhain, Horst; Benz, August D.; Getsoian, John
1991-01-01
A method and apparatus for removing light hydrocarbons, such as heptane, from coal agglomerates includes an enclosed chamber having a substantially horizontal perforate surface therein. The coal agglomerates are introduced into a water bath within the chamber. The agglomerates are advanced over the surface while steam is substantially continuously introduced through the surface into the water bath. Steam heats the water and causes volatilization of the light hydrocarbons, which may be collected from the overhead of the chamber. The resulting agglomerates may be collected at the opposite end from the surface and subjected to final draining processes prior to transportation or use.
Novel Binders and Methods for Agglomeration of Ore
S. K. Kawatra; T. C. Eisele; K. A. Lewandowski; J. A. Gurtler
2006-09-30
Heap leaching is one of the methods being used to recover metal from low grade ore deposits. The main problem faced during heap leaching is the migration of fine grained particles through the heap, forming impermeable beds which result in poor solution flow. The poor solution flow leads to less contact between the leach solution and the ore, resulting in low recovery rates. Agglomeration of ore into coarse, porous masses prevents fine particles from migrating and clogging the spaces and channels between the larger ore particles. Currently, there is one facility in the United States which uses agglomeration. This operation agglomerates their ore using leach solution (raffinate), but is still experiencing undesirable metal recovery from the heaps due to agglomerate breakdown. The use of a binder, in addition to the leach solution, during agglomeration would help to produce stronger agglomerates that did not break down during processing. However, there are no known binders that will work satisfactorily in the acidic environment of a heap, at a reasonable cost. As a result, operators of many facilities see a large loss of process efficiency due to their inability to take advantage of agglomeration. Increasing copper recovery in heap leaching by the use of binders and agglomeration would result in a significant decrease in the amount of energy consumed. Assuming that 70% of all the leaching heaps would convert to using agglomeration technology, as much as 1.64*10{sup 12} BTU per year would be able to be saved if a 25% increase in copper recovery was experienced, which is equivalent to saving approximately 18% of the energy currently being used in leaching heaps. For every week a leach cycle was decreased, a savings of as much as 1.23*10{sup 11} BTU per week would result. This project has identified several acid-resistant binders and agglomeration procedures. These binders and experimental procedures will be able to be used for use in improving the energy efficiency of
NASA Technical Reports Server (NTRS)
Fay, John F.
1990-01-01
A calculation is made of the stability of various relaxation schemes for the numerical solution of partial differential equations. A multigrid acceleration method is introduced, and its effects on stability are explored. A detailed stability analysis of a simple case is carried out and verified by numerical experiment. It is shown that the use of multigrids can speed convergence by several orders of magnitude without adversely affecting stability.
Copper Mountain conference on multigrid methods. Preliminary proceedings -- List of abstracts
1995-12-31
This report contains abstracts of the papers presented at the conference. Papers cover multigrid algorithms and applications of multigrid methods. Applications include the following: solution of elliptical problems; electric power grids; fluid mechanics; atmospheric data assimilation; thermocapillary effects on weld pool shape; boundary-value problems; prediction of hurricane tracks; modeling multi-dimensional combustion and detailed chemistry; black-oil reservoir simulation; image processing; and others.
Recent developments in multigrid methods for the steady Euler equations
NASA Technical Reports Server (NTRS)
Jespersen, D. C.
1984-01-01
The solution by multigrid techniques of the steady inviscid compressible equations of gas dynamics, the Euler equations is investigated. Steady two dimensional transonic flow over an airfoil section is studied intensively. Most of the material is applicable to three dimensional flow problems of aerodynamic interest.
Multigrid lattice Boltzmann method for accelerated solution of elliptic equations
NASA Astrophysics Data System (ADS)
Patil, Dhiraj V.; Premnath, Kannan N.; Banerjee, Sanjoy
2014-05-01
A new solver for second-order elliptic partial differential equations (PDEs) based on the lattice Boltzmann method (LBM) and the multigrid (MG) technique is presented. Several benchmark elliptic equations are solved numerically with the inclusion of multiple grid-levels in two-dimensional domains at an optimal computational cost within the LB framework. The results are compared with the corresponding analytical solutions and numerical solutions obtained using the Stone's strongly implicit procedure. The classical PDEs considered in this article include the Laplace and Poisson equations with Dirichlet boundary conditions, with the latter involving both constant and variable coefficients. A detailed analysis of solution accuracy, convergence and computational efficiency of the proposed solver is given. It is observed that the use of a high-order stencil (for smoothing) improves convergence and accuracy for an equivalent number of smoothing sweeps. The effect of the type of scheduling cycle (V- or W-cycle) on the performance of the MG-LBM is analyzed. Next, a parallel algorithm for the MG-LBM solver is presented and then its parallel performance on a multi-core cluster is analyzed. Lastly, a practical example is provided wherein the proposed elliptic PDE solver is used to compute the electro-static potential encountered in an electro-chemical cell, which demonstrates the effectiveness of this new solver in complex coupled systems. Several orders of magnitude gains in convergence and parallel scaling for the canonical problems, and a factor of 5 reduction for the multiphysics problem are achieved using the MG-LBM.
A highly parallel multigrid-like method for the solution of the Euler equations
NASA Technical Reports Server (NTRS)
Tuminaro, Ray S.
1989-01-01
We consider a highly parallel multigrid-like method for the solution of the two dimensional steady Euler equations. The new method, introduced as filtering multigrid, is similar to a standard multigrid scheme in that convergence on the finest grid is accelerated by iterations on coarser grids. In the filtering method, however, additional fine grid subproblems are processed concurrently with coarse grid computations to further accelerate convergence. These additional problems are obtained by splitting the residual into a smooth and an oscillatory component. The smooth component is then used to form a coarse grid problem (similar to standard multigrid) while the oscillatory component is used for a fine grid subproblem. The primary advantage in the filtering approach is that fewer iterations are required and that most of the additional work per iteration can be performed in parallel with the standard coarse grid computations. We generalize the filtering algorithm to a version suitable for nonlinear problems. We emphasize that this generalization is conceptually straight-forward and relatively easy to implement. In particular, no explicit linearization (e.g., formation of Jacobians) needs to be performed (similar to the FAS multigrid approach). We illustrate the nonlinear version by applying it to the Euler equations, and presenting numerical results. Finally, a performance evaluation is made based on execution time models and convergence information obtained from numerical experiments.
Multigrid for the Galerkin least squares method in linear elasticity: The pure displacement problem
Yoo, Jaechil
1996-12-31
Franca and Stenberg developed several Galerkin least squares methods for the solution of the problem of linear elasticity. That work concerned itself only with the error estimates of the method. It did not address the related problem of finding effective methods for the solution of the associated linear systems. In this work, we prove the convergence of a multigrid (W-cycle) method. This multigrid is robust in that the convergence is uniform as the parameter, v, goes to 1/2 Computational experiments are included.
On multigrid methods for the Navier-Stokes Computer
NASA Technical Reports Server (NTRS)
Nosenchuck, D. M.; Krist, S. E.; Zang, T. A.
1988-01-01
The overall architecture of the multipurpose parallel-processing Navier-Stokes Computer (NSC) being developed by Princeton and NASA Langley (Nosenchuck et al., 1986) is described and illustrated with extensive diagrams, and the NSC implementation of an elementary multigrid algorithm for simulating isotropic turbulence (based on solution of the incompressible time-dependent Navier-Stokes equations with constant viscosity) is characterized in detail. The present NSC design concept calls for 64 nodes, each with the performance of a class VI supercomputer, linked together by a fiber-optic hypercube network and joined to a front-end computer by a global bus. In this configuration, the NSC would have a storage capacity of over 32 Gword and a peak speed of over 40 Gflops. The multigrid Navier-Stokes code discussed would give sustained operation rates of about 25 Gflops.
A positivity-preserving, implicit defect-correction multigrid method for turbulent combustion
NASA Astrophysics Data System (ADS)
Wasserman, M.; Mor-Yossef, Y.; Greenberg, J. B.
2016-07-01
A novel, robust multigrid method for the simulation of turbulent and chemically reacting flows is developed. A survey of previous attempts at implementing multigrid for the problems at hand indicated extensive use of artificial stabilization to overcome numerical instability arising from non-linearity of turbulence and chemistry model source-terms, small-scale physics of combustion, and loss of positivity. These issues are addressed in the current work. The highly stiff Reynolds-averaged Navier-Stokes (RANS) equations, coupled with turbulence and finite-rate chemical kinetics models, are integrated in time using the unconditionally positive-convergent (UPC) implicit method. The scheme is successfully extended in this work for use with chemical kinetics models, in a fully-coupled multigrid (FC-MG) framework. To tackle the degraded performance of multigrid methods for chemically reacting flows, two major modifications are introduced with respect to the basic, Full Approximation Storage (FAS) approach. First, a novel prolongation operator that is based on logarithmic variables is proposed to prevent loss of positivity due to coarse-grid corrections. Together with the extended UPC implicit scheme, the positivity-preserving prolongation operator guarantees unconditional positivity of turbulence quantities and species mass fractions throughout the multigrid cycle. Second, to improve the coarse-grid-correction obtained in localized regions of high chemical activity, a modified defect correction procedure is devised, and successfully applied for the first time to simulate turbulent, combusting flows. The proposed modifications to the standard multigrid algorithm create a well-rounded and robust numerical method that provides accelerated convergence, while unconditionally preserving the positivity of model equation variables. Numerical simulations of various flows involving premixed combustion demonstrate that the proposed MG method increases the efficiency by a factor of
Novel Binders and Methods for Agglomeration of Ore
S. K. Kawatra; T. C. Eisele; K. A. Lewandowski; J. A. Gurtler
2006-12-31
Many metal extraction operations, such as leaching of copper, leaching of precious metals, and reduction of metal oxides to metal in high-temperature furnaces, require agglomeration of ore to ensure that reactive liquids or gases are evenly distributed throughout the ore being processed. Agglomeration of ore into coarse, porous masses achieves this even distribution of fluids by preventing fine particles from migrating and clogging the spaces and channels between the larger ore particles. Binders are critically necessary to produce agglomerates that will not break down during processing. However, for many important metal extraction processes there are no binders known that will work satisfactorily. Primary examples of this are copper heap leaching, where there are no binders that will work in the acidic environment encountered in this process, and advanced ironmaking processes, where binders must function satisfactorily over an extraordinarily large range of temperatures (from room temperature up to over 1200 C). As a result, operators of many facilities see a large loss of process efficiency due to their inability to take advantage of agglomeration. The large quantities of ore that must be handled in metal extraction processes also means that the binder must be inexpensive and useful at low dosages to be economical. The acid-resistant binders and agglomeration procedures developed in this project will also be adapted for use in improving the energy efficiency and performance of a broad range of mineral agglomeration applications, particularly heap leaching and advanced primary ironmaking. This project has identified several acid-resistant binders and agglomeration procedures that can be used for improving the energy efficiency of heap leaching, by preventing the ''ponding'' and ''channeling'' effects that currently cause reduced recovery and extended leaching cycle times. Methods have also been developed for iron ore processing which are intended to improve the
Continuous air agglomeration method for high carbon fly ash beneficiation
Gray, McMahon L.; Champagne, Kenneth J.; Finseth, Dennis H.
2000-01-01
The carbon and mineral components of fly ash are effectively separated by a continuous air agglomeration method, resulting in a substantially carboree mineral stream and a highly concentrated carbon product. The method involves mixing the fly ash comprised of carbon and inorganic mineral matter with a liquid hydrocarbon to form a slurry, contacting the slurry with an aqueous solution, dispersing the hydrocarbon slurry into small droplets within the aqueous solution by mechanical mixing and/or aeration, concentrating the inorganic mineral matter in the aqueous solution, agglomerating the carbon and hydrocarbon in the form of droplets, collecting the droplets, separating the hydrocarbon from the concentrated carbon product, and recycling the hydrocarbon.
The block adaptive multigrid method applied to the solution of the Euler equations
NASA Technical Reports Server (NTRS)
Pantelelis, Nikos
1993-01-01
In the present study, a scheme capable of solving very fast and robust complex nonlinear systems of equations is presented. The Block Adaptive Multigrid (BAM) solution method offers multigrid acceleration and adaptive grid refinement based on the prediction of the solution error. The proposed solution method was used with an implicit upwind Euler solver for the solution of complex transonic flows around airfoils. Very fast results were obtained (18-fold acceleration of the solution) using one fourth of the volumes of a global grid with the same solution accuracy for two test cases.
Simulation of viscous flows using a multigrid-control volume finite element method
Hookey, N.A.
1994-12-31
This paper discusses a multigrid control volume finite element method (MG CVFEM) for the simulation of viscous fluid flows. The CVFEM is an equal-order primitive variables formulation that avoids spurious solution fields by incorporating an appropriate pressure gradient in the velocity interpolation functions. The resulting set of discretized equations is solved using a coupled equation line solver (CELS) that solves the discretized momentum and continuity equations simultaneously along lines in the calculation domain. The CVFEM has been implemented in the context of both FMV- and V-cycle multigrid algorithms, and preliminary results indicate a five to ten fold reduction in execution times.
Spectral multigrid methods for the solution of homogeneous turbulence problems
NASA Technical Reports Server (NTRS)
Erlebacher, G.; Zang, T. A.; Hussaini, M. Y.
1987-01-01
New three-dimensional spectral multigrid algorithms are analyzed and implemented to solve the variable coefficient Helmholtz equation. Periodicity is assumed in all three directions which leads to a Fourier collocation representation. Convergence rates are theoretically predicted and confirmed through numerical tests. Residual averaging results in a spectral radius of 0.2 for the variable coefficient Poisson equation. In general, non-stationary Richardson must be used for the Helmholtz equation. The algorithms developed are applied to the large-eddy simulation of incompressible isotropic turbulence.
NASA Technical Reports Server (NTRS)
Dendy, J. E., Jr.
1981-01-01
The black box multigrid (BOXMG) code, which only needs specification of the matrix problem for application in the multigrid method was investigated. It is contended that a major problem with the multigrid method is that each new grid configuration requires a major programming effort to develop a code that specifically handles that grid configuration. The SOR and ICCG methods only specify the matrix problem, no matter what the grid configuration. It is concluded that the BOXMG does everything else necessary to set up the auxiliary coarser problems to achieve a multigrid solution.
A multigrid Newton-Krylov method for flux-limited radiation diffusion
Rider, W.J.; Knoll, D.A.; Olson, G.L.
1998-09-01
The authors focus on the integration of radiation diffusion including flux-limited diffusion coefficients. The nonlinear integration is accomplished with a Newton-Krylov method preconditioned with a multigrid Picard linearization of the governing equations. They investigate the efficiency of the linear and nonlinear iterative techniques.
New Nonlinear Multigrid Analysis
NASA Technical Reports Server (NTRS)
Xie, Dexuan
1996-01-01
The nonlinear multigrid is an efficient algorithm for solving the system of nonlinear equations arising from the numerical discretization of nonlinear elliptic boundary problems. In this paper, we present a new nonlinear multigrid analysis as an extension of the linear multigrid theory presented by Bramble. In particular, we prove the convergence of the nonlinear V-cycle method for a class of mildly nonlinear second order elliptic boundary value problems which do not have full elliptic regularity.
An overlapped grid method for multigrid, finite volume/difference flow solvers: MaGGiE
NASA Technical Reports Server (NTRS)
Baysal, Oktay; Lessard, Victor R.
1990-01-01
The objective is to develop a domain decomposition method via overlapping/embedding the component grids, which is to be used by upwind, multi-grid, finite volume solution algorithms. A computer code, given the name MaGGiE (Multi-Geometry Grid Embedder) is developed to meet this objective. MaGGiE takes independently generated component grids as input, and automatically constructs the composite mesh and interpolation data, which can be used by the finite volume solution methods with or without multigrid convergence acceleration. Six demonstrative examples showing various aspects of the overlap technique are presented and discussed. These cases are used for developing the procedure for overlapping grids of different topologies, and to evaluate the grid connection and interpolation data for finite volume calculations on a composite mesh. Time fluxes are transferred between mesh interfaces using a trilinear interpolation procedure. Conservation losses are minimal at the interfaces using this method. The multi-grid solution algorithm, using the coaser grid connections, improves the convergence time history as compared to the solution on composite mesh without multi-gridding.
Multigrid methods for differential equations with highly oscillatory coefficients
NASA Technical Reports Server (NTRS)
Engquist, Bjorn; Luo, Erding
1993-01-01
New coarse grid multigrid operators for problems with highly oscillatory coefficients are developed. These types of operators are necessary when the characters of the differential equations on coarser grids or longer wavelengths are different from that on the fine grid. Elliptic problems for composite materials and different classes of hyperbolic problems are practical examples. The new coarse grid operators can be constructed directly based on the homogenized differential operators or hierarchically computed from the finest grid. Convergence analysis based on the homogenization theory is given for elliptic problems with periodic coefficients and some hyperbolic problems. These are classes of equations for which there exists a fairly complete theory for the interaction between shorter and longer wavelengths in the problems. Numerical examples are presented.
Development of methods to predict agglomeration and disposition in FBCs
Mann, M.D.; Henderson, A.K.; Swanson, M.K.; Erickson, T.A.
1995-11-01
This 3-year, multiclient program is providing the information needed to determine the behavior of inorganic components in FBC units using advanced methods of analysis coupled with bench-scale combustion experiments. The major objectives of the program are as follows: (1) To develop further our advanced ash and deposit characterization techniques to quantify the effects of the liquid-phase components in terms of agglomerate formation and ash deposits, (2) To determine the mechanisms of inorganic transformations that lead to bed agglomeration and ash deposition in FBC systems, and (3) To develop a better means to predict the behavior of inorganic components as a function of coal composition, bed material characteristics, and combustion conditions.
An automatic multigrid method for the solution of sparse linear systems
NASA Technical Reports Server (NTRS)
Shapira, Yair; Israeli, Moshe; Sidi, Avram
1993-01-01
An automatic version of the multigrid method for the solution of linear systems arising from the discretization of elliptic PDE's is presented. This version is based on the structure of the algebraic system solely, and does not use the original partial differential operator. Numerical experiments show that for the Poisson equation the rate of convergence of our method is equal to that of classical multigrid methods. Moreover, the method is robust in the sense that its high rate of convergence is conserved for other classes of problems: non-symmetric, hyperbolic (even with closed characteristics) and problems on non-uniform grids. No double discretization or special treatment of sub-domains (e.g. boundaries) is needed. When supplemented with a vector extrapolation method, high rates of convergence are achieved also for anisotropic and discontinuous problems and also for indefinite Helmholtz equations. A new double discretization strategy is proposed for finite and spectral element schemes and is found better than known strategies.
NASA Astrophysics Data System (ADS)
Lavery, N.; Taylor, C.
1999-07-01
Multigrid and iterative methods are used to reduce the solution time of the matrix equations which arise from the finite element (FE) discretisation of the time-independent equations of motion of the incompressible fluid in turbulent motion. Incompressible flow is solved by using the method of reduce interpolation for the pressure to satisfy the Brezzi-Babuska condition. The k-l model is used to complete the turbulence closure problem. The non-symmetric iterative matrix methods examined are the methods of least squares conjugate gradient (LSCG), biconjugate gradient (BCG), conjugate gradient squared (CGS), and the biconjugate gradient squared stabilised (BCGSTAB). The multigrid algorithm applied is based on the FAS algorithm of Brandt, and uses two and three levels of grids with a V-cycling schedule. These methods are all compared to the non-symmetric frontal solver. Copyright
Multilevel local refinement and multigrid methods for 3-D turbulent flow
Liao, C.; Liu, C.; Sung, C.H.; Huang, T.T.
1996-12-31
A numerical approach based on multigrid, multilevel local refinement, and preconditioning methods for solving incompressible Reynolds-averaged Navier-Stokes equations is presented. 3-D turbulent flow around an underwater vehicle is computed. 3 multigrid levels and 2 local refinement grid levels are used. The global grid is 24 x 8 x 12. The first patch is 40 x 16 x 20 and the second patch is 72 x 32 x 36. 4th order artificial dissipation are used for numerical stability. The conservative artificial compressibility method are used for further improvement of convergence. To improve the accuracy of coarse/fine grid interface of local refinement, flux interpolation method for refined grid boundary is used. The numerical results are in good agreement with experimental data. The local refinement can improve the prediction accuracy significantly. The flux interpolation method for local refinement can keep conservation for a composite grid, therefore further modify the prediction accuracy.
Parallel Multigrid Equation Solver
2001-09-07
Prometheus is a fully parallel multigrid equation solver for matrices that arise in unstructured grid finite element applications. It includes a geometric and an algebraic multigrid method and has solved problems of up to 76 mullion degrees of feedom, problems in linear elasticity on the ASCI blue pacific and ASCI red machines.
NASA Astrophysics Data System (ADS)
Lee, Ping-Chang
2014-03-01
Computed tomography (CT) plays a key role in modern medical system, whether it be for diagnosis or therapy. As an increased risk of cancer development is associated with exposure to radiation, reducing radiation exposure in CT becomes an essential issue. Based on the compressive sensing (CS) theory, iterative based method with total variation (TV) minimization is proven to be a powerful framework for few-view tomographic image reconstruction. Multigrid method is an iterative method for solving both linear and nonlinear systems, especially when the system contains a huge number of components. In medical imaging, image background is often defined by zero intensity, thus attaining spatial support of the image, which is helpful for iterative reconstruction. In the proposed method, the image support is not considered as a priori knowledge. Rather, it evolves during the reconstruction process. Based on the CS framework, we proposed a multigrid method with adaptive spatial support constraint. The simultaneous algebraic reconstruction (SART) with TV minimization is implemented for comparison purpose. The numerical result shows: 1. Multigrid method has better performance while less than 60 views of projection data were used, 2. Spatial support highly improves the CS reconstruction, and 3. When few views of projection data were measured, our method performs better than the SART+TV method with spatial support constraint.
Analysis of multigrid methods on massively parallel computers: Architectural implications
NASA Technical Reports Server (NTRS)
Matheson, Lesley R.; Tarjan, Robert E.
1993-01-01
We study the potential performance of multigrid algorithms running on massively parallel computers with the intent of discovering whether presently envisioned machines will provide an efficient platform for such algorithms. We consider the domain parallel version of the standard V cycle algorithm on model problems, discretized using finite difference techniques in two and three dimensions on block structured grids of size 10(exp 6) and 10(exp 9), respectively. Our models of parallel computation were developed to reflect the computing characteristics of the current generation of massively parallel multicomputers. These models are based on an interconnection network of 256 to 16,384 message passing, 'workstation size' processors executing in an SPMD mode. The first model accomplishes interprocessor communications through a multistage permutation network. The communication cost is a logarithmic function which is similar to the costs in a variety of different topologies. The second model allows single stage communication costs only. Both models were designed with information provided by machine developers and utilize implementation derived parameters. With the medium grain parallelism of the current generation and the high fixed cost of an interprocessor communication, our analysis suggests an efficient implementation requires the machine to support the efficient transmission of long messages, (up to 1000 words) or the high initiation cost of a communication must be significantly reduced through an alternative optimization technique. Furthermore, with variable length message capability, our analysis suggests the low diameter multistage networks provide little or no advantage over a simple single stage communications network.
On Efficient Multigrid Methods for Materials Processing Flows with Small Particles
NASA Technical Reports Server (NTRS)
Thomas, James (Technical Monitor); Diskin, Boris; Harik, VasylMichael
2004-01-01
Multiscale modeling of materials requires simulations of multiple levels of structural hierarchy. The computational efficiency of numerical methods becomes a critical factor for simulating large physical systems with highly desperate length scales. Multigrid methods are known for their superior efficiency in representing/resolving different levels of physical details. The efficiency is achieved by employing interactively different discretizations on different scales (grids). To assist optimization of manufacturing conditions for materials processing with numerous particles (e.g., dispersion of particles, controlling flow viscosity and clusters), a new multigrid algorithm has been developed for a case of multiscale modeling of flows with small particles that have various length scales. The optimal efficiency of the algorithm is crucial for accurate predictions of the effect of processing conditions (e.g., pressure and velocity gradients) on the local flow fields that control the formation of various microstructures or clusters.
Rotor-stator interaction analysis using the Navier-Stokes equations and a multigrid method
Arnone, A.; Pacciani, R.
1996-10-01
A recently developed, time-accurate multigrid viscous solver has been extended to the analysis of unsteady rotor-stator interaction. In the proposed method, a fully implicit discretization is used to remove stability limitations. By means of a dual time-stepping approach, a four-stage Runge-Kutta scheme is used in conjunction with several accelerating techniques typical of steady-state solvers, instead of traditional time-expensive factorizations. The accelerating strategies include local time stepping, residual smoothing, and multigrid. Two-dimensional viscous calculations of unsteady rotor-stator interaction in the first stage of a modern gas turbine are presented. The stage analysis is based on the introduction of several blade passages to approximate the stator:rotor count ratio. Particular attention is dedicated to grid dependency in space and time as well as to the influence of the number of blades included in the calculations.
Numerical solution of flame sheet problems with and without multigrid methods
NASA Technical Reports Server (NTRS)
Douglas, Craig C.; Ern, Alexandre
1993-01-01
Flame sheet problems are on the natural route to the numerical solution of multidimensional flames, which, in turn, are important in many engineering applications. In order to model the structure of flames more accurately, we use the vorticity-velocity formulation of the fluid flow equations, as opposed to the streamfunction-vorticity approach. The numerical solution of the resulting nonlinear coupled elliptic partial differential equations involves a pseudo transient process and a steady state Newton iteration. Rather than working with dimensionless variables, we introduce scale factors that can yield significant savings in the execution time. In this context, we also investigate the applicability and performance of several multigrid methods, focusing on nonlinear damped Newton multigrid, using either one way or correction schemes.
A Parallel Multigrid Method for the Finite Element Analysis of Mechanical Contact
Hales, J D; Parsons, I D
2002-03-21
A geometrical multigrid method for solving the linearized matrix equations arising from node-on-face three-dimensional finite element contact is described. The development of an efficient implementation of this combination that minimizes both the memory requirements and the computational cost requires careful construction and storage of the portion of the coarse mesh stiffness matrices that are associated with the contact stiffness on the fine mesh. The multigrid contact algorithm is parallelized in a manner suitable for distributed memory architectures: results are presented that demonstrates the scheme's scalability. The solution of a large contact problem derived from an analysis of the factory joints present in the Space Shuttle reusable solid rocket motor demonstrates the usefulness of the general approach.
Multigrid techniques for unstructured meshes
NASA Technical Reports Server (NTRS)
Mavriplis, D. J.
1995-01-01
An overview of current multigrid techniques for unstructured meshes is given. The basic principles of the multigrid approach are first outlined. Application of these principles to unstructured mesh problems is then described, illustrating various different approaches, and giving examples of practical applications. Advanced multigrid topics, such as the use of algebraic multigrid methods, and the combination of multigrid techniques with adaptive meshing strategies are dealt with in subsequent sections. These represent current areas of research, and the unresolved issues are discussed. The presentation is organized in an educational manner, for readers familiar with computational fluid dynamics, wishing to learn more about current unstructured mesh techniques.
Agglomerating combustor-gasifier method and apparatus for coal gasification
Chen, Joseph L. P.; Archer, David H.
1976-09-21
A method and apparatus for gasifying coal wherein the gasification takes place in a spout fluid bed at a pressure of about 10 to 30 atmospheres and a temperature of about 1800.degree. to 2200.degree.F and wherein the configuration of the apparatus and the manner of introduction of gases for combustion and fluidization is such that agglomerated ash can be withdrawn from the bottom of the apparatus and gas containing very low dust loading is produced. The gasification reaction is self-sustaining through the burning of a stoichiometric amount of coal with air in the lower part of the apparatus to form the spout within the fluid bed. The method and apparatus are particularly suitable for gasifying coarse coal particles.
A comparison of locally adaptive multigrid methods: LDC, FAC and FIC
NASA Technical Reports Server (NTRS)
Khadra, Khodor; Angot, Philippe; Caltagirone, Jean-Paul
1993-01-01
This study is devoted to a comparative analysis of three 'Adaptive ZOOM' (ZOom Overlapping Multi-level) methods based on similar concepts of hierarchical multigrid local refinement: LDC (Local Defect Correction), FAC (Fast Adaptive Composite), and FIC (Flux Interface Correction)--which we proposed recently. These methods are tested on two examples of a bidimensional elliptic problem. We compare, for V-cycle procedures, the asymptotic evolution of the global error evaluated by discrete norms, the corresponding local errors, and the convergence rates of these algorithms.
Final Report on Subcontract B605152. Multigrid Methods for Systems of PDEs
Brannick, James; Xu, Jinchao
2015-07-07
The project team has continued with work on developing aggressive coarsening techniques for AMG methods. Of particular interest is the idea to use aggressive coarsening with polynomial smoothing. Using local Fourier analysis the optimal values for the parameters involved in defining the polynomial smoothers are determined automatically in a way to achieve fast convergence of cycles with aggressive coarsening. Numerical tests have the sharpness of the theoretical results. The methods are highly parallelizable and efficient multigrid algorithms on structured and semistructured grids in two and three spatial dimensions.
Multigrid methods for a semilinear PDE in the theory of pseudoplastic fluids
NASA Technical Reports Server (NTRS)
Henson, Van Emden; Shaker, A. W.
1993-01-01
We show that by certain transformations the boundary layer equations for the class of non-Newtonian fluids named pseudoplastic can be generalized in the form the vector differential operator(u) + p(x)u(exp -lambda) = 0, where x is a member of the set Omega and Omega is a subset of R(exp n), n is greater than or equal to 1 under the classical conditions for steady flow over a semi-infinite flat plate. We provide a survey of the existence, uniqueness, and analyticity of the solutions for this problem. We also establish numerical solutions in one- and two-dimensional regions using multigrid methods.
NASA Astrophysics Data System (ADS)
Lin, Xue-lei; Lu, Xin; Ng, Micheal K.; Sun, Hai-Wei
2016-10-01
A fast accurate approximation method with multigrid solver is proposed to solve a two-dimensional fractional sub-diffusion equation. Using the finite difference discretization of fractional time derivative, a block lower triangular Toeplitz matrix is obtained where each main diagonal block contains a two-dimensional matrix for the Laplacian operator. Our idea is to make use of the block ɛ-circulant approximation via fast Fourier transforms, so that the resulting task is to solve a block diagonal system, where each diagonal block matrix is the sum of a complex scalar times the identity matrix and a Laplacian matrix. We show that the accuracy of the approximation scheme is of O (ɛ). Because of the special diagonal block structure, we employ the multigrid method to solve the resulting linear systems. The convergence of the multigrid method is studied. Numerical examples are presented to illustrate the accuracy of the proposed approximation scheme and the efficiency of the proposed solver.
Novel Binders and Methods for Agglomeration of Ore
S. K. Kawatra; T. C. Eisele; J. A. Gurtler; K. Lewandowski
2005-09-30
Many metal extraction operations, such as leaching of copper, leaching of precious metals, and reduction of metal oxides to metal in high-temperature furnaces, require agglomeration of ore to ensure that reactive liquids or gases are evenly distributed throughout the ore being processed. Agglomeration of ore into coarse, porous masses achieves this even distribution of fluids by preventing fine particles from migrating and clogging the spaces and channels between the larger ore particles. Binders are critically necessary to produce agglomerates that will not break down during processing. However, for many important metal extraction processes there are no binders known that will work satisfactorily at a reasonable cost. A primary example of this is copper heap leaching, where there are no binders currently encountered in this acidic environment process. As a result, operators of many facilities see a large loss of process efficiency due to their inability to take advantage of agglomeration. The large quantities of ore that must be handled in metal extraction processes also means that the binder must be inexpensive and useful at low dosages to be economical. The acid-resistant binders and agglomeration procedures developed in this project will also be adapted for use in improving the energy efficiency and performance of a broad range of mineral agglomeration applications, particularly heap leaching. The active involvement of our industrial partners will help to ensure rapid commercialization of any agglomeration technologies developed by this project.
Novel Binders and Methods for Agglomeration of Ore
S. K. Kawatra; T. C. Eisele; K. A. Lewandowski; J. A. Gurtler
2006-03-31
Many metal extraction operations, such as leaching of copper, leaching of precious metals, and reduction of metal oxides to metal in high-temperature furnaces, require agglomeration of ore to ensure that reactive liquids or gases are evenly distributed throughout the ore being processed. Agglomeration of ore into coarse, porous masses achieves this even distribution of fluids by preventing fine particles from migrating and clogging the spaces and channels between the larger ore particles. Binders are critically necessary to produce agglomerates that will not break down during processing. However, for many important metal extraction processes there are no binders known that will work satisfactorily at a reasonable cost. A primary example of this is copper heap leaching, where there are no binders currently encountered in this acidic environment process. As a result, operators of many facilities see a large loss of process efficiency due to their inability to take advantage of agglomeration. The large quantities of ore that must be handled in metal extraction processes also means that the binder must be inexpensive and useful at low dosages to be economical. The acid-resistant binders and agglomeration procedures developed in this project will also be adapted for use in improving the energy efficiency and performance of a broad range of mineral agglomeration applications, particularly heap leaching. The active involvement of our industrial partners will help to ensure rapid commercialization of any agglomeration technologies developed by this project.
Sixth Copper Mountain Conference on Multigrid Methods. Final report
Not Available
1994-07-01
During the 5-day meeting, 112 half-hour talks on current research topics were presented. Session topics included: fluids, domain decomposition, iterative methods, Basics I and II, adaptive methods, nonlinear filtering, CFD I, II, and III, applications, transport, algebraic solvers, supercomputing, and student paper winners.
Multigrid methods for flow transition in three-dimensional boundary layers with surface roughness
NASA Technical Reports Server (NTRS)
Liu, Chaoqun; Liu, Zhining; Mccormick, Steve
1993-01-01
The efficient multilevel adaptive method has been successfully applied to perform direct numerical simulations (DNS) of flow transition in 3-D channels and 3-D boundary layers with 2-D and 3-D isolated and distributed roughness in a curvilinear coordinate system. A fourth-order finite difference technique on stretched and staggered grids, a fully-implicit time marching scheme, a semi-coarsening multigrid method associated with line distributive relaxation scheme, and an improved outflow boundary-condition treatment, which needs only a very short buffer domain to damp all order-one wave reflections, are developed. These approaches make the multigrid DNS code very accurate and efficient. This allows us not only to be able to do spatial DNS for the 3-D channel and flat plate at low computational costs, but also to do spatial DNS for transition in the 3-D boundary layer with 3-D single and multiple roughness elements, which would have extremely high computational costs with conventional methods. Numerical results show good agreement with the linear stability theory, the secondary instability theory, and a number of laboratory experiments. The contribution of isolated and distributed roughness to transition is analyzed.
NOVEL BINDERS AND METHODS FOR AGGLOMERATION OF ORE
S.K. Kawatra; T.C. Eisele; J.A. Gurtler; C.A. Hardison; K. Lewandowski
2004-04-01
Many metal extraction operations, such as leaching of copper, leaching of precious metals, and reduction of metal oxides to metal in high-temperature furnaces, require agglomeration of ore to ensure that reactive liquids or gases are evenly distributed throughout the ore being processed. Agglomeration of ore into coarse, porous masses achieves this even distribution of fluids by preventing fine particles from migrating and clogging the spaces and channels between the larger ore particles. Binders are critically necessary to produce agglomerates that will not break down during processing. However, for many important metal extraction processes there are no binders known that will work satisfactorily. Primary examples of this are copper heap leaching, where there are no binders that will work in the acidic environment encountered in this process, and advanced ironmaking processes, where binders must function satisfactorily over an extraordinarily large range of temperatures (from room temperature up to over 1200 C). As a result, operators of many facilities see a large loss of process efficiency due to their inability to take advantage of agglomeration. The large quantities of ore that must be handled in metal extraction processes also means that the binder must be inexpensive and useful at low dosages to be economical. The acid-resistant binders and agglomeration procedures developed in this project will also be adapted for use in improving the energy efficiency and performance of a broad range of mineral agglomeration applications, particularly heap leaching and advanced primary ironmaking.
Novel Binders and Methods for Agglomeration of Ore
S. K. Kawatra; T. C. Eisele; J. A. Gurtler
2004-03-31
Many metal extraction operations, such as leaching of copper, leaching of precious metals, and reduction of metal oxides to metal in high-temperature furnaces, require agglomeration of ore to ensure that reactive liquids or gases are evenly distributed throughout the ore being processed. Agglomeration of ore into coarse, porous masses achieves this even distribution of fluids by preventing fine particles from migrating and clogging the spaces and channels between the larger ore particles. Binders are critically necessary to produce agglomerates that will not break down during processing. However, for many important metal extraction processes there are no binders known that will work satisfactorily. A primary example of this is copper heap leaching, where there are no binders that will work in the acidic environment encountered in this process. As a result, operators of acidic heap-leach facilities see a large loss of process efficiency due to their inability to take advantage of agglomeration. The large quantities of ore that must be handled in metal extraction processes also means that the binder must be inexpensive and useful at low dosages to be economical. The acid-resistant binders and agglomeration procedures developed in this project will also be adapted for use in improving the energy efficiency and performance of other agglomeration applications, particularly advanced primary ironmaking.
On multigrid methods for image reconstruction from projections
Henson, V.E.; Robinson, B.T.; Limber, M.
1994-12-31
The sampled Radon transform of a 2D function can be represented as a continuous linear map R : L{sup 1} {yields} R{sup N}. The image reconstruction problem is: given a vector b {element_of} R{sup N}, find an image (or density function) u(x, y) such that Ru = b. Since in general there are infinitely many solutions, the authors pick the solution with minimal 2-norm. Numerous proposals have been made regarding how best to discretize this problem. One can, for example, select a set of functions {phi}{sub j} that span a particular subspace {Omega} {contained_in} L{sup 1}, and model R : {Omega} {yields} R{sup N}. The subspace {Omega} may be chosen as a member of a sequence of subspaces whose limit is dense in L{sup 1}. One approach to the choice of {Omega} gives rise to a natural pixel discretization of the image space. Two possible choices of the set {phi}{sub j} are the set of characteristic functions of finite-width `strips` representing energy transmission paths and the set of intersections of such strips. The authors have studied the eigenstructure of the matrices B resulting from these choices and the effect of applying a Gauss-Seidel iteration to the problem Bw = b. There exists a near null space into which the error vectors migrate with iteration, after which Gauss-Seidel iteration stalls. The authors attempt to accelerate convergence via a multilevel scheme, based on the principles of McCormick`s Multilevel Projection Method (PML). Coarsening is achieved by thickening the rays which results in a much smaller discretization of an optimal grid, and a halving of the number of variables. This approach satisfies all the requirements of the PML scheme. They have observed that a multilevel approach based on this idea accelerates convergence at least to the point where noise in the data dominates.
Ku, Bon Ki; Kulkarni, Pramod
2015-01-01
We compare different approaches to measure surface area of aerosol agglomerates. The objective was to compare field methods, such as mobility and diffusion charging based approaches, with laboratory approach, such as Brunauer, Emmett, Teller (BET) method used for bulk powder samples. To allow intercomparison of various surface area measurements, we defined ‘geometric surface area’ of agglomerates (assuming agglomerates are made up of ideal spheres), and compared various surface area measurements to the geometric surface area. Four different approaches for measuring surface area of agglomerate particles in the size range of 60–350 nm were compared using (i) diffusion charging-based sensors from three different manufacturers, (ii) mobility diameter of an agglomerate, (iii) mobility diameter of an agglomerate assuming a linear chain morphology with uniform primary particle size, and (iv) surface area estimation based on tandem mobility–mass measurement and microscopy. Our results indicate that the tandem mobility–mass measurement, which can be applied directly to airborne particles unlike the BET method, agrees well with the BET method. It was also shown that the three diffusion charging-based surface area measurements of silver agglomerates were similar within a factor of 2 and were lower than those obtained from the tandem mobility–mass and microscopy method by a factor of 3–10 in the size range studied. Surface area estimated using the mobility diameter depended on the structure or morphology of the agglomerate with significant underestimation at high fractal dimensions approaching 3. PMID:26692585
NASA Technical Reports Server (NTRS)
1981-01-01
Developments in numerical solution of certain types of partial differential equations by rapidly converging sequences of operations on supporting grids that range from very fine to very coarse are presented.
Multigrid one shot methods for optimal control problems: Infinite dimensional control
NASA Technical Reports Server (NTRS)
Arian, Eyal; Taasan, Shlomo
1994-01-01
The multigrid one shot method for optimal control problems, governed by elliptic systems, is introduced for the infinite dimensional control space. ln this case, the control variable is a function whose discrete representation involves_an increasing number of variables with grid refinement. The minimization algorithm uses Lagrange multipliers to calculate sensitivity gradients. A preconditioned gradient descent algorithm is accelerated by a set of coarse grids. It optimizes for different scales in the representation of the control variable on different discretization levels. An analysis which reduces the problem to the boundary is introduced. It is used to approximate the two level asymptotic convergence rate, to determine the amplitude of the minimization steps, and the choice of a high pass filter to be used when necessary. The effectiveness of the method is demonstrated on a series of test problems. The new method enables the solutions of optimal control problems at the same cost of solving the corresponding analysis problems just a few times.
NASA Technical Reports Server (NTRS)
Atkins, H. L.; Helenbrook, B. T.
2005-01-01
This paper describes numerical experiments with P-multigrid to corroborate analysis, validate the present implementation, and to examine issues that arise in the implementations of the various combinations of relaxation schemes, discretizations and P-multigrid methods. The two approaches to implement P-multigrid presented here are equivalent for most high-order discretization methods such as spectral element, SUPG, and discontinuous Galerkin applied to advection; however it is discovered that the approach that mimics the common geometric multigrid implementation is less robust, and frequently unstable when applied to discontinuous Galerkin discretizations of di usion. Gauss-Seidel relaxation converges 40% faster than block Jacobi, as predicted by analysis; however, the implementation of Gauss-Seidel is considerably more expensive that one would expect because gradients in most neighboring elements must be updated. A compromise quasi Gauss-Seidel relaxation method that evaluates the gradient in each element twice per iteration converges at rates similar to those predicted for true Gauss-Seidel.
Implementation of multigrid methods for solving Navier-Stokes equations on a multiprocessor system
NASA Technical Reports Server (NTRS)
Naik, Vijay K.; Taasan, Shlomo
1987-01-01
Presented are schemes for implementing multigrid algorithms on message based MIMD multiprocessor systems. To address the various issues involved, a nontrivial problem of solving the 2-D incompressible Navier-Stokes equations is considered as the model problem. Three different multigrid algorithms are considered. Results from implementing these algorithms on an Intel iPSC are presented.
Multigrid Method for Modeling Multi-Dimensional Combustion with Detailed Chemistry
NASA Technical Reports Server (NTRS)
Zheng, Xiaoqing; Liu, Chaoqun; Liao, Changming; Liu, Zhining; McCormick, Steve
1996-01-01
A highly accurate and efficient numerical method is developed for modeling 3-D reacting flows with detailed chemistry. A contravariant velocity-based governing system is developed for general curvilinear coordinates to maintain simplicity of the continuity equation and compactness of the discretization stencil. A fully-implicit backward Euler technique and a third-order monotone upwind-biased scheme on a staggered grid are used for the respective temporal and spatial terms. An efficient semi-coarsening multigrid method based on line-distributive relaxation is used as the flow solver. The species equations are solved in a fully coupled way and the chemical reaction source terms are treated implicitly. Example results are shown for a 3-D gas turbine combustor with strong swirling inflows.
A Full Multi-Grid Method for the Solution of the Cell Vertex Finite Volume Cauchy-Riemann Equations
NASA Technical Reports Server (NTRS)
Borzi, A.; Morton, K. W.; Sueli, E.; Vanmaele, M.
1996-01-01
The system of inhomogeneous Cauchy-Riemann equations defined on a square domain and subject to Dirichlet boundary conditions is considered. This problem is discretised by using the cell vertex finite volume method on quadrilateral meshes. The resulting algebraic problem is overdetermined and the solution is defined in a least squares sense. By this approach a consistent algebraic problem is obtained which differs from the original one by O(h(exp 2)) perturbations of the right-hand side. A suitable cell-based convergent smoothing iteration is presented which is naturally linked to the least squares formulation. Hence, a standard multi-grid algorithm is reported which combines the given smoother and cell-based transfer operators. Some remarkable reduction properties of these operators are shown. A full multi-grid method is discussed which solves the discrete problem to the level of truncation error by employing one multi-grid cycle at each current level of discretisation. Experiments and applications of the full multi-grid scheme are presented.
Practical improvements of multi-grid iteration for adaptive mesh refinement method
NASA Astrophysics Data System (ADS)
Miyashita, Hisashi; Yamada, Yoshiyuki
2005-03-01
Adaptive mesh refinement(AMR) is a powerful tool to efficiently solve multi-scaled problems. However, the vanilla AMR method has a well-known critical demerit, i.e., it cannot be applied to non-local problems. Although multi-grid iteration (MGI) can be regarded as a good remedy for a non-local problem such as the Poisson equation, we observed fundamental difficulties in applying the MGI technique in AMR to realistic problems under complicated mesh layouts because it does not converge or it requires too many iterations even if it does converge. To cope with the problem, when updating the next approximation in the MGI process, we calculate the precise total corrections that are relatively accurate to the current residual by introducing a new iteration for such a total correction. This procedure greatly accelerates the MGI convergence speed especially under complicated mesh layouts.
NASA Technical Reports Server (NTRS)
Zeng, S.; Wesseling, P.
1993-01-01
The performance of a linear multigrid method using four smoothing methods, called SCGS (Symmetrical Coupled GauBeta-Seidel), CLGS (Collective Line GauBeta-Seidel), SILU (Scalar ILU), and CILU (Collective ILU), is investigated for the incompressible Navier-Stokes equations in general coordinates, in association with Galerkin coarse grid approximation. Robustness and efficiency are measured and compared by application to test problems. The numerical results show that CILU is the most robust, SILU the least, with CLGS and SCGS in between. CLGS is the best in efficiency, SCGS and CILU follow, and SILU is the worst.
NASA Astrophysics Data System (ADS)
Al-Chalabi, Rifat M. Khalil
1997-09-01
Development of an improvement to the computational efficiency of the existing nested iterative solution strategy of the Nodal Exapansion Method (NEM) nodal based neutron diffusion code NESTLE is presented. The improvement in the solution strategy is the result of developing a multilevel acceleration scheme that does not suffer from the numerical stalling associated with a number of iterative solution methods. The acceleration scheme is based on the multigrid method, which is specifically adapted for incorporation into the NEM nonlinear iterative strategy. This scheme optimizes the computational interplay between the spatial discretization and the NEM nonlinear iterative solution process through the use of the multigrid method. The combination of the NEM nodal method, calculation of the homogenized, neutron nodal balance coefficients (i.e. restriction operator), efficient underlying smoothing algorithm (power method of NESTLE), and the finer mesh reconstruction algorithm (i.e. prolongation operator), all operating on a sequence of coarser spatial nodes, constitutes the multilevel acceleration scheme employed in this research. Two implementations of the multigrid method into the NESTLE code were examined; the Imbedded NEM Strategy and the Imbedded CMFD Strategy. The main difference in implementation between the two methods is that in the Imbedded NEM Strategy, the NEM solution is required at every MG level. Numerical tests have shown that the Imbedded NEM Strategy suffers from divergence at coarse- grid levels, hence all the results for the different benchmarks presented here were obtained using the Imbedded CMFD Strategy. The novelties in the developed MG method are as follows: the formulation of the restriction and prolongation operators, and the selection of the relaxation method. The restriction operator utilizes a variation of the reactor physics, consistent homogenization technique. The prolongation operator is based upon a variant of the pin power
Magnetic agglomeration method for size control in the synthesis of magnetic nanoparticles
Huber, Dale L.
2011-07-05
A method for controlling the size of chemically synthesized magnetic nanoparticles that employs magnetic interaction between particles to control particle size and does not rely on conventional kinetic control of the reaction to control particle size. The particles are caused to reversibly agglomerate and precipitate from solution; the size at which this occurs can be well controlled to provide a very narrow particle size distribution. The size of particles is controllable by the size of the surfactant employed in the process; controlling the size of the surfactant allows magnetic control of the agglomeration and precipitation processes. Agglomeration is used to effectively stop particle growth to provide a very narrow range of particle sizes.
NASA Technical Reports Server (NTRS)
Atkins, Harold
1991-01-01
A multiple block multigrid method for the solution of the three dimensional Euler and Navier-Stokes equations is presented. The basic flow solver is a cell vertex method which employs central difference spatial approximations and Runge-Kutta time stepping. The use of local time stepping, implicit residual smoothing, multigrid techniques and variable coefficient numerical dissipation results in an efficient and robust scheme is discussed. The multiblock strategy places the block loop within the Runge-Kutta Loop such that accuracy and convergence are not affected by block boundaries. This has been verified by comparing the results of one and two block calculations in which the two block grid is generated by splitting the one block grid. Results are presented for both Euler and Navier-Stokes computations of wing/fuselage combinations.
Development of a pressure based multigrid solution method for complex fluid flows
NASA Technical Reports Server (NTRS)
Shyy, Wei
1991-01-01
In order to reduce the computational difficulty associated with a single grid (SG) solution procedure, the multigrid (MG) technique was identified as a useful means for improving the convergence rate of iterative methods. A full MG full approximation storage (FMG/FAS) algorithm is used to solve the incompressible recirculating flow problems in complex geometries. The algorithm is implemented in conjunction with a pressure correction staggered grid type of technique using the curvilinear coordinates. In order to show the performance of the method, two flow configurations, one a square cavity and the other a channel, are used as test problems. Comparisons are made between the iterations, equivalent work units, and CPU time. Besides showing that the MG method can yield substantial speed-up with wide variations in Reynolds number, grid distributions, and geometry, issues such as the convergence characteristics of different grid levels, the choice of convection schemes, and the effectiveness of the basic iteration smoothers are studied. An adaptive grid scheme is also combined with the MG procedure to explore the effects of grid resolution on the MG convergence rate as well as the numerical accuracy.
Final Report on Subcontract B591217: Multigrid Methods for Systems of PDEs
Xu, J; Brannick, J J; Zikatanov, L
2011-10-25
Progress is summarized in the following areas of study: (1) Compatible relaxation; (2) Improving aggregation-based MG solver performance - variable cycle; (3) First Order System Least Squares (FOSLS) for LQCD; (4) Auxiliary space preconditioners; (5) Bootstrap algebraic multigrid; and (6) Practical applications of AMG and fast auxiliary space preconditioners.
NASA Astrophysics Data System (ADS)
Gravemeier, Volker; Wall, Wolfgang A.
2010-08-01
An algebraic variational multiscale-multigrid method is proposed for large-eddy simulation of turbulent variable-density flow at low Mach number. Scale-separating operators generated by level-transfer operators from plain aggregation algebraic multigrid methods enable the application of modeling terms to selected scale groups (here, the smaller of the resolved scales) in a purely algebraic way. Thus, for scale separation, no additional discretization besides the basic one is required, in contrast to earlier approaches based on geometric multigrid methods. The proposed method is thoroughly validated via three numerical test cases of increasing complexity: a Rayleigh-Taylor instability, turbulent channel flow with a heated and a cooled wall, and turbulent flow past a backward-facing step with heating. Results obtained with the algebraic variational multiscale-multigrid method are compared to results obtained with residual-based variational multiscale methods as well as reference results from direct numerical simulation, experiments and LES published elsewhere. Particularly, mean and various second-order velocity and temperature results obtained for turbulent channel flow with a heated and a cooled wall indicate the higher prediction quality achievable when adding a small-scale subgrid-viscosity term within the algebraic multigrid framework instead of residual-based terms accounting for the subgrid-scale part of the non-linear convective term.
Another look at neural multigrid
Baeker, M.
1997-04-01
We present a new multigrid method called neural multigrid which is based on joining multigrid ideas with concepts from neural nets. The main idea is to use the Greenbaum criterion as a cost functional for the neural net. The algorithm is able to learn efficient interpolation operators in the case of the ordered Laplace equation with only a very small critical slowing down and with a surprisingly small amount of work comparable to that of a Conjugate Gradient solver. In the case of the two-dimensional Laplace equation with SU(2) gauge fields at {beta}=0 the learning exhibits critical slowing down with an exponent of about z {approx} 0.4. The algorithm is able to find quite good interpolation operators in this case as well. Thereby it is proven that a practical true multigrid algorithm exists even for a gauge theory. An improved algorithm using dynamical blocks that will hopefully overcome the critical slowing down completely is sketched.
Analysis of a parallel multigrid algorithm
NASA Technical Reports Server (NTRS)
Chan, Tony F.; Tuminaro, Ray S.
1989-01-01
The parallel multigrid algorithm of Frederickson and McBryan (1987) is considered. This algorithm uses multiple coarse-grid problems (instead of one problem) in the hope of accelerating convergence and is found to have a close relationship to traditional multigrid methods. Specifically, the parallel coarse-grid correction operator is identical to a traditional multigrid coarse-grid correction operator, except that the mixing of high and low frequencies caused by aliasing error is removed. Appropriate relaxation operators can be chosen to take advantage of this property. Comparisons between the standard multigrid and the new method are made.
New convergence estimates for multigrid algorithms
Bramble, J.H.; Pasciak, J.E.
1987-10-01
In this paper, new convergence estimates are proved for both symmetric and nonsymmetric multigrid algorithms applied to symmetric positive definite problems. Our theory relates the convergence of multigrid algorithms to a ''regularity and approximation'' parameter ..cap alpha.. epsilon (0, 1) and the number of relaxations m. We show that for the symmetric and nonsymmetric ..nu.. cycles, the multigrid iteration converges for any positive m at a rate which deteriorates no worse than 1-cj/sup -(1-//sup ..cap alpha..//sup )///sup ..cap alpha../, where j is the number of grid levels. We then define a generalized ..nu.. cycle algorithm which involves exponentially increasing (for example, doubling) the number of smoothings on successively coarser grids. We show that the resulting symmetric and nonsymmetric multigrid iterations converge for any ..cap alpha.. with rates that are independent of the mesh size. The theory is presented in an abstract setting which can be applied to finite element multigrid and finite difference multigrid methods.
Element Agglomeration Algebraic Multigrid and Upscaling Library
2015-02-11
ELAG is a serial C++ library for numerical upscaling of finite element discretizations. It provides optimal complexity algorithms to build multilevel hierarchies and solvers that can be used for solving a wide class of partial differential equation (elliptic, hyperbolic, saddle point problems) on general unstructured mesh. Additionally, a novel multilevel solver for saddle point problems with divergence constraint is implemented.
NASA Technical Reports Server (NTRS)
Demuren, A. O.
1990-01-01
A multigrid method is presented for calculating turbulent jets in crossflow. Fairly rapid convergence is obtained with the k-epsilon turbulence model, but computations with a full Reynolds stress turbulence model (RSM) are not yet very efficient. Grid dependency tests show that there are slight differences between results obtained on the two finest grid levels. Computations using the RSM are significantly different from those with k-epsilon model and compare better to experimental data. Some work is still required to improve the efficiency of the computations with the RSM.
NASA Astrophysics Data System (ADS)
Ishida, Haruma
2014-01-01
An improved solution scheme is developed for the three-dimensional radiative transfer equation (RTE) in inhomogeneous cloudy atmospheres. This solution scheme is deterministic (explicit) and utilizes spherical harmonics series expansion and the finite-volume method for discretization of the RTE. The first-order upwind finite difference is modified to take into account bidirectional flow of radiance in spherical harmonics space, and an iterative solution method is applied. The multigrid method, which is generally employed to achieve rapid convergence in iterative calculation, is incorporated into the solution scheme. The present study suggests that the restriction and prolongation procedure for the multigrid method must be also modified to account for bidirectional flow, and proposes an efficient bidirectional restriction/prolongation procedure that does not increase the computational effort for coarser grids, resulting in a type of wavelet low-pass filter. Several calculation examples for various atmosphere models indicate that the proposed solution scheme is effective for rapid convergence and suitable for obtaining adequate radiation fields in inhomogeneous cloudy atmospheres, although a comparison with the Monte Carlo method suggests that the radiances obtained by this solution scheme at certain angles tends to be smoother.
Lignite pellets and methods of agglomerating or pelletizing
Baker, Albert F.; Blaustein, Eric W.; Deurbrouck, Albert W.; Garvin, John P.; McKeever, Robert E.
1981-01-01
The specification discloses lignite pellets which are relatively hard, dust resistant, of generally uniform size and free from spontaneous ignition and general degradation. Also disclosed are methods for making such pellets which involve crushing as mined lignite, mixing said lignite with a binder such as asphalt, forming the lignite binder mixture into pellets, and drying the pellets.
NASA Astrophysics Data System (ADS)
Caughey, David A.
2005-11-01
The efficient symmetric Gauss-Seidel (SGS) algorithm for solving the Euler equations of inviscid, compressible flow on structured grids, developed in collaboration with Jameson of Stanford University, is extended to unstructured grids. The algorithm uses a nonlinear formulation of an SGS solver, implemented within the framework of multigrid. The earlier form of the algorithm used the natural (lexicographic) ordering of the mesh cells available on structured grids for the SGS sweeps, but a number of features of the method that are believed to contribute to its success can also be implemented for computations on unstructured grids. The present paper reviews, the features of the SGS multigrid solver for structured gr0ids, including its nonlinear implementation, its use of “absolute” Jacobian matrix preconditioning, and its incorporation of multigrid, and then describes the incorporation of these features into an algorithm suitable for computations on unstructured grids. The implementation on unstructured grids is based on the agglomerated multigrid method developed by Sørensen, which uses an explicit Runge-Kutta smoothing algorithm. Results of computations for steady, transonic flows past two-dimensional airfoils are presented, and the efficiency of the method is evaluated for computations on both structured and unstructured meshes.
MGLab: An Interactive Multigrid Environment
NASA Technical Reports Server (NTRS)
Bordner, James; Saied, Faisal
1996-01-01
MGLab is a set of Matlab functions that defines an interactive environment for experimenting with multigrid algorithms. The package solves two-dimensional elliptic partial differential equations discretized using either finite differences or finite volumes, depending on the problem. Built-in problems include the Poisson equation, the Helmholtz equation, a convection-diffusion problem, and a discontinuous coefficient problem. A number of parameters controlling the multigrid V-cycle can be set using a point-and-click mechanism. The menu-based user interface also allows a choice of several Krylov subspace methods, including CG, GMRES(k), and Bi-CGSTAB, which can be used either as stand-alone solvers or as multigrid acceleration schemes. The package exploits Matlab's visualization and sparse matrix features and has been structured to be easily extensible.
Canonical-variables multigrid method for steady-state Euler equations
NASA Technical Reports Server (NTRS)
Taasan, Shlomo
1994-01-01
A novel approach for the solution of inviscid flow problems for subsonic compressible flows is described. The approach is based on canonical forms of the equations, in which subsystems governed by hyperbolic operators are separated from those governed by elliptic ones. The discretizations used as well as the iterative techniques for the different subsystems are inherently different. Hyperbolic parts, which describe, in general, propagation phenomena, are discretized using upwind schemes and are solved by marching techniques. Elliptic parts, which are directionally unbiased, are discretized using h-elliptic central discretizations, and are solved by pointwise relaxations together with coarse grid acceleration. The resulting discretization schemes introduce artificial viscosity only for the hyperbolic parts of the system; thus a smaller total artificial viscosity is used, while the multigrid solvers used are much more efficient. Solutions of the subsonic compressible Euler equations are achieved at the same efficiency as the full potential equation.
NASA Technical Reports Server (NTRS)
Yang, Cheng I.; Guo, Yan-Hu; Liu, C.- H.
1996-01-01
The analysis and design of a submarine propulsor requires the ability to predict the characteristics of both laminar and turbulent flows to a higher degree of accuracy. This report presents results of certain benchmark computations based on an upwind, high-resolution, finite-differencing Navier-Stokes solver. The purpose of the computations is to evaluate the ability, the accuracy and the performance of the solver in the simulation of detailed features of viscous flows. Features of interest include flow separation and reattachment, surface pressure and skin friction distributions. Those features are particularly relevant to the propulsor analysis. Test cases with a wide range of Reynolds numbers are selected; therefore, the effects of the convective and the diffusive terms of the solver can be evaluated separately. Test cases include flows over bluff bodies, such as circular cylinders and spheres, at various low Reynolds numbers, flows over a flat plate with and without turbulence effects, and turbulent flows over axisymmetric bodies with and without propulsor effects. Finally, to enhance the iterative solution procedure, a full approximation scheme V-cycle multigrid method is implemented. Preliminary results indicate that the method significantly reduces the computational effort.
NASA Astrophysics Data System (ADS)
Debreu, Laurent; Neveu, Emilie; Simon, Ehouarn; Le Dimet, Francois Xavier; Vidard, Arthur
2014-05-01
In order to lower the computational cost of the variational data assimilation process, we investigate the use of multigrid methods to solve the associated optimal control system. On a linear advection equation, we study the impact of the regularization term on the optimal control and the impact of discretization errors on the efficiency of the coarse grid correction step. We show that even if the optimal control problem leads to the solution of an elliptic system, numerical errors introduced by the discretization can alter the success of the multigrid methods. The view of the multigrid iteration as a preconditioner for a Krylov optimization method leads to a more robust algorithm. A scale dependent weighting of the multigrid preconditioner and the usual background error covariance matrix based preconditioner is proposed and brings significant improvements. [1] Laurent Debreu, Emilie Neveu, Ehouarn Simon, François-Xavier Le Dimet and Arthur Vidard, 2014: Multigrid solvers and multigrid preconditioners for the solution of variational data assimilation problems, submitted to QJRMS, http://hal.inria.fr/hal-00874643 [2] Emilie Neveu, Laurent Debreu and François-Xavier Le Dimet, 2011: Multigrid methods and data assimilation - Convergence study and first experiments on non-linear equations, ARIMA, 14, 63-80, http://intranet.inria.fr/international/arima/014/014005.html
Large-Scale Parallel Viscous Flow Computations using an Unstructured Multigrid Algorithm
NASA Technical Reports Server (NTRS)
Mavriplis, Dimitri J.
1999-01-01
The development and testing of a parallel unstructured agglomeration multigrid algorithm for steady-state aerodynamic flows is discussed. The agglomeration multigrid strategy uses a graph algorithm to construct the coarse multigrid levels from the given fine grid, similar to an algebraic multigrid approach, but operates directly on the non-linear system using the FAS (Full Approximation Scheme) approach. The scalability and convergence rate of the multigrid algorithm are examined on the SGI Origin 2000 and the Cray T3E. An argument is given which indicates that the asymptotic scalability of the multigrid algorithm should be similar to that of its underlying single grid smoothing scheme. For medium size problems involving several million grid points, near perfect scalability is obtained for the single grid algorithm, while only a slight drop-off in parallel efficiency is observed for the multigrid V- and W-cycles, using up to 128 processors on the SGI Origin 2000, and up to 512 processors on the Cray T3E. For a large problem using 25 million grid points, good scalability is observed for the multigrid algorithm using up to 1450 processors on a Cray T3E, even when the coarsest grid level contains fewer points than the total number of processors.
Vectorized multigrid Poisson solver for the CDC CYBER 205
NASA Technical Reports Server (NTRS)
Barkai, D.; Brandt, M. A.
1984-01-01
The full multigrid (FMG) method is applied to the two dimensional Poisson equation with Dirichlet boundary conditions. This has been chosen as a relatively simple test case for examining the efficiency of fully vectorizing of the multigrid method. Data structure and programming considerations and techniques are discussed, accompanied by performance details.
NASA Technical Reports Server (NTRS)
Ruge, J. W.; Stueben, K.
1987-01-01
The state of the art in algebraic multgrid (AMG) methods is discussed. The interaction between the relaxation process and the coarse grid correction necessary for proper behavior of the solution probes is discussed in detail. Sufficient conditions on relaxation and interpolation for the convergence of the V-cycle are given. The relaxation used in AMG, what smoothing means in an algebraic setting, and how it relates to the existing theory are considered. Some properties of the coarse grid operator are discussed, and results on the convergence of two-level and multilevel convergence are given. Details of an algorithm particularly studied for problems obtained by discretizing a single elliptic, second order partial differential equation are given. Results of experiments with such problems using both finite difference and finite element discretizations are presented.
Toward textbook multigrid efficiency for fully implicit resistive magnetohydrodynamics
Adams, Mark F.; Samtaney, Ravi; Brandt, Achi
2010-09-01
Multigrid methods can solve some classes of elliptic and parabolic equations to accuracy below the truncation error with a work-cost equivalent to a few residual calculations – so-called ‘‘textbook” multigrid efficiency. We investigate methods to solve the system of equations that arise in time dependent magnetohydrodynamics (MHD) simulations with textbook multigrid efficiency. We apply multigrid techniques such as geometric interpolation, full approximate storage, Gauss–Seidel smoothers, and defect correction for fully implicit, nonlinear, second-order finite volume discretizations of MHD. We apply these methods to a standard resistive MHD benchmark problem, the GEM reconnection problem, and add a strong magnetic guide field,more » which is a critical characteristic of magnetically confined fusion plasmas. We show that our multigrid methods can achieve near textbook efficiency on fully implicit resistive MHD simulations.« less
Toward textbook multigrid efficiency for fully implicit resistive magnetohydrodynamics
Adams, Mark F.; Samtaney, Ravi; Brandt, Achi
2010-09-01
Multigrid methods can solve some classes of elliptic and parabolic equations to accuracy below the truncation error with a work-cost equivalent to a few residual calculations – so-called ‘‘textbook” multigrid efficiency. We investigate methods to solve the system of equations that arise in time dependent magnetohydrodynamics (MHD) simulations with textbook multigrid efficiency. We apply multigrid techniques such as geometric interpolation, full approximate storage, Gauss–Seidel smoothers, and defect correction for fully implicit, nonlinear, second-order finite volume discretizations of MHD. We apply these methods to a standard resistive MHD benchmark problem, the GEM reconnection problem, and add a strong magnetic guide field, which is a critical characteristic of magnetically confined fusion plasmas. We show that our multigrid methods can achieve near textbook efficiency on fully implicit resistive MHD simulations.
Toward textbook multigrid efficiency for fully implicit resistive magnetohydrodynamics
Adams, Mark F.; Samtaney, Ravi; Brandt, Achi
2013-12-14
Multigrid methods can solve some classes of elliptic and parabolic equations to accuracy below the truncation error with a work-cost equivalent to a few residual calculations – so-called “textbook” multigrid efficiency. We investigate methods to solve the system of equations that arise in time dependent magnetohydrodynamics (MHD) simulations with textbook multigrid efficiency. We apply multigrid techniques such as geometric interpolation, full approximate storage, Gauss-Seidel smoothers, and defect correction for fully implicit, nonlinear, second-order finite volume discretizations of MHD. We apply these methods to a standard resistive MHD benchmark problem, the GEM reconnection problem, and add a strong magnetic guide field, which is a critical characteristic of magnetically confined fusion plasmas. We show that our multigrid methods can achieve near textbook efficiency on fully implicit resistive MHD simulations.
NASA Technical Reports Server (NTRS)
1982-01-01
Papers presented in this volume provide an overview of recent work on numerical boundary condition procedures and multigrid methods. The topics discussed include implicit boundary conditions for the solution of the parabolized Navier-Stokes equations for supersonic flows; far field boundary conditions for compressible flows; and influence of boundary approximations and conditions on finite-difference solutions. Papers are also presented on fully implicit shock tracking and on the stability of two-dimensional hyperbolic initial boundary value problems for explicit and implicit schemes.
Tsujita, K.; Endo, T.; Yamamoto, A.
2013-07-01
An efficient numerical method for time-dependent transport equation, the mutigrid amplitude function (MAF) method, is proposed. The method of characteristics (MOC) is being widely used for reactor analysis thanks to the advances of numerical algorithms and computer hardware. However, efficient kinetic calculation method for MOC is still desirable since it requires significant computation time. Various efficient numerical methods for solving the space-dependent kinetic equation, e.g., the improved quasi-static (IQS) and the frequency transform methods, have been developed so far mainly for diffusion calculation. These calculation methods are known as effective numerical methods and they offer a way for faster computation. However, they have not been applied to the kinetic calculation method using MOC as the authors' knowledge. Thus, the MAF method is applied to the kinetic calculation using MOC aiming to reduce computation time. The MAF method is a unified numerical framework of conventional kinetic calculation methods, e.g., the IQS, the frequency transform, and the theta methods. Although the MAF method is originally developed for the space-dependent kinetic calculation based on the diffusion theory, it is extended to transport theory in the present study. The accuracy and computational time are evaluated though the TWIGL benchmark problem. The calculation results show the effectiveness of the MAF method. (authors)
MueLu Multigrid Preconditioning Package
2012-09-11
MueLu is intended for the research and development of multigrid algorithms used in the solution of sparse linear systems arising from systems of partial differential equations. The software provides multigrid source code, test programs, and short example programs to demonstrate the various interfaces for creating, accessing, and applying the solvers. MueLu currently provides an implementation of smoothed aggregation algebraic multigrid method and interfaces to many commonly used smoothers. However, the software is intended to bemore » extensible, and new methods can be incorporated easily. MueLu also allows for advanced usage, such as combining multiple methods and segregated solves. The library supports point and block access to matrix data. All algorithms and methods in MueLu have been or will be published in the open scientific literature.« less
NASA Astrophysics Data System (ADS)
Cools, S.; Vanroose, W.
2016-03-01
This paper improves the convergence and robustness of a multigrid-based solver for the cross sections of the driven Schrödinger equation. Adding a Coupled Channel Correction Step (CCCS) after each multigrid (MG) V-cycle efficiently removes the errors that remain after the V-cycle sweep. The combined iterative solution scheme (MG-CCCS) is shown to feature significantly improved convergence rates over the classical MG method at energies where bound states dominate the solution, resulting in a fast and scalable solution method for the complex-valued Schrödinger break-up problem for any energy regime. The proposed solver displays optimal scaling; a solution is found in a time that is linear in the number of unknowns. The method is validated on a 2D Temkin-Poet model problem, and convergence results both as a solver and preconditioner are provided to support the O (N) scalability of the method. This paper extends the applicability of the complex contour approach for far field map computation (Cools et al. (2014) [10]).
Some multigrid algorithms for SIMD machines
Dendy, J.E. Jr.
1996-12-31
Previously a semicoarsening multigrid algorithm suitable for use on SIMD architectures was investigated. Through the use of new software tools, the performance of this algorithm has been considerably improved. The method has also been extended to three space dimensions. The method performs well for strongly anisotropic problems and for problems with coefficients jumping by orders of magnitude across internal interfaces. The parallel efficiency of this method is analyzed, and its actual performance on the CM-5 is compared with its performance on the CRAY-YMP. A standard coarsening multigrid algorithm is also considered, and we compare its performance on these two platforms as well.
Multigrid method applied to the solution of an elliptic, generalized eigenvalue problem
Alchalabi, R.M.; Turinsky, P.J.
1996-12-31
The work presented in this paper is concerned with the development of an efficient MG algorithm for the solution of an elliptic, generalized eigenvalue problem. The application is specifically applied to the multigroup neutron diffusion equation which is discretized by utilizing the Nodal Expansion Method (NEM). The underlying relaxation method is the Power Method, also known as the (Outer-Inner Method). The inner iterations are completed using Multi-color Line SOR, and the outer iterations are accelerated using Chebyshev Semi-iterative Method. Furthermore, the MG algorithm utilizes the consistent homogenization concept to construct the restriction operator, and a form function as a prolongation operator. The MG algorithm was integrated into the reactor neutronic analysis code NESTLE, and numerical results were obtained from solving production type benchmark problems.
Augustin, Christoph M.; Neic, Aurel; Liebmann, Manfred; Prassl, Anton J.; Niederer, Steven A.; Haase, Gundolf; Plank, Gernot
2016-01-01
Electromechanical (EM) models of the heart have been used successfully to study fundamental mechanisms underlying a heart beat in health and disease. However, in all modeling studies reported so far numerous simplifications were made in terms of representing biophysical details of cellular function and its heterogeneity, gross anatomy and tissue microstructure, as well as the bidirectional coupling between electrophysiology (EP) and tissue distension. One limiting factor is the employed spatial discretization methods which are not sufficiently flexible to accommodate complex geometries or resolve heterogeneities, but, even more importantly, the limited efficiency of the prevailing solver techniques which are not sufficiently scalable to deal with the incurring increase in degrees of freedom (DOF) when modeling cardiac electromechanics at high spatio-temporal resolution. This study reports on the development of a novel methodology for solving the nonlinear equation of finite elasticity using human whole organ models of cardiac electromechanics, discretized at a high para-cellular resolution. Three patient-specific, anatomically accurate, whole heart EM models were reconstructed from magnetic resonance (MR) scans at resolutions of 220 μm, 440 μm and 880 μm, yielding meshes of approximately 184.6, 24.4 and 3.7 million tetrahedral elements and 95.9, 13.2 and 2.1 million displacement DOF, respectively. The same mesh was used for discretizing the governing equations of both electrophysiology (EP) and nonlinear elasticity. A novel algebraic multigrid (AMG) preconditioner for an iterative Krylov solver was developed to deal with the resulting computational load. The AMG preconditioner was designed under the primary objective of achieving favorable strong scaling characteristics for both setup and solution runtimes, as this is key for exploiting current high performance computing hardware. Benchmark results using the 220 μm, 440 μm and 880 μm meshes demonstrate
NASA Astrophysics Data System (ADS)
Augustin, Christoph M.; Neic, Aurel; Liebmann, Manfred; Prassl, Anton J.; Niederer, Steven A.; Haase, Gundolf; Plank, Gernot
2016-01-01
Electromechanical (EM) models of the heart have been used successfully to study fundamental mechanisms underlying a heart beat in health and disease. However, in all modeling studies reported so far numerous simplifications were made in terms of representing biophysical details of cellular function and its heterogeneity, gross anatomy and tissue microstructure, as well as the bidirectional coupling between electrophysiology (EP) and tissue distension. One limiting factor is the employed spatial discretization methods which are not sufficiently flexible to accommodate complex geometries or resolve heterogeneities, but, even more importantly, the limited efficiency of the prevailing solver techniques which is not sufficiently scalable to deal with the incurring increase in degrees of freedom (DOF) when modeling cardiac electromechanics at high spatio-temporal resolution. This study reports on the development of a novel methodology for solving the nonlinear equation of finite elasticity using human whole organ models of cardiac electromechanics, discretized at a high para-cellular resolution. Three patient-specific, anatomically accurate, whole heart EM models were reconstructed from magnetic resonance (MR) scans at resolutions of 220 μm, 440 μm and 880 μm, yielding meshes of approximately 184.6, 24.4 and 3.7 million tetrahedral elements and 95.9, 13.2 and 2.1 million displacement DOF, respectively. The same mesh was used for discretizing the governing equations of both electrophysiology (EP) and nonlinear elasticity. A novel algebraic multigrid (AMG) preconditioner for an iterative Krylov solver was developed to deal with the resulting computational load. The AMG preconditioner was designed under the primary objective of achieving favorable strong scaling characteristics for both setup and solution runtimes, as this is key for exploiting current high performance computing hardware. Benchmark results using the 220 μm, 440 μm and 880 μm meshes demonstrate
Seynaeve, Bert; Rosseel, Eveline; Nicolai, Bart; Vandewalle, Stefan . E-mail: Stefan.Vandewalle@cs.kuleuven.be
2007-05-20
Partial differential equations with random coefficients appear for example in reliability problems and uncertainty propagation models. Various approaches exist for computing the stochastic characteristics of the solution of such a differential equation. In this paper, we consider the spectral expansion approach. This method transforms the continuous model into a large discrete algebraic system. We study the convergence properties of iterative methods for solving this discretized system. We consider one-level and multi-level methods. The classical Fourier mode analysis technique is extended towards the stochastic case. This is done by taking the eigenstructure into account of a certain matrix that depends on the random structure of the problem. We show how the convergence properties depend on the particulars of the algorithm, on the discretization parameters and on the stochastic characteristics of the model. Numerical results are added to illustrate some of our theoretical findings.
3D magnetospheric parallel hybrid multi-grid method applied to planet-plasma interactions
NASA Astrophysics Data System (ADS)
Leclercq, L.; Modolo, R.; Leblanc, F.; Hess, S.; Mancini, M.
2016-03-01
We present a new method to exploit multiple refinement levels within a 3D parallel hybrid model, developed to study planet-plasma interactions. This model is based on the hybrid formalism: ions are kinetically treated whereas electrons are considered as a inertia-less fluid. Generally, ions are represented by numerical particles whose size equals the volume of the cells. Particles that leave a coarse grid subsequently entering a refined region are split into particles whose volume corresponds to the volume of the refined cells. The number of refined particles created from a coarse particle depends on the grid refinement rate. In order to conserve velocity distribution functions and to avoid calculations of average velocities, particles are not coalesced. Moreover, to ensure the constancy of particles' shape function sizes, the hybrid method is adapted to allow refined particles to move within a coarse region. Another innovation of this approach is the method developed to compute grid moments at interfaces between two refinement levels. Indeed, the hybrid method is adapted to accurately account for the special grid structure at the interfaces, avoiding any overlapping grid considerations. Some fundamental test runs were performed to validate our approach (e.g. quiet plasma flow, Alfven wave propagation). Lastly, we also show a planetary application of the model, simulating the interaction between Jupiter's moon Ganymede and the Jovian plasma.
Application of multigrid methods to the solution of liquid crystal equations on a SIMD computer
NASA Technical Reports Server (NTRS)
Farrell, Paul A.; Ruttan, Arden; Zeller, Reinhardt R.
1993-01-01
We will describe a finite difference code for computing the equilibrium configurations of the order-parameter tensor field for nematic liquid crystals in rectangular regions by minimization of the Landau-de Gennes Free Energy functional. The implementation of the free energy functional described here includes magnetic fields, quadratic gradient terms, and scalar bulk terms through the fourth order. Boundary conditions include the effects of strong surface anchoring. The target architectures for our implementation are SIMD machines, with interconnection networks which can be configured as 2 or 3 dimensional grids, such as the Wavetracer DTC. We also discuss the relative efficiency of a number of iterative methods for the solution of the linear systems arising from this discretization on such architectures.
Selective oil agglomeration of lignite
Halime Abakay Temel; Volkan Bozkurt; Arun Kumar Majumder
2009-01-15
In this study, desulfurization and deashing of Adiyaman-Glbai lignite by the agglomeration method were studied. For this purpose, three groups of agglomeration experiments were made. The effects of solid concentration, bridging liquid type and dosage, pH, and screen size on the agglomeration after desliming were investigated in the first group of experiments. The effects of lake water and sea water (the Mediterranean Sea water, the Aegean Sea water, and the Black Sea water) on the agglomeration were investigated in the second group of experiments. The effects of different salts (NaCl, MgCl{sub 2}, and FeCl{sub 3}) on the agglomeration were investigated in the third group of experiments. Agglomeration results showed that the usage of sea waters and soda lake water in the agglomeration medium had a positive effect on the reduction of total sulfur content of agglomerates. In addition, the usage of NaCl, MgCl{sub 2}, and FeCl{sub 3} in the agglomeration medium had a positive effect on the ash content reduction of the agglomerates. 27 refs., 10 figs., 6 tabs.
Multigrid semi-implicit hydrodynamics revisited
Dendy, J.E.
1983-01-01
The multigrid method has for several years been very successful for simple equations like Laplace's equation on a rectangle. For more complicated situations, however, success has been more elusive. Indeeed, there are only a few applications in which the multigrid method is now being successfully used in complicated production codes. The one with which we are most familiar is the application by Alcouffe to TTDAMG. We are more familiar with this second application in which, for a set of test problems, TTDAMG ran seven to twenty times less expensively (on a CRAY-1 computer) than its best competitor. This impressive performance, in a field where a factor of two improvement is considered significant, encourages one to attempt the application of the multigrid method in other complicated situations. The application discussed in this paper was actually attempted several years ago. In that paper the multigrid method was applied to the pressure iteration in three Eulerian and Lagrangian codes. The application to the Eulerian codes, both incompressible and compressible, was successful, but the application to the Lagrangian code was less so. The reason given for this lack of success was that the differencing for the pressure equation in the Lagrangian code, SALE, was bad. In this paper, we examine again the application of multigrad to the pressure equation in SALE with the goal of succeeding this time without cheating.
Unsteady Analysis of Separated Aerodynamic Flows Using an Unstructured Multigrid Algorithm
NASA Technical Reports Server (NTRS)
Pelaez, Juan; Mavriplis, Dimitri J.; Kandil, Osama
2001-01-01
An implicit method for the computation of unsteady flows on unstructured grids is presented. The resulting nonlinear system of equations is solved at each time step using an agglomeration multigrid procedure. The method allows for arbitrarily large time steps and is efficient in terms of computational effort and storage. Validation of the code using a one-equation turbulence model is performed for the well-known case of flow over a cylinder. A Detached Eddy Simulation model is also implemented and its performance compared to the one equation Spalart-Allmaras Reynolds Averaged Navier-Stokes (RANS) turbulence model. Validation cases using DES and RANS include flow over a sphere and flow over a NACA 0012 wing including massive stall regimes. The project was driven by the ultimate goal of computing separated flows of aerodynamic interest, such as massive stall or flows over complex non-streamlined geometries.
Segmental Refinement: A Multigrid Technique for Data Locality
Adams, Mark
2014-10-27
We investigate a technique - segmental refinement (SR) - proposed by Brandt in the 1970s as a low memory multigrid method. The technique is attractive for modern computer architectures because it provides high data locality, minimizes network communication, is amenable to loop fusion, and is naturally highly parallel and asynchronous. The network communication minimization property was recognized by Brandt and Diskin in 1994; we continue this work by developing a segmental refinement method for a finite volume discretization of the 3D Laplacian on massively parallel computers. An understanding of the asymptotic complexities, required to maintain textbook multigrid efficiency, are explored experimentally with a simple SR method. A two-level memory model is developed to compare the asymptotic communication complexity of a proposed SR method with traditional parallel multigrid. Performance and scalability are evaluated with a Cray XC30 with up to 64K cores. We achieve modest improvement in scalability from traditional parallel multigrid with a simple SR implementation.
Conduct of the International Multigrid Conference
NASA Technical Reports Server (NTRS)
Mccormick, S.
1984-01-01
The 1983 International Multigrid Conference was held at Colorado's Copper Mountain Ski Resort, April 5-8. It was organized jointly by the Institute for Computational Studies at Colorado State University, U.S.A., and the Gasellschaft fur Mathematik und Datenverarbeitung Bonn, F.R. Germany, and was sponsored by the Air Force Office of Sponsored Research and National Aeronautics and Space Administration Headquarters. The conference was attended by 80 scientists, divided by institution almost equally into private industry, research laboratories, and academia. Fifteen attendees came from countries other than the U.S.A. In addition to the fruitful discussions, the most significant factor of the conference was of course the lectures. The lecturers include most of the leaders in the field of multigrid research. The program offered a nice integrated blend of theory, numerical studies, basic research, and applications. Some of the new areas of research that have surfaced since the Koln-Porz conference include: the algebraic multigrid approach; multigrid treatment of Euler equations for inviscid fluid flow problems; 3-D problems; and the application of MG methods on vector and parallel computers.
Matrix-dependent multigrid-homogenization for diffusion problems
Knapek, S.
1996-12-31
We present a method to approximately determine the effective diffusion coefficient on the coarse scale level of problems with strongly varying or discontinuous diffusion coefficients. It is based on techniques used also in multigrid, like Dendy`s matrix-dependent prolongations and the construction of coarse grid operators by means of the Galerkin approximation. In numerical experiments, we compare our multigrid-homogenization method with homogenization, renormalization and averaging approaches.
On the connection between multigrid and cyclic reduction
NASA Technical Reports Server (NTRS)
Merriam, M. L.
1984-01-01
A technique is shown whereby it is possible to relate a particular multigrid process to cyclic reduction using purely mathematical arguments. This technique suggest methods for solving Poisson's equation in 1-, 2-, or 3-dimensions with Dirichlet or Neumann boundary conditions. In one dimension the method is exact and, in fact, reduces to cyclic reduction. This provides a valuable reference point for understanding multigrid techniques. The particular multigrid process analyzed is referred to here as Approximate Cyclic Reduction (ACR) and is one of a class known as Multigrid Reduction methods in the literature. It involves one approximation with a known error term. It is possible to relate the error term in this approximation with certain eigenvector components of the error. These are sharply reduced in amplitude by classical relaxation techniques. The approximation can thus be made a very good one.
2013-05-06
AMG2013 is a parallel algebraic multigrid solver for linear systems arising from problems on unstructured grids. It has been derived directly from the Boomer AMG solver in the hypre library, a large linear solvers library that is being developed in the Center for Applied Scientific Computing (CASC) at LLNL. The driver provided in the benchmark can build various test problems. The default problem is a Laplace type problem on an unstructured domain with various jumps and an anisotropy in one part.
Applications of multigrid software in the atmospheric sciences
NASA Technical Reports Server (NTRS)
Adams, J.; Garcia, R.; Gross, B.; Hack, J.; Haidvogel, D.; Pizzo, V.
1992-01-01
Elliptic partial differential equations from different areas in the atmospheric sciences are efficiently and easily solved utilizing the multigrid software package named MUDPACK. It is demonstrated that the multigrid method is more efficient than other commonly employed techniques, such as Gaussian elimination and fixed-grid relaxation. The efficiency relative to other techniques, both in terms of storage requirement and computational time, increases quickly with grid size.
Progress with multigrid schemes for hypersonic flow problems
NASA Technical Reports Server (NTRS)
Radespiel, R.; Swanson, R. C.
1991-01-01
Several multigrid schemes are considered for the numerical computation of viscous hypersonic flows. For each scheme, the basic solution algorithm uses upwind spatial discretization with explicit multistage time stepping. Two level versions of the various multigrid algorithms are applied to the two dimensional advection equation, and Fourier analysis is used to determine their damping properties. The capabilities of the multigrid methods are assessed by solving three different hypersonic flow problems. Some new multigrid schemes based on semicoarsening strategies are shown to be quite effective in relieving the stiffness caused by the high aspect ratio cells required to resolve high Reynolds number flows. These schemes exhibit good convergence rates for Reynolds numbers up to 200 x 10(exp 6) and Mach numbers up to 25.
Progress with multigrid schemes for hypersonic flow problems
Radespiel, R.; Swanson, R.C.
1995-01-01
Several multigrid schemes are considered for the numerical computation of viscous hypersonic flows. For each scheme, the basic solution algorithm employs upwind spatial discretization with explicit multistage time stepping. Two-level versions of the various multigrid algorithms are applied to the two-dimensional advection equation, and Fourier analysis is used to determine their damping properties. The capabilities of the multigrid methods are assessed by solving three different hypersonic flow problems. Some new multigrid schemes based on semicoarsening strategies are shown to be quite effective in relieving the stiffness caused by the high-aspect-ratio cells required to resolve high Reynolds number flows. These schemes exhibit good convergence rates for Reynolds numbers up to 200 X 10{sup 6} and Mach numbers up to 25. 32 refs., 31 figs., 1 tab.
Updated users' guide for TAWFIVE with multigrid
NASA Technical Reports Server (NTRS)
Melson, N. Duane; Streett, Craig L.
1989-01-01
A program for the Transonic Analysis of a Wing and Fuselage with Interacted Viscous Effects (TAWFIVE) was improved by the incorporation of multigrid and a method to specify lift coefficient rather than angle-of-attack. A finite volume full potential multigrid method is used to model the outer inviscid flow field. First order viscous effects are modeled by a 3-D integral boundary layer method. Both turbulent and laminar boundary layers are treated. Wake thickness effects are modeled using a 2-D strip method. A brief discussion of the engineering aspects of the program is given. The input, output, and use of the program are covered in detail. Sample results are given showing the effects of boundary layer corrections and the capability of the lift specification method.
Compositions for agglomerating solid contaminants in well fluids and methods for using same
Gabel, R.K.; Law, R.E.
1989-01-10
A composition is described useful for agglomerating solid contaminants in a well fluid comprising: (a) at least about 10 percent by weight, relative to the total composition weight, of a surfactant comprising amides and glycerides formed by contacting one or more secondary amines selected from the group consisting of Alkyl secondary amines having from 2 to 8 carbon atoms, saturated aliphatic hydroxyl-containing secondary amines having from 2 to 8 carbon atoms, and mixtures thereof with triglyceride fats, triglyceride oils or mixtures thereof; and (b) a carrier capable of forming a solution with the surfactant and which is substantially insoluble in the well fluid and is selected from the group consisting of alkanolamines having from 2 to 8 carbons, alcohols having from 6 to 24 carbons, fatty acids having 12 to 24 carbons, aliphatic hydrocarbons selected from the group consisting of straight chain hydrocarbons, branched hydrocarbons and cycloaliphatic hydrocarbons having 8 to 20 carbons, aromatic hydrocarbons selected from group consisting of substituted and unsubstituted benzenes and napthalenes and mixtures thereof.
2013-05-06
AMG2013 is a parallel algebraic multigrid solver for linear systems arising from problems on unstructured grids. It has been derived directly from the Boomer AMG solver in the hypre library, a large linear solvers library that is being developed in the Center for Applied Scientific Computing (CASC) at LLNL. The driver provided in the benchmark can build various test problems. The default problem is a Laplace type problem on an unstructured domain with various jumpsmore » and an anisotropy in one part.« less
Element Agglomeration Algebraic Multilevel Monte-Carlo Library
2015-02-19
ElagMC is a parallel C++ library for Multilevel Monte Carlo simulations with algebraically constructed coarse spaces. ElagMC enables Multilevel variance reduction techniques in the context of general unstructured meshes by using the specialized element-based agglomeration techniques implemented in ELAG (the Element-Agglomeration Algebraic Multigrid and Upscaling Library developed by U. Villa and P. Vassilevski and currently under review for public release). The ElabMC library can support different type of deterministic problems, including mixed finite element discretizations of subsurface flow problems.
Element Agglomeration Algebraic Multilevel Monte-Carlo Library
2015-02-19
ElagMC is a parallel C++ library for Multilevel Monte Carlo simulations with algebraically constructed coarse spaces. ElagMC enables Multilevel variance reduction techniques in the context of general unstructured meshes by using the specialized element-based agglomeration techniques implemented in ELAG (the Element-Agglomeration Algebraic Multigrid and Upscaling Library developed by U. Villa and P. Vassilevski and currently under review for public release). The ElabMC library can support different type of deterministic problems, including mixed finite element discretizationsmore » of subsurface flow problems.« less
NASA Technical Reports Server (NTRS)
Jentink, Thomas Neil; Usab, William J., Jr.
1990-01-01
An explicit, Multigrid algorithm was written to solve the Euler and Navier-Stokes equations with special consideration given to the coarse mesh boundary conditions. These are formulated in a manner consistent with the interior solution, utilizing forcing terms to prevent coarse-mesh truncation error from affecting the fine-mesh solution. A 4-Stage Hybrid Runge-Kutta Scheme is used to advance the solution in time, and Multigrid convergence is further enhanced by using local time-stepping and implicit residual smoothing. Details of the algorithm are presented along with a description of Jameson's standard Multigrid method and a new approach to formulating the Multigrid equations.
Axelsson, O.
1986-07-01
The cost of smoothing is usually a major expense in multigrid codes. Efficient vectorizable and parallelizable versions of incomplete block-matrix factorization methods used as smoothers for multigrid methods are discussed in this paper. The methods are particularly interesting for computers with parallel processors with pipelines, because both multitasking with little overhead and vectorization can be achieved. 21 references.
NASA Technical Reports Server (NTRS)
Mineck, Raymond E.; Thomas, James L.; Biedron, Robert T.; Diskin, Boris
2005-01-01
FMG3D (full multigrid 3 dimensions) is a pilot computer program that solves equations of fluid flow using a finite difference representation on a structured grid. Infrastructure exists for three dimensions but the current implementation treats only two dimensions. Written in Fortran 90, FMG3D takes advantage of the recursive subroutine feature, dynamic memory allocation, and structured-programming constructs of that language. FMG3D supports multi-block grids with three types of block-to-block interfaces: periodic, C-zero, and C-infinity. For all three types, grid points must match at interfaces. For periodic and C-infinity types, derivatives of grid metrics must be continuous at interfaces. The available equation sets are as follows: scalar elliptic equations, scalar convection equations, and the pressure-Poisson formulation of the Navier-Stokes equations for an incompressible fluid. All the equation sets are implemented with nonzero forcing functions to enable the use of user-specified solutions to assist in verification and validation. The equations are solved with a full multigrid scheme using a full approximation scheme to converge the solution on each succeeding grid level. Restriction to the next coarser mesh uses direct injection for variables and full weighting for residual quantities; prolongation of the coarse grid correction from the coarse mesh to the fine mesh uses bilinear interpolation; and prolongation of the coarse grid solution uses bicubic interpolation.
A multigrid solver for the semiconductor equations
NASA Technical Reports Server (NTRS)
Bachmann, Bernhard
1993-01-01
We present a multigrid solver for the exponential fitting method. The solver is applied to the current continuity equations of semiconductor device simulation in two dimensions. The exponential fitting method is based on a mixed finite element discretization using the lowest-order Raviart-Thomas triangular element. This discretization method yields a good approximation of front layers and guarantees current conservation. The corresponding stiffness matrix is an M-matrix. 'Standard' multigrid solvers, however, cannot be applied to the resulting system, as this is dominated by an unsymmetric part, which is due to the presence of strong convection in part of the domain. To overcome this difficulty, we explore the connection between Raviart-Thomas mixed methods and the nonconforming Crouzeix-Raviart finite element discretization. In this way we can construct nonstandard prolongation and restriction operators using easily computable weighted L(exp 2)-projections based on suitable quadrature rules and the upwind effects of the discretization. The resulting multigrid algorithm shows very good results, even for real-world problems and for locally refined grids.
Coal Cleaning by Gas Agglomeration
Meiyu Shen; Royce Abbott; T. D. Wheelock
1998-03-01
The gas agglomeration method of coal cleaning was demonstrated with laboratory scale mixing equipment which made it possible to generate microscopic gas bubbles in aqueous suspensions of coal particles. A small amount of i-octane was introduced to enhance the hydrophobicity of the coal. Between 1.0 and 2.5 v/w% i-octane was sufficient based on coal weight. Coal agglomerates or aggregates were produced which were bound together by small gas bubbles.
Multigrid approaches to non-linear diffusion problems on unstructured meshes
NASA Technical Reports Server (NTRS)
Mavriplis, Dimitri J.; Bushnell, Dennis M. (Technical Monitor)
2001-01-01
The efficiency of three multigrid methods for solving highly non-linear diffusion problems on two-dimensional unstructured meshes is examined. The three multigrid methods differ mainly in the manner in which the nonlinearities of the governing equations are handled. These comprise a non-linear full approximation storage (FAS) multigrid method which is used to solve the non-linear equations directly, a linear multigrid method which is used to solve the linear system arising from a Newton linearization of the non-linear system, and a hybrid scheme which is based on a non-linear FAS multigrid scheme, but employs a linear solver on each level as a smoother. Results indicate that all methods are equally effective at converging the non-linear residual in a given number of grid sweeps, but that the linear solver is more efficient in cpu time due to the lower cost of linear versus non-linear grid sweeps.
Multigrid solution of the convection-diffusion equation with high-Reynolds number
Zhang, Jun
1996-12-31
A fourth-order compact finite difference scheme is employed with the multigrid technique to solve the variable coefficient convection-diffusion equation with high-Reynolds number. Scaled inter-grid transfer operators and potential on vectorization and parallelization are discussed. The high-order multigrid method is unconditionally stable and produces solution of 4th-order accuracy. Numerical experiments are included.
Choi, Young Joon; Jorshari, Razzi Movassaghi; Djilali, Ned
2015-03-10
Direct numerical simulations of the flow-nanoparticle interaction in a colloidal suspension are presented using an extended finite element method (XFEM) in which the dynamics of the nanoparticles is solved in a fully-coupled manner with the flow. The method is capable of accurately describing solid-fluid interfaces without the need of boundary-fitted meshes to investigate the dynamics of particles in complex flows. In order to accurately compute the high interparticle shear stresses and pressures while minimizing computing costs, an adaptive meshing technique is incorporated with the fluid-structure interaction algorithm. The particle-particle interaction at the microscopic level is modeled using the Lennard-Jones (LJ) potential and the corresponding potential parameters are determined by a scaling procedure. The study is relevant to the preparation of inks used in the fabrication of catalyst layers for fuel cells. In this paper, we are particularly interested in investigating agglomeration of the nanoparticles under external shear flow in a sliding bi-periodic Lees-Edwards frame. The results indicate that the external shear has a crucial impact on the structure formation of colloidal particles in a suspension.
Mechanisms for selective agglomeration of coals
Wheelock, T.D.; Drzymala, J.; Allen, R.W.; Hu, Y.-C.; Tyson, D.; Xiaoping, Qiu; Lessa, A.
1989-05-01
Work continued on the basic mechanisms which underlie various processes for beneficiating aqueous suspensions of coal by selective agglomeration with oil. A new method was demonstrated for characterizing the agglomerability of coal suspensions. This method utilizes a photometric dispersion analyzer to monitor changes in the turbidity of a particle suspension as increasing amounts of oil are added to the suspension in a batch agglomeration test. Agglomeration of the particles leads to a marked decrease in the turbidity of the suspension. Another experimental technique was also demonstrated for characterizing oil agglomeration. This technique involves measuring the rate of growth of agglomerates in a continuous flow system operating under stead-state conditions. The data are analyzed by means of a population balance. The results of a preliminary set of experiments in which Indiana V seam coal was agglomerated with tetralin seemed to fit a particular growth model very well. Equipment was also constructed for studying the kinetics of agglomeration in a batch process. While earlier work showed that quebracho (a commercially available dispersant) is a strong agglomeration depressant for pyrite, recent experiments with mixtures of Upper Freeport coal and mineral pyrite showed that quebracho does not appear to be sufficiently selective. Further consideration was given to the separation of mixtures of coal and pyrite agglomeration with heptane. 2 refs., 17 figs., 1 tab.
Evaluation of a Multigrid Scheme for the Incompressible Navier-Stokes Equations
NASA Technical Reports Server (NTRS)
Swanson, R. C.
2004-01-01
A fast multigrid solver for the steady, incompressible Navier-Stokes equations is presented. The multigrid solver is based upon a factorizable discrete scheme for the velocity-pressure form of the Navier-Stokes equations. This scheme correctly distinguishes between the advection-diffusion and elliptic parts of the operator, allowing efficient smoothers to be constructed. To evaluate the multigrid algorithm, solutions are computed for flow over a flat plate, parabola, and a Karman-Trefftz airfoil. Both nonlifting and lifting airfoil flows are considered, with a Reynolds number range of 200 to 800. Convergence and accuracy of the algorithm are discussed. Using Gauss-Seidel line relaxation in alternating directions, multigrid convergence behavior approaching that of O(N) methods is achieved. The computational efficiency of the numerical scheme is compared with that of Runge-Kutta and implicit upwind based multigrid methods.
Towards Optimal Multigrid Efficiency for the Navier-Stokes Equations
NASA Technical Reports Server (NTRS)
Swanson, R. C.
2001-01-01
A fast multigrid solver for the steady incompressible Navier-Stokes equations is presented. Unlike time-marching schemes, this approach uses relaxation of the steady equations. Application of this method results in a discretization that correctly distinguishes between the advection and elliptic parts of the operator, allowing efficient smoothers to be constructed. Numerical solutions are shown for flow over a flat plate and a Karman-Trefftz airfoil. Using collective Gauss-Seidel line relaxation in both the vertical and horizontal directions, multigrid convergence behavior approaching that of O(N) methods is achieved. The computational efficiency of the numerical scheme is compared with that of a Runge-Kutta based multigrid method.
Black box multigrid solver for definite and indefinite problems
Shapira, Yair
1997-02-01
A two-level analysis method for certain separable problems is introduced. It motivates the definition of improved versions of Black Box Multigrid for diffusion problems with discontinuous coefficients and indefinite Helmholtz equations. For anisotropic problems, it helps in choosing suitable implementations for frequency decomposition multigrid methods. For highly indefinite problems, it provides a way to choose in advance a suitable mesh size for the coarsest grid used. Numerical experiments confirm the analysis and show the advantage of the present methods for several examples.
Fast Multigrid Techniques in Total Variation-Based Image Reconstruction
NASA Technical Reports Server (NTRS)
Oman, Mary Ellen
1996-01-01
Existing multigrid techniques are used to effect an efficient method for reconstructing an image from noisy, blurred data. Total Variation minimization yields a nonlinear integro-differential equation which, when discretized using cell-centered finite differences, yields a full matrix equation. A fixed point iteration is applied with the intermediate matrix equations solved via a preconditioned conjugate gradient method which utilizes multi-level quadrature (due to Brandt and Lubrecht) to apply the integral operator and a multigrid scheme (due to Ewing and Shen) to invert the differential operator. With effective preconditioning, the method presented seems to require Omicron(n) operations. Numerical results are given for a two-dimensional example.
Spectral Element Agglomerate AMGe
Chartier, T; Falgout, R; Henson, V E; Jones, J E; Vassilevski, P S; Manteuffel, T A; McCormick, S F; Ruge, J W
2005-05-20
The purpose of this note is to describe an algorithm resulting from the uniting of two ideas introduced and applied elsewhere. For many problems, AMG has always been difficult due to complexities whose natures are difficult to discern from the entries of matrix A alone. Element-based interpolation has been shown to be an effective method for some of these problems, but it requires access to the element matrices on all levels. One way to obtain these has been to perform element agglomeration to form coarse elements, but in complicated situations defining the coarse degrees of freedom (dofs) is not easy. The spectral approach to coarse dof selection is very attractive due to its elegance and simplicity. The algorithm presented here combines the robustness of element interpolation, the ease of coarsening by element agglomeration, and the simplicity of defining coarse dofs through the spectral approach. As demonstrated in the numerical results, the method does yield a reasonable solver for the problems described. It can, however, be an expensive method due to the number and cost of the local, small dense linear algebra problems; making it a generally competitive method remains an area for further research.
A diagonally inverted LU implicit multigrid scheme
NASA Technical Reports Server (NTRS)
Yokota, Jeffrey W.; Caughey, David A.; Chima, Rodrick V.
1988-01-01
A new Diagonally Inverted LU Implicit scheme is developed within the framework of the multigrid method for the 3-D unsteady Euler equations. The matrix systems that are to be inverted in the LU scheme are treated by local diagonalizing transformations that decouple them into systems of scalar equations. Unlike the Diagonalized ADI method, the time accuracy of the LU scheme is not reduced since the diagonalization procedure does not destroy time conservation. Even more importantly, this diagonalization significantly reduces the computational effort required to solve the LU approximation and therefore transforms it into a more efficient method of numerically solving the 3-D Euler equations.
Multigrid and cyclic reduction applied to the Helmholtz equation
NASA Technical Reports Server (NTRS)
Brackenridge, Kenneth
1993-01-01
We consider the Helmholtz equation with a discontinuous complex parameter and inhomogeneous Dirichlet boundary conditions in a rectangular domain. A variant of the direct method of cyclic reduction (CR) is employed to facilitate the design of improved multigrid (MG) components, resulting in the method of CR-MG. We demonstrate the improved convergence properties of this method.
On Multigrid for Overlapping Grids
Henshaw, W
2004-01-13
The solution of elliptic partial differential equations on composite overlapping grids using multigrid is discussed. An approach is described that provides a fast and memory efficient scheme for the solution of boundary value problems in complex geometries. The key aspects of the new scheme are an automatic coarse grid generation algorithm, an adaptive smoothing technique for adjusting residuals on different component grids, and the use of local smoothing near interpolation boundaries. Other important features include optimizations for Cartesian component grids, the use of over-relaxed Red-Black smoothers and the generation of coarse grid operators through Galerkin averaging. Numerical results in two and three dimensions show that very good multigrid convergence rates can be obtained for both Dirichlet and Neumann/mixed boundary conditions. A comparison to Krylov based solvers shows that the multigrid solver can be much faster and require significantly less memory.
Multigrid and multilevel domain decomposition for unstructured grids
Chan, T.; Smith, B.
1994-12-31
Multigrid has proven itself to be a very versatile method for the iterative solution of linear and nonlinear systems of equations arising from the discretization of PDES. In some applications, however, no natural multilevel structure of grids is available, and these must be generated as part of the solution procedure. In this presentation the authors will consider the problem of generating a multigrid algorithm when only a fine, unstructured grid is given. Their techniques generate a sequence of coarser grids by first forming an approximate maximal independent set of the vertices and then applying a Cavendish type algorithm to form the coarser triangulation. Numerical tests indicate that convergence using this approach can be as fast as standard multigrid on a structured mesh, at least in two dimensions.
Reducing Communication in Algebraic Multigrid Using Additive Variants
Vassilevski, Panayot S.; Yang, Ulrike Meier
2014-02-12
Algebraic multigrid (AMG) has proven to be an effective scalable solver on many high performance computers. However, its increasing communication complexity on coarser levels has shown to seriously impact its performance on computers with high communication cost. Moreover, additive AMG variants provide not only increased parallelism as well as decreased numbers of messages per cycle but also generally exhibit slower convergence. Here we present various new additive variants with convergence rates that are significantly improved compared to the classical additive algebraic multigrid method and investigate their potential for decreased communication, and improved communication-computation overlap, features that are essential for good performance on future exascale architectures.
Compatible Relaxation and Coarsening in Algebraic Multigrid
Brannick, J J; Falgout, R D
2009-09-22
We introduce a coarsening algorithm for algebraic multigrid (AMG) based on the concept of compatible relaxation (CR). The algorithm is significantly different from standard methods, most notably because it does not rely on any notion of strength of connection. We study its behavior on a number of model problems, and evaluate the performance of an AMG algorithm that incorporates the coarsening approach. Lastly, we introduce a variant of CR that provides a sharper metric of coarse-grid quality and demonstrate its potential with two simple examples.
Multigrid solution strategies for adaptive meshing problems
NASA Technical Reports Server (NTRS)
Mavriplis, Dimitri J.
1995-01-01
This paper discusses the issues which arise when combining multigrid strategies with adaptive meshing techniques for solving steady-state problems on unstructured meshes. A basic strategy is described, and demonstrated by solving several inviscid and viscous flow cases. Potential inefficiencies in this basic strategy are exposed, and various alternate approaches are discussed, some of which are demonstrated with an example. Although each particular approach exhibits certain advantages, all methods have particular drawbacks, and the formulation of a completely optimal strategy is considered to be an open problem.
A multigrid preconditioner for the semiconductor equations
Meza, J.C.; Tuminaro, R.S.
1994-12-31
Currently, integrated circuits are primarily designed in a {open_quote}trial and error{close_quote} fashion. That is, prototypes are built and improved via experimentation and testing. In the near future, however, it may be possible to significantly reduce the time and cost of designing new devices by using computer simulations. To accurately perform these complex simulations in three dimensions, however, new algorithms and high performance computers are necessary. In this paper the authors discuss the use of multigrid preconditioning inside a semiconductor device modeling code, DANCIR. The DANCIR code is a full three-dimensional simulator capable of computing steady-state solutions of the drift-diffusion equations for a single semiconductor device and has been used to simulate a wide variety of different devices. At the inner core of DANCIR is a solver for the nonlinear equations that arise from the spatial discretization of the drift-diffusion equations on a rectangular grid. These nonlinear equations are resolved using Gummel`s method which requires three symmetric linear systems to be solved within each Gummel iteration. It is the resolution of these linear systems which comprises the dominant computational cost of this code. The original version of DANCIR uses a Cholesky preconditioned conjugate gradient algorithm to solve these linear systems. Unfortunately, this algorithm has a number of disadvantages: (1) it takes many iterations to converge (if it converges), (2) it can require a significant amount of computing time, and (3) it is not very parallelizable. To improve the situation, the authors consider a multigrid preconditioner. The multigrid method uses iterations on a hierarchy of grids to accelerate the convergence on the finest grid.
Möller, T; Korsatko, W
2000-06-01
Due to its low melting range approx. 53 degrees C optically pure ibuprofen can be regarded as problematic in a pharmaceutic-technological sense. With regard to the non-solvent shock agglomeration method this means that the process and product temperatures must strictly be kept in the range of 10 K above the melting point of the substance. Higher temperatures can induce degradation of S(+)ibuprofen. During storage under stress conditions (31 degrees C for a period of 18 months) ibuprofen shows extreme stability independent of its optical activity. Racemic ibuprofen is inert to the influence of light; in individual cases optically pure substance containing an increased level of impurities can show slight degradation tendencies. The thermal and photo stability of ibuprofen is independent of the preparation technology. For comparison, conventional, fluid bed granulated, briquetted and from organic solvents especially recrystallised and optically active substances were investigated besides the shock agglomerated substances. PMID:10907254
Crane, N K; Parsons, I D; Hjelmstad, K D
2002-03-21
Adaptive mesh refinement selectively subdivides the elements of a coarse user supplied mesh to produce a fine mesh with reduced discretization error. Effective use of adaptive mesh refinement coupled with an a posteriori error estimator can produce a mesh that solves a problem to a given discretization error using far fewer elements than uniform refinement. A geometric multigrid solver uses increasingly finer discretizations of the same geometry to produce a very fast and numerically scalable solution to a set of linear equations. Adaptive mesh refinement is a natural method for creating the different meshes required by the multigrid solver. This paper describes the implementation of a scalable adaptive multigrid method on a distributed memory parallel computer. Results are presented that demonstrate the parallel performance of the methodology by solving a linear elastic rocket fuel deformation problem on an SGI Origin 3000. Two challenges must be met when implementing adaptive multigrid algorithms on massively parallel computing platforms. First, although the fine mesh for which the solution is desired may be large and scaled to the number of processors, the multigrid algorithm must also operate on much smaller fixed-size data sets on the coarse levels. Second, the mesh must be repartitioned as it is adapted to maintain good load balancing. In an adaptive multigrid algorithm, separate mesh levels may require separate partitioning, further complicating the load balance problem. This paper shows that, when the proper optimizations are made, parallel adaptive multigrid algorithms perform well on machines with several hundreds of processors.
An evaluation of parallel multigrid as a solver and a preconditioner for singular perturbed problems
Oosterlee, C.W.; Washio, T.
1996-12-31
In this paper we try to achieve h-independent convergence with preconditioned GMRES and BiCGSTAB for 2D singular perturbed equations. Three recently developed multigrid methods are adopted as a preconditioner. They are also used as solution methods in order to compare the performance of the methods as solvers and as preconditioners. Two of the multigrid methods differ only in the transfer operators. One uses standard matrix- dependent prolongation operators from. The second uses {open_quotes}upwind{close_quotes} prolongation operators, developed. Both employ the Galerkin coarse grid approximation and an alternating zebra line Gauss-Seidel smoother. The third method is based on the block LU decomposition of a matrix and on an approximate Schur complement. This multigrid variant is presented in. All three multigrid algorithms are algebraic methods.
NASA Technical Reports Server (NTRS)
Thomas, J. L.; Diskin, B.; Brandt, A.
1999-01-01
The distributed-relaxation multigrid and defect- correction methods are applied to the two- dimensional compressible Navier-Stokes equations. The formulation is intended for high Reynolds number applications and several applications are made at a laminar Reynolds number of 10,000. A staggered- grid arrangement of variables is used; the coupled pressure and internal energy equations are solved together with multigrid, requiring a block 2x2 matrix solution. Textbook multigrid efficiencies are attained for incompressible and slightly compressible simulations of the boundary layer on a flat plate. Textbook efficiencies are obtained for compressible simulations up to Mach numbers of 0.7 for a viscous wake simulation.
Implicit Multigrid Solutions for Compressible Flows in Complex Geometries.
NASA Astrophysics Data System (ADS)
Wang, Lixia
Two implicit multigrid algorithms for the two and three dimensional compressible Euler equations have been developed in this dissertation. First, a diagonal implicit multigrid method is developed for solving a finite-volume approximation to the Euler equations in which the dependent variables are stored at the cell vertices. The spatial derivatives in the two dimensional Euler equations are approximated using a conservative cell-vertex finite volume formulation. Artificial dissipation is provided by adding an adaptive blend of second and fourth differences of the solution to maintain stability and accuracy. A Diagonal Alternating Directional Implicit method is used to advance the solution in time. Rapid convergence to a steady-state solution is achieved with local time stepping and the multigrid algorithm. Results for the transonic flow past the NACA 0012 airfoil are presented to verify the accuracy and efficiency of the scheme. Second, the development of an efficient and flexible multiblock/multigrid Euler solver and its application to realistic engineering problems are presented. A cell-centered finite volume method with a multigrid implementation of the Diagonal Alternating Direction Implicit algorithm is used to solve the Euler equations. A fully conservative inter-block boundary condition, which permits the passage of discontinuities across block boundaries with minimum distortion of the solution, is developed for cases in which the grid lines at the inter-block boundaries can be completely continuous or discontinuous. Information is exchanged between blocks by using surface arrays, which contain all the data needed to update the inter-block boundary conditions. Results demonstrate the feasibility of using the present multi -block/multigrid approach to solve flow problems involving complex geometries. Two dimensional results for several types of grids and various free stream conditions have been presented to verify the accuracy and computational efficiency of
Implicit multigrid solutions for compressible flows in complex geometries
NASA Astrophysics Data System (ADS)
Wang, Lixia
Two implicit multigrid algorithms for the two and three dimensional compressible Euler equations are developed. First, a diagonal implicit multigrid method is developed for solving a finite-volume approximation to the Euler equations in which the dependent variables are stored at the cell vertices. The spatial derivatives in the two dimensional Euler equations are approximated using a conservative cell-vertex finite volume formulation. Artificial dissipation is provided by adding an adaptive blend of second and fourth differences of the solution to maintain stability and accuracy. A diagonal alternating directional implicit method is used to advance the solution in time. Rapid convergence to a steady-state solution is achieved with local time stepping and the multigrid algorithm. Results for the transonic flow past the NACA 0012 airfoil are presented to verify the accuracy and efficiency of the scheme. Second, the development of an efficient and flexible multiblock/multigrid Euler solver and its application to realistic engineering problems are presented. A cell-centered finite volume method with a multigrid implementation of the diagonal alternating direction implicit algorithm is used to solve the Euler equations. A fully conservative interblock boundary condition, which permits the passage of discontinuities across block boundaries with minimum distortion of the solution, is developed for cases in which the grid lines at the interblock boundaries can be completely continuous or discontinuous. Information is exchanged between blocks by using surface arrays, which contain all the data needed to update the interblock boundary conditions. Results demonstrate the feasibility of using the present multiblock/multigrid approach to solve flow problems involving complex geometries. Two dimensional results for several types of grids and various free stream conditions have been presented to verify the accuracy and computational efficiency of the method. The application of
Coarse Spaces by Algebraic Multigrid: Multigrid Convergence and Upscaled Error Estimates
Vassilevski, P S
2010-04-30
We give an overview of a number of algebraic multigrid methods targeting finite element discretization problems. The focus is on the properties of the constructed hierarchy of coarse spaces that guarantee (two-grid) convergence. In particular, a necessary condition known as 'weak approximation property', and a sufficient one, referred to as 'strong approximation property' are discussed. Their role in proving convergence of the TG method (as iterative method) and also on the approximation properties of the AMG coarse spaces if used as discretization tool is pointed out. Some preliminary numerical results illustrating the latter aspect are also reported.
Analysis Tools for CFD Multigrid Solvers
NASA Technical Reports Server (NTRS)
Mineck, Raymond E.; Thomas, James L.; Diskin, Boris
2004-01-01
Analysis tools are needed to guide the development and evaluate the performance of multigrid solvers for the fluid flow equations. Classical analysis tools, such as local mode analysis, often fail to accurately predict performance. Two-grid analysis tools, herein referred to as Idealized Coarse Grid and Idealized Relaxation iterations, have been developed and evaluated within a pilot multigrid solver. These new tools are applicable to general systems of equations and/or discretizations and point to problem areas within an existing multigrid solver. Idealized Relaxation and Idealized Coarse Grid are applied in developing textbook-efficient multigrid solvers for incompressible stagnation flow problems.
Operator induced multigrid algorithms using semirefinement
NASA Technical Reports Server (NTRS)
Decker, Naomi; Vanrosendale, John
1989-01-01
A variant of multigrid, based on zebra relaxation, and a new family of restriction/prolongation operators is described. Using zebra relaxation in combination with an operator-induced prolongation leads to fast convergence, since the coarse grid can correct all error components. The resulting algorithms are not only fast, but are also robust, in the sense that the convergence rate is insensitive to the mesh aspect ratio. This is true even though line relaxation is performed in only one direction. Multigrid becomes a direct method if an operator-induced prolongation is used, together with the induced coarse grid operators. Unfortunately, this approach leads to stencils which double in size on each coarser grid. The use of an implicit three point restriction can be used to factor these large stencils, in order to retain the usual five or nine point stencils, while still achieving fast convergence. This algorithm achieves a V-cycle convergence rate of 0.03 on Poisson's equation, using 1.5 zebra sweeps per level, while the convergence rate improves to 0.003 if optimal nine point stencils are used. Numerical results for two and three dimensional model problems are presented, together with a two level analysis explaining these results.
Operator induced multigrid algorithms using semirefinement
NASA Technical Reports Server (NTRS)
Decker, Naomi Henderson; Van Rosendale, John
1989-01-01
A variant of multigrid, based on zebra relaxation, and a new family of restriction/prolongation operators is described. Using zebra relaxation in combination with an operator-induced prolongation leads to fast convergence, since the coarse grid can correct all error components. The resulting algorithms are not only fast, but are also robust, in the sense that the convergence rate is insensitive to the mesh aspect ratio. This is true even though line relaxation is performed in only one direction. Multigrid becomes a direct method if an operator-induced prolongation is used, together with the induced coarse grid operators. Unfortunately, this approach leads to stencils which double in size on each coarser grid. The use of an implicit three point restriction can be used to factor these large stencils, in order to retain the usual five or nine point stencils, while still achieving fast convergence. This algorithm achieves a V-cycle convergence rate of 0.03 on Poisson's equation, using 1.5 zebra sweeps per level, while the convergence rate improves to 0.003 if optimal nine point stencils are used. Numerical results for two- and three-dimensional model problems are presented, together with a two level analysis explaining these results.
Multigrid solutions of elliptic fluid flow problems
NASA Astrophysics Data System (ADS)
Wright, Nigel George
1988-06-01
An efficient FAS multigrid solution strategy is presented for the accurate and economic simulation of convection dominated flows. The use of a high-order approximation to the convective transport terms found in the governing equations of motion was investigated in conjunction with an unsegregated smoothing technique. Results are presented for a sequence of problems of increasing complexity requiring that careful attention be directed toward the proper treatment of different types of boundary condition. The classical two-dimensional problem of flow in a lid-driven cavity is investigated in depth for flows at Reynolds number of 100, 400 and 1000. This gives an extremely good indication of the power of a multigrid approach. Next, the solution methodology is applied to flow in a three-dimensional lid-driven cavity at different Reynolds numbers, with cross-reference being made to predictions obtained in the corresponding two-dimensional simulations, and to the flow over a step discontinuity in the case of an abruptly expanding channel. Although, at first sight, these problems appear to require only minor extensions to the existing approach, it is found that they are rather more idiosyncratic. Finally, the governing equations and numerical algorithm are extended to encompass the treatment of thermally driven flows. The solution to two such problems is presented and compared with corresponding results obtained by traditional methods.
Uniform convergence of multigrid v-cycle iterations for indefinite and nonsymmetric problems
Bramble, J.H. . Dept. of Mathematics); Kwak, D.Y. . Dept. of Mathematics); Pasciak, J.E. . Dept. of Applied Science)
1994-12-01
In this paper, an analysis of a multigrid method for nonsymmetric and/or indefinite elliptic problems is presented. In this multigrid method various types of smothers may be used. One type of smoother considered is defined in terms of an associated symmetric problem and includes point and line, Jacobi, and Gauss-Seidel iterations. Smothers based entirely on the original operator are also considered. One smoother is based on the normal form, that is, the product of the operator and its transpose. Other smothers studied include point and line, Jacobi, and Gauss-Seidel. It is shown that the uniform estimates for symmetric positive definite problems carry over to these algorithms. More precisely, the multigrid iteration for the nonsymmetric and/or indefinite problem is shown to converge at a uniform rate provided that the coarsest grid in the multilevel iteration is sufficiently fine (but not dependent on the number of multigrid levels).
Uniform convergence of multigrid V-cycle iterations for indefinite and nonsymmetric problems
NASA Technical Reports Server (NTRS)
Bramble, James H.; Kwak, Do Y.; Pasciak, Joseph E.
1993-01-01
In this paper, we present an analysis of a multigrid method for nonsymmetric and/or indefinite elliptic problems. In this multigrid method various types of smoothers may be used. One type of smoother which we consider is defined in terms of an associated symmetric problem and includes point and line, Jacobi, and Gauss-Seidel iterations. We also study smoothers based entirely on the original operator. One is based on the normal form, that is, the product of the operator and its transpose. Other smoothers studied include point and line, Jacobi, and Gauss-Seidel. We show that the uniform estimates for symmetric positive definite problems carry over to these algorithms. More precisely, the multigrid iteration for the nonsymmetric and/or indefinite problem is shown to converge at a uniform rate provided that the coarsest grid in the multilevel iteration is sufficiently fine (but not depending on the number of multigrid levels).
Annaratone, B. M.; Arnas, C.; Elskens, Y.
2008-09-07
The agglomeration of the matter in plasma, from the atomic level up to millimetre size particles, is here considered. In general we identify a continuous growth, due to deposition, and two agglomeration steps, the first at the level of tens of nanometres and the second above the micron. The agglomeration of nano-particles is attributed to electrostatic forces in presence of charge polarity fluctuations. Here we present a model based on discrete currents. With increasing grain size the positive charge permanence decreases, tending to zero. This effect is only important in the range of nanometre for dust of highly dispersed size. When the inter-particle distance is of the order of the screening length another agglomeration mechanism dominates. It is based on attractive forces, shadow forces or dipole-dipole interaction, overcoming the electrostatic repulsion. In bright plasma radiation pressure also plays a role.
Adaptive Multigrid Solution of Stokes' Equation on CELL Processor
NASA Astrophysics Data System (ADS)
Elgersma, M. R.; Yuen, D. A.; Pratt, S. G.
2006-12-01
We are developing an adaptive multigrid solver for treating nonlinear elliptic partial-differential equations, needed for mantle convection problems. Since multigrid is being used for the complete solution, not just as a preconditioner, spatial difference operators are kept nearly diagonally dominant by increasing density of the coarsest grid in regions where coefficients have rapid spatial variation. At each time step, the unstructured coarse grid is refined in regions where coefficients associated with the differential operators or boundary conditions have rapid spatial variation, and coarsened in regions where there is more gradual spatial variation. For three-dimensional problems, the boundary is two-dimensional, and regions where coefficients change rapidly are often near two-dimensional surfaces, so the coarsest grid is only fine near two-dimensional subsets of the three-dimensional space. Coarse grid density drops off exponentially with distance from boundary surfaces and rapid-coefficient-change surfaces. This unstructured coarse grid results in the number of coarse grid voxels growing proportional to surface area, rather than proportional to volume. This results in significant computational savings for the coarse-grid solution. This coarse-grid solution is then refined for the fine-grid solution, and multigrid methods have memory usage and runtime proportional to the number of fine-grid voxels. This adaptive multigrid algorithm is being implemented on the CELL processor, where each chip has eight floating point processors and each processor operates on four floating point numbers each clock cycle. Both the adaptive grid algorithm and the multigrid solver have very efficient parallel implementations, in order to take advantage of the CELL processor architecture.
Electrostatic formation of liquid marbles and agglomerates
NASA Astrophysics Data System (ADS)
Liyanaarachchi, K. R.; Ireland, P. M.; Webber, G. B.; Galvin, K. P.
2013-07-01
We report observations of a sudden, explosive release of electrostatically charged 100 μm glass beads from a particle bed. These cross an air gap of several millimeters, are engulfed by an approaching pendant water drop, and form a metastable spherical agglomerate on the bed surface. The stability transition of the particle bed is explained by promotion of internal friction by in-plane electrostatic stresses. The novel agglomerates formed this way resemble the "liquid marbles" formed by coating a drop with hydrophobic particles. Complex multi-layered agglomerates may also be produced by this method, with potential industrial, pharmaceutical, environmental, and biological applications.
Three-Dimensional High-Lift Analysis Using a Parallel Unstructured Multigrid Solver
NASA Technical Reports Server (NTRS)
Mavriplis, Dimitri J.
1998-01-01
A directional implicit unstructured agglomeration multigrid solver is ported to shared and distributed memory massively parallel machines using the explicit domain-decomposition and message-passing approach. Because the algorithm operates on local implicit lines in the unstructured mesh, special care is required in partitioning the problem for parallel computing. A weighted partitioning strategy is described which avoids breaking the implicit lines across processor boundaries, while incurring minimal additional communication overhead. Good scalability is demonstrated on a 128 processor SGI Origin 2000 machine and on a 512 processor CRAY T3E machine for reasonably fine grids. The feasibility of performing large-scale unstructured grid calculations with the parallel multigrid algorithm is demonstrated by computing the flow over a partial-span flap wing high-lift geometry on a highly resolved grid of 13.5 million points in approximately 4 hours of wall clock time on the CRAY T3E.
Successfully use agglomeration for size enlargement
Pietsch, W.
1996-04-01
The processing of fine and ultrafine particles by size enlargement finds an ever increasing application. At the same time, undesirable agglomeration such as buildup, caking, bridging, and uncontrolled aggregation of fine particles can occur during processing and handling of these particulate solids. This article will provide a survey of the phenomena of agglomeration and discuss the unit operation of size enlargement by agglomeration. This article is also an invitation, particularly to young engineers, to become interested in agglomeration. Considering that mechanical process technologies are requiring more energy every year than any other group of consumers and efficiencies are typically in the single digits or teens at best, considerable rewards can be expected from the development of scientifically modified, more energy-efficient methods and equipment.
Segmented Domain Decomposition Multigrid For 3-D Turbomachinery Flows
NASA Technical Reports Server (NTRS)
Celestina, M. L.; Adamczyk, J. J.; Rubin, S. G.
2001-01-01
A Segmented Domain Decomposition Multigrid (SDDMG) procedure was developed for three-dimensional viscous flow problems as they apply to turbomachinery flows. The procedure divides the computational domain into a coarse mesh comprised of uniformly spaced cells. To resolve smaller length scales such as the viscous layer near a surface, segments of the coarse mesh are subdivided into a finer mesh. This is repeated until adequate resolution of the smallest relevant length scale is obtained. Multigrid is used to communicate information between the different grid levels. To test the procedure, simulation results will be presented for a compressor and turbine cascade. These simulations are intended to show the ability of the present method to generate grid independent solutions. Comparisons with data will also be presented. These comparisons will further demonstrate the usefulness of the present work for they allow an estimate of the accuracy of the flow modeling equations independent of error attributed to numerical discretization.
Reducing Communication in Algebraic Multigrid Using Additive Variants
Vassilevski, Panayot S.; Yang, Ulrike Meier
2014-02-12
Algebraic multigrid (AMG) has proven to be an effective scalable solver on many high performance computers. However, its increasing communication complexity on coarser levels has shown to seriously impact its performance on computers with high communication cost. Moreover, additive AMG variants provide not only increased parallelism as well as decreased numbers of messages per cycle but also generally exhibit slower convergence. Here we present various new additive variants with convergence rates that are significantly improved compared to the classical additive algebraic multigrid method and investigate their potential for decreased communication, and improved communication-computation overlap, features that are essential for goodmore » performance on future exascale architectures.« less
Multigrid applied to implicit well problems
Dendy, J.E. Jr.; Tchelepi, Hamdi
1996-10-01
This paper discusses the application of multigrid techniques to the solution of implicit well equations, which arise in the numerical simulation of oil reservoirs. The emphasis is on techniques which can exploit parallel computation.
Rapid determination of plasmonic nanoparticle agglomeration status in blood.
Jenkins, Samir V; Qu, Haiou; Mudalige, Thilak; Ingle, Taylor M; Wang, Rongrong; Wang, Feng; Howard, Paul C; Chen, Jingyi; Zhang, Yongbin
2015-05-01
Plasmonic nanomaterials as drug delivery or bio-imaging agents are typically introduced to biological systems through intravenous administration. However, the potential for agglomeration of nanoparticles in biological systems could dramatically affect their pharmacokinetic profile and toxic potential. Development of rapid screening methods to evaluate agglomeration is urgently needed to monitor the physical nature of nanoparticles as they are introduced into blood. Here, we establish novel methods using darkfield microscopy with hyperspectral detection (hsDFM), single particle inductively-coupled plasma mass spectrometry (spICP-MS), and confocal Raman microscopy (cRM) to discriminate gold nanoparticles (AuNPs) and their agglomerates in blood. Rich information about nanoparticle agglomeration in situ is provided by hsDFM monitoring of the plasmon resonance of primary nanoparticles and their agglomerates in whole blood; cRM is an effective complement to hsDFM to detect AuNP agglomerates in minimally manipulated samples. The AuNPs and the particle agglomerates were further distinguished in blood for the first time by quantification of particle mass using spICP-MS with excellent sensitivity and specificity. Furthermore, the agglomeration status of synthesized and commercial NPs incubated in blood was successfully assessed using the developed methods. Together, these complementary methods enable rapid determination of the agglomeration status of plasmonic nanomaterials in biological systems, specifically blood.
Rapid determination of plasmonic nanoparticle agglomeration status in blood.
Jenkins, Samir V; Qu, Haiou; Mudalige, Thilak; Ingle, Taylor M; Wang, Rongrong; Wang, Feng; Howard, Paul C; Chen, Jingyi; Zhang, Yongbin
2015-05-01
Plasmonic nanomaterials as drug delivery or bio-imaging agents are typically introduced to biological systems through intravenous administration. However, the potential for agglomeration of nanoparticles in biological systems could dramatically affect their pharmacokinetic profile and toxic potential. Development of rapid screening methods to evaluate agglomeration is urgently needed to monitor the physical nature of nanoparticles as they are introduced into blood. Here, we establish novel methods using darkfield microscopy with hyperspectral detection (hsDFM), single particle inductively-coupled plasma mass spectrometry (spICP-MS), and confocal Raman microscopy (cRM) to discriminate gold nanoparticles (AuNPs) and their agglomerates in blood. Rich information about nanoparticle agglomeration in situ is provided by hsDFM monitoring of the plasmon resonance of primary nanoparticles and their agglomerates in whole blood; cRM is an effective complement to hsDFM to detect AuNP agglomerates in minimally manipulated samples. The AuNPs and the particle agglomerates were further distinguished in blood for the first time by quantification of particle mass using spICP-MS with excellent sensitivity and specificity. Furthermore, the agglomeration status of synthesized and commercial NPs incubated in blood was successfully assessed using the developed methods. Together, these complementary methods enable rapid determination of the agglomeration status of plasmonic nanomaterials in biological systems, specifically blood. PMID:25771013
Rapid Determination of Plasmonic Nanoparticle Agglomeration Status in Blood
Jenkins, Samir V.; Qu, Haiou; Mudalige, Thilak; Ingle, Taylor; Wang, RongRong; Wang, Feng; Howard, Paul C.; Chen, Jingyi; Zhang, Yongbin
2015-01-01
Plasmonic nanomaterials as drug delivery or bio-imaging agents are typically introduced to biological systems through intravenous administration. However, the potential for agglomeration of nanoparticles in biological systems could dramatically affect their pharmacokinetic profile and toxic potential. Development of rapid screening methods to evaluate agglomeration is urgently needed to monitor the physical nature of nanoparticles as they are introduced into blood. Here, we establish novel methods using darkfield microscopy with hyperspectral detection (hsDFM), single particle inductively-coupled plasma mass spectrometry (spICP-MS), and confocal Raman microscopy (cRM) to discriminate gold nanoparticles (AuNPs) and their agglomerates in blood. Rich information about nanoparticle agglomeration in situ is provided by hsDFM monitoring of the plasmon resonance of primary nanoparticles and their agglomerates in whole blood; cRM is an effective complement to hsDFM to detect AuNP agglomerates in minimally manipulated samples. The AuNPs and the particle agglomerates were further distinguished in blood for the first time by quantification of particle mass using spICP-MS with excellent sensitivity and specificity. Furthermore, the agglomeration status of synthesized and commercial NPs incubated in blood was successfully assessed using the developed methods. Together, these complementary methods enable rapid determination of the agglomeration status of plasmonic nanomaterials in biological systems, specifically blood. PMID:25771013
Analysis and synthesis of solutions for the agglomeration process modeling
NASA Astrophysics Data System (ADS)
Babuk, V. A.; Dolotkazin, I. N.; Nizyaev, A. A.
2013-03-01
The present work is devoted development of model of agglomerating process for propellants based on ammonium perchlorate (AP), ammonium dinitramide (ADN), HMX, inactive binder, and nanoaluminum. Generalization of experimental data, development of physical picture of agglomeration for listed propellants, development and analysis of mathematical models are carried out. Synthesis of models of various phenomena taking place at agglomeration implementation allows predicting of size and quantity, chemical composition, structure of forming agglomerates and its fraction in set of condensed combustion products. It became possible in many respects due to development of new model of agglomerating particle evolution on the surface of burning propellant. Obtained results correspond to available experimental data. It is supposed that analogical method based on analysis of mathematical models of particular phenomena and their synthesis will allow implementing of the agglomerating process modeling for other types of metalized solid propellants.
A multigrid based computational procedure to predict internal flows with heat transfer
Kiris, I.; Parameswaran, S.; Carroll, G.
1995-12-31
In this study, a formally third-order, finite volume, unstaggered (co-located), modified SIMPLE algorithm-based 2D code was created utilizing multigrid for fast convergence. Stone`s Strongly Implicit Procedure (SIP) is employed as a relaxation (smoother, matrix eq. solver) method, due to its high performance. The quadratic formulations QUICK, mixed and UTOPIA were used to discretize the convective terms in momentum equations. Velocity and pressure coupling was addressed via modified SIMPLE algorithm. Due to the co-located nature of method, the cell fact velocities are obtained via the so called momentum balancing technique introduced before. The Multigrid idea is implemented to the solution of pressure correction equation. Various ways of implementing Multigrid algorithms are discussed. An ASME benchmark case (backward facing step with heat transfer) is chosen as the problem. The so called accommodative FAS-FMG was used. Predictions show that high order convective term discretization improves the predictions, while multigrid enables about an order of magnitude CPU time savings. Results point out that the promises of both high order discretization and multigrid can be harvested for recirculating flows.
Mechanics and charging of nanoparticle agglomerates
NASA Astrophysics Data System (ADS)
Shin, Weon Gyu
This thesis consists of two parts. The first part concerns studies on mechanics of real agglomerate particles and the second part involves studies on unipolar diffusion charging of agglomerates. Understanding mechanics of real agglomerate particles consisting of multiple primary particles is important for aerosol sizing instrumentation using electrical mobility and nanoparticle manufacturing process where coagulation and sedimentation occur. A key quantity determining transport properties of agglomerates is the friction coefficient. However, quantitative studies for the friction coefficient of agglomerates are very limited. Transmission Electron Microscopy (TEM) image analysis results of silver agglomerates provides a basis for the comparison of experimental data with estimates based on free molecular models. A new quantitative method to determine the dynamic shape factor and the two exponents, eta and Dfm, which characterize the power law dependence of friction coefficient on the number of primary spheres and the mass on the mobility diameter, was developed using Differential Mobility Analyzer (DMA)-Aerosol Particle Mass (APM) analyzer. Model predictions indicate that eta is independent of agglomerate size while Dfm is sensitive to agglomerate size. Experimentally, it appears the opposite is true. Tandem DMA (TDMA) results also show that the mass-mobility diameter scaling exponent is not dependent on mobility size range. Estimates of non-ideal effects on the agglomerate dynamics were computed as perturbations to the Chan-Dahneke agglomerate model. After the corrections, an agreement between experimental data and model predictions becomes significantly improved. Unipolar diffusion charging becomes more attractive because it has higher charging efficiency than bipolar charging as well as important applications in aerosol sizing instrumentation using electrical mobility, powder coating, and the removal of toxic particles from air stream using Electrostatic
Comparative Convergence Analysis of Nonlinear AMLI-Cycle Multigrid
Hu, Xiaozhe; Vassilevski, Panayot S.; Xu, Jinchao
2013-04-30
The purpose of our paper is to provide a comprehensive convergence analysis of the nonlinear algebraic multilevel iteration (AMLI)-cycle multigrid (MG) method for symmetric positive definite problems. We show that the nonlinear AMLI-cycle MG method is uniformly convergent, based on classical assumptions for approximation and smoothing properties. Furthermore, under only the assumption that the smoother is convergent, we show that the nonlinear AMLI-cycle method is always better (or not worse) than the respective V-cycle MG method. Finally, numerical experiments are presented to illustrate the theoretical results.
Multigrid solution of the Navier-Stokes equations on highly stretched grids with defect correction
NASA Technical Reports Server (NTRS)
Sockol, Peter M.
1993-01-01
Relaxation-based multigrid solvers for the steady incompressible Navier-Stokes equations are examined to determine their computational speed and robustness. Four relaxation methods with a common discretization have been used as smoothers in a single tailored multigrid procedure. The equations are discretized on a staggered grid with first order upwind used for convection in the relaxation process on all grids and defect correction to second order central on the fine grid introduced once per multigrid cycle. A fixed W(1,1) cycle with full weighting of residuals is used in the FAS multigrid process. The resulting solvers have been applied to three 2D flow problems, over a range of Reynolds numbers, on both uniform and highly stretched grids. In all cases the L(sub 2) norm of the velocity changes is reduced to 10(exp -6) in a few 10's of fine grid sweeps. The results from this study are used to draw conclusions on the strengths and weaknesses of the individual relaxation schemes as well as those of the overall multigrid procedure when used as a solver on highly stretched grids.
Implementation and Optimization of miniGMG - a Compact Geometric Multigrid Benchmark
Williams, Samuel; Kalamkar, Dhiraj; Singh, Amik; Deshpande, Anand M.; Straalen, Brian Van; Smelyanskiy, Mikhail; Almgren, Ann; Dubey, Pradeep; Shalf, John; Oliker, Leonid
2012-12-01
Multigrid methods are widely used to accelerate the convergence of iterative solvers for linear systems used in a number of different application areas. In this report, we describe miniGMG, our compact geometric multigrid benchmark designed to proxy the multigrid solves found in AMR applications. We explore optimization techniques for geometric multigrid on existing and emerging multicore systems including the Opteron-based Cray XE6, Intel Sandy Bridge and Nehalem-based Infiniband clusters, as well as manycore-based architectures including NVIDIA's Fermi and Kepler GPUs and Intel's Knights Corner (KNC) co-processor. This report examines a variety of novel techniques including communication-aggregation, threaded wavefront-based DRAM communication-avoiding, dynamic threading decisions, SIMDization, and fusion of operators. We quantify performance through each phase of the V-cycle for both single-node and distributed-memory experiments and provide detailed analysis for each class of optimization. Results show our optimizations yield significant speedups across a variety of subdomain sizes while simultaneously demonstrating the potential of multi- and manycore processors to dramatically accelerate single-node performance. However, our analysis also indicates that improvements in networks and communication will be essential to reap the potential of manycore processors in large-scale multigrid calculations.
Multigrid-based 'shifted-Laplacian' preconditioning for the time-harmonic elastic wave equation
NASA Astrophysics Data System (ADS)
Rizzuti, G.; Mulder, W. A.
2016-07-01
We investigate the numerical performance of an iterative solver for a frequency-domain finite-difference discretization of the isotropic elastic wave equation. The solver is based on the 'shifted-Laplacian' preconditioner, originally designed for the acoustic wave equation. This preconditioner represents a discretization of a heavily damped wave equation and can be efficiently inverted by a multigrid iteration. However, the application of multigrid to the elastic case is not straightforward because standard methods, such as point-Jacobi, fail to smooth the S-wave wavenumber components of the error when high P-to-S velocity ratios are present. We consider line smoothers as an alternative and apply local-mode analysis to evaluate the performance of the various components of the multigrid preconditioner. Numerical examples in 2-D demonstrate the efficacy of our method.
Adaptive Algebraic Multigrid for Finite Element Elliptic Equations with Random Coefficients
Kalchev, D
2012-04-02
This thesis presents a two-grid algorithm based on Smoothed Aggregation Spectral Element Agglomeration Algebraic Multigrid (SA-{rho}AMGe) combined with adaptation. The aim is to build an efficient solver for the linear systems arising from discretization of second-order elliptic partial differential equations (PDEs) with stochastic coefficients. Examples include PDEs that model subsurface flow with random permeability field. During a Markov Chain Monte Carlo (MCMC) simulation process, that draws PDE coefficient samples from a certain distribution, the PDE coefficients change, hence the resulting linear systems to be solved change. At every such step the system (discretized PDE) needs to be solved and the computed solution used to evaluate some functional(s) of interest that then determine if the coefficient sample is acceptable or not. The MCMC process is hence computationally intensive and requires the solvers used to be efficient and fast. This fact that at every step of MCMC the resulting linear system changes, makes an already existing solver built for the old problem perhaps not as efficient for the problem corresponding to the new sampled coefficient. This motivates the main goal of our study, namely, to adapt an already existing solver to handle the problem (with changed coefficient) with the objective to achieve this goal to be faster and more efficient than building a completely new solver from scratch. Our approach utilizes the local element matrices (for the problem with changed coefficients) to build local problems associated with constructed by the method agglomerated elements (a set of subdomains that cover the given computational domain). We solve a generalized eigenproblem for each set in a subspace spanned by the previous local coarse space (used for the old solver) and a vector, component of the error, that the old solver cannot handle. A portion of the spectrum of these local eigen-problems (corresponding to eigenvalues close to zero) form the
Eigensystem analysis of classical relaxation techniques with applications to multigrid analysis
NASA Technical Reports Server (NTRS)
Lomax, Harvard; Maksymiuk, Catherine
1987-01-01
Classical relaxation techniques are related to numerical methods for solution of ordinary differential equations. Eigensystems for Point-Jacobi, Gauss-Seidel, and SOR methods are presented. Solution techniques such as eigenvector annihilation, eigensystem mixing, and multigrid methods are examined with regard to the eigenstructure.
Multigrid on unstructured grids using an auxiliary set of structured grids
Douglas, C.C.; Malhotra, S.; Schultz, M.H.
1996-12-31
Unstructured grids do not have a convenient and natural multigrid framework for actually computing and maintaining a high floating point rate on standard computers. In fact, just the coarsening process is expensive for many applications. Since unstructured grids play a vital role in many scientific computing applications, many modifications have been proposed to solve this problem. One suggested solution is to map the original unstructured grid onto a structured grid. This can be used as a fine grid in a standard multigrid algorithm to precondition the original problem on the unstructured grid. We show that unless extreme care is taken, this mapping can lead to a system with a high condition number which eliminates the usefulness of the multigrid method. Theorems with lower and upper bounds are provided. Simple examples show that the upper bounds are sharp.
Garala, Kevin; Patel, Jaydeep; Patel, Anjali; Raval, Mihir; Dharamsi, Abhay
2012-01-01
Purpose: The purpose of the present investigation was to improve the flow and mechanical properties of racecadotril by a crystallo-co-agglomeration (CCA) technique. Direct tableting is a requirement of pharmaceutical industries. Poor mechanical properties of crystalline drug particles require wet granulation which is uneconomical, laborious, and tedious. Materials and Methods: The objective of this work was to study the influence of various polymers/excipients and processing conditions on the formation of directly compressible agglomerates of the water-insoluble drug, racecadotril, an antidiarrheal agent. The agglomerates of racecadotril were prepared using dichloromethane (DCM)–water as the crystallization system. DCM acted as a good solvent for racecadotril as well as a bridging liquid for the agglomeration of the crystallized drug and water as the nonsolvent. The prepared agglomerates were tested for micromeritic and mechanical properties. Results: The process yielded ~90 to 96% wt/ wt spherical agglomerates containing racecadotril with the diameter between 299 and 521 μ. A higher rotational speed of crystallization system reduces the size of the agglomerates and disturbs the sphericity. Spherical agglomerates were generated with a uniform dispersion of the crystallized drug. CCA showed excellent flowability and crushing strength. Conclusion: Excipients and processing conditions can play a key role in preparing spherical agglomerates of racecadotril by CCA, an excellent alternative to the wet granulation process to prepare intermediates for direct compression. PMID:23580935
Multigrid Approach to Incompressible Viscous Cavity Flows
NASA Technical Reports Server (NTRS)
Wood, William A.
1996-01-01
Two-dimensional incompressible viscous driven-cavity flows are computed for Reynolds numbers on the range 100-20,000 using a loosely coupled, implicit, second-order centrally-different scheme. Mesh sequencing and three-level V-cycle multigrid error smoothing are incorporated into the symmetric Gauss-Seidel time-integration algorithm. Parametrics on the numerical parameters are performed, achieving reductions in solution times by more than 60 percent with the full multigrid approach. Details of the circulation patterns are investigated in cavities of 2-to-1, 1-to-1, and 1-to-2 depth to width ratios.
Highly indefinite multigrid for eigenvalue problems
Borges, L.; Oliveira, S.
1996-12-31
Eigenvalue problems are extremely important in understanding dynamic processes such as vibrations and control systems. Large scale eigenvalue problems can be very difficult to solve, especially if a large number of eigenvalues and the corresponding eigenvectors need to be computed. For solving this problem a multigrid preconditioned algorithm is presented in {open_quotes}The Davidson Algorithm, preconditioning and misconvergence{close_quotes}. Another approach for solving eigenvalue problems is by developing efficient solutions for highly indefinite problems. In this paper we concentrate on the use of new highly indefinite multigrid algorithms for the eigenvalue problem.
A multigrid LU-SSOR scheme for approximate Newton iteration applied to the Euler equations
NASA Technical Reports Server (NTRS)
Yoon, Seokkwan; Jameson, Antony
1986-01-01
A new efficient relaxation scheme in conjunction with a multigrid method is developed for the Euler equations. The LU SSOR scheme is based on a central difference scheme and does not need flux splitting for Newton iteration. Application to transonic flow shows that the new method surpasses the performance of the LU implicit scheme.
An improved convergence analysis of smoothed aggregation algebraic multigrid
Brezina, Marian; Vaněk, Petr; Vassilevski, Panayot S.
2011-03-02
We present an improved analysis of the smoothed aggregation (SA) alge- braic multigrid method (AMG) extending the original proof in [SA] and its modification in [Va08]. The new result imposes fewer restrictions on the aggregates that makes it eas- ier to verify in practice. Also, we extend a result in [Van] that allows us to use aggressive coarsening at all levels due to the special properties of the polynomial smoother, that we use and analyze, and thus provide a multilevel convergence estimate with bounds independent of the coarsening ratio.
Coagulation of Agglomerates Consisting of Polydisperse Primary Particles.
Goudeli, E; Eggersdorfer, M L; Pratsinis, S E
2016-09-13
The ballistic agglomeration of polydisperse particles is investigated by an event-driven (ED) method and compared to the coagulation of spherical particles and agglomerates consisting of monodisperse primary particles (PPs). It is shown for the first time to our knowledge that increasing the width or polydispersity of the PP size distribution initially accelerates the coagulation rate of their agglomerates but delays the attainment of their asymptotic fractal-like structure and self-preserving size distribution (SPSD) without altering them, provided that sufficiently large numbers of PPs are employed. For example, the standard asymptotic mass fractal dimension, Df, of 1.91 is attained when clusters are formed containing, on average, about 15 monodisperse PPs, consistent with fractal theory and the literature. In contrast, when polydisperse PPs with a geometric standard deviation of 3 are employed, about 500 PPs are needed to attain that Df. Even though the same asymptotic Df and mass-mobility exponent, Dfm, are attained regardless of PP polydispersity, the asymptotic prefactors or lacunarities of Df and Dfm increase with PP polydispersity. For monodisperse PPs, the average agglomerate radius of gyration, rg, becomes larger than the mobility radius, rm, when agglomerates consist of more than 15 PPs. Increasing PP polydispersity increases that number of PPs similarly to the above for the attainment of the asymptotic Df or Dfm. The agglomeration kinetics are quantified by the overall collision frequency function. When the SPSD is attained, the collision frequency is independent of PP polydispersity. Accounting for the SPSD polydispersity in the overall agglomerate collision frequency is in good agreement with that frequency from detailed ED simulations once the SPSD is reached. Most importantly, the coagulation of agglomerates is described well by a monodisperse model for agglomerate and PP sizes, whereas the detailed agglomerate size distribution can be obtained by
Textbook Multigrid Efficiency for Leading Edge Stagnation
NASA Technical Reports Server (NTRS)
Diskin, Boris; Thomas, James L.; Mineck, Raymond E.
2004-01-01
A multigrid solver is defined as having textbook multigrid efficiency (TME) if the solutions to the governing system of equations are attained in a computational work which is a small (less than 10) multiple of the operation count in evaluating the discrete residuals. TME in solving the incompressible inviscid fluid equations is demonstrated for leading- edge stagnation flows. The contributions of this paper include (1) a special formulation of the boundary conditions near stagnation allowing convergence of the Newton iterations on coarse grids, (2) the boundary relaxation technique to facilitate relaxation and residual restriction near the boundaries, (3) a modified relaxation scheme to prevent initial error amplification, and (4) new general analysis techniques for multigrid solvers. Convergence of algebraic errors below the level of discretization errors is attained by a full multigrid (FMG) solver with one full approximation scheme (F.4S) cycle per grid. Asymptotic convergence rates of the F.4S cycles for the full system of flow equations are very fast, approaching those for scalar elliptic equations.
Textbook Multigrid Efficiency for Leading Edge Stagnation
NASA Technical Reports Server (NTRS)
Diskin, Boris; Thomas, James L.; Mineck, Raymond E.
2004-01-01
A multigrid solver is defined as having textbook multigrid efficiency (TME) if the solutions to the governing system of equations are attained in a computational work which is a small (less than 10) multiple of the operation count in evaluating the discrete residuals. TME in solving the incompressible inviscid fluid equations is demonstrated for leading-edge stagnation flows. The contributions of this paper include (1) a special formulation of the boundary conditions near stagnation allowing convergence of the Newton iterations on coarse grids, (2) the boundary relaxation technique to facilitate relaxation and residual restriction near the boundaries, (3) a modified relaxation scheme to prevent initial error amplification, and (4) new general analysis techniques for multigrid solvers. Convergence of algebraic errors below the level of discretization errors is attained by a full multigrid (FMG) solver with one full approximation scheme (FAS) cycle per grid. Asymptotic convergence rates of the FAS cycles for the full system of flow equations are very fast, approaching those for scalar elliptic equations.
Parallel Algebraic Multigrids for Structural mechanics
Brezina, M; Tong, C; Becker, R
2004-05-11
This paper presents the results of a comparison of three parallel algebraic multigrid (AMG) preconditioners for structural mechanics applications. In particular, they are interested in investigating both the scalability and robustness of the preconditioners. Numerical results are given for a range of structural mechanics problems with various degrees of difficulty.
Robust Multigrid Smoothers for Three Dimensional Elliptic Equations with Strong Anisotropies
NASA Technical Reports Server (NTRS)
Llorente, Ignacio M.; Melson, N. Duane
1998-01-01
We discuss the behavior of several plane relaxation methods as multigrid smoothers for the solution of a discrete anisotropic elliptic model problem on cell-centered grids. The methods compared are plane Jacobi with damping, plane Jacobi with partial damping, plane Gauss-Seidel, plane zebra Gauss-Seidel, and line Gauss-Seidel. Based on numerical experiments and local mode analysis, we compare the smoothing factor of the different methods in the presence of strong anisotropies. A four-color Gauss-Seidel method is found to have the best numerical and architectural properties of the methods considered in the present work. Although alternating direction plane relaxation schemes are simpler and more robust than other approaches, they are not currently used in industrial and production codes because they require the solution of a two-dimensional problem for each plane in each direction. We verify the theoretical predictions of Thole and Trottenberg that an exact solution of each plane is not necessary and that a single two-dimensional multigrid cycle gives the same result as an exact solution, in much less execution time. Parallelization of the two-dimensional multigrid cycles, the kernel of the three-dimensional implicit solver, is also discussed. Alternating-plane smoothers are found to be highly efficient multigrid smoothers for anisotropic elliptic problems.
An efficient non-linear multigrid procedure for the incompressible Navier-Stokes equations
NASA Astrophysics Data System (ADS)
Sivaloganathan, S.; Shaw, G. J.
An efficient Full Approximation multigrid scheme for finite volume discretizations of the Navier-Stokes equations is presented. The algorithm is applied to the driven cavity test problem. Numerical results are presented and a comparison made with PACE, a Rolls-Royce industrial code, which uses the SIMPLE pressure correction method as an iterative solver.
A fast multigrid algorithm for energy minimization under planar density constraints.
Ron, D.; Safro, I.; Brandt, A.; Mathematics and Computer Science; Weizmann Inst. of Science
2010-09-07
The two-dimensional layout optimization problem reinforced by the efficient space utilization demand has a wide spectrum of practical applications. Formulating the problem as a nonlinear minimization problem under planar equality and/or inequality density constraints, we present a linear time multigrid algorithm for solving a correction to this problem. The method is demonstrated in various graph drawing (visualization) instances.
Particle Agglomeration in Bipolar Barb Agglomerator Under AC Electric Field
NASA Astrophysics Data System (ADS)
Huang, Chao; Ma, Xiuqin; Sun, Youshan; Wang, Meiyan; Zhang, Changping; Lou, Yueya
2015-04-01
The development of an efficient technology for removing fine particles in flue gas is essential as the haze is becoming more and more serious. To improve agglomeration effectiveness of fine particles, a dual zone electric agglomeration device consisting of a charging chamber and an agglomeration chamber with bipolar barb electrodes was developed. The bipolar barb electric agglomerator with a polar distance of 200 mm demonstrates good agglomeration effectiveness for particles with a size less than 8.0 μm under applied AC electric field. An optimal condition for achieving better agglomeration effectiveness was found to be as follows: flue gas flow velocity of 3.00 m/s, particle concentration of 2.00 g/m3, output voltage of 35 kV and length of the barb of 16 mm. In addition, 4.0-6.0 μm particles have the best effectiveness with the variation of particle volume occupancy of -3.2. supported by the Key Technology R&D Program of Hebei, China (No. 13211207D)
A Cell-Centered Multigrid Algorithm for All Grid Sizes
NASA Technical Reports Server (NTRS)
Gjesdal, Thor
1996-01-01
Multigrid methods are optimal; that is, their rate of convergence is independent of the number of grid points, because they use a nested sequence of coarse grids to represent different scales of the solution. This nesting does, however, usually lead to certain restrictions of the permissible size of the discretised problem. In cases where the modeler is free to specify the whole problem, such constraints are of little importance because they can be taken into consideration from the outset. We consider the situation in which there are other competing constraints on the resolution. These restrictions may stem from the physical problem (e.g., if the discretised operator contains experimental data measured on a fixed grid) or from the need to avoid limitations set by the hardware. In this paper we discuss a modification to the cell-centered multigrid algorithm, so that it can be used br problems with any resolution. We discuss in particular a coarsening strategy and choice of intergrid transfer operators that can handle grids with both an even or odd number of cells. The method is described and applied to linear equations obtained by discretization of two- and three-dimensional second-order elliptic PDEs.
Agglomeration and Sedimentation of MWCNTS in Chloroform
NASA Astrophysics Data System (ADS)
Eremin, Yu. S.; Kolesnikova, A. A.; Grekhov, A. M.
The kinetics of agglomeration of multiwalled carbon nanotubes dispersed in chloroform has been studied by the methods of optical spectroscopy and dynamic light scattering. With the use of the models of the diffusion of cylindrical particles, the sizes of particles obtained by this method can be recalculated to the DLS data and the concentration at which the dispersion of individual МWCNTs occurs can be determined.
Multigrid calculations of 3-D turbulent viscous flows
NASA Technical Reports Server (NTRS)
Yokota, Jeffrey W.
1989-01-01
Convergence properties of a multigrid algorithm, developed to calculate compressible viscous flows, are analyzed by a vector sequence eigenvalue estimate. The full 3-D Reynolds-averaged Navier-Stokes equations are integrated by an implicit multigrid scheme while a k-epsilon turbulence model is solved, uncoupled from the flow equations. Estimates of the eigenvalue structure for both single and multigrid calculations are compared in an attempt to analyze the process as well as the results of the multigrid technique. The flow through an annular turbine is used to illustrate the scheme's ability to calculate complex 3-D flows.
MTCI acoustic agglomeration particulate control
Chandran, R.R.; Mansour, M.N.; Scaroni, A.W.; Koopmann, G.H.; Loth, J.L.
1994-10-01
The overall objective of this project is to demonstrate pulse combination induced acoustic enhancement of coal ash agglomeration and sulfur capture at conditions typical of direct coal-fired turbines and PFBC hot gas cleanup. MTCI has developed an advanced compact pulse combustor island for direct coal-firing in combustion gas turbines. This combustor island comprises a coal-fired pulse combustor, a combined ash agglomeration and sulfur capture chamber (CAASCC), and a hot cyclone. In the MTCI proprietary approach, the pulse combustion-induced high intensity sound waves improve sulfur capture efficiency and ash agglomeration. The resulting agglomerates allow the use of commercial cyclones and achieve very high particulate collection efficiency. In the MTCI proprietary approach, sorbent particles are injected into a gas stream subjected to an intense acoustic field. The acoustic field serves to improve sulfur capture efficiency by enhancing both gas film and intra-particle mass transfer rates. In addition, the sorbent particles act as dynamic filter foci, providing a high density of stagnant agglomerating centers for trapping the finer entrained (in the oscillating flow field) fly ash fractions. A team has been formed with MTCI as the prime contractor and Penn State University and West Virginia University as subcontractors to MTCI. MTCI is focusing on hardware development and system demonstration, PSU is investigating and modeling acoustic agglomeration and sulfur capture, and WVU is studying aerovalve fluid dynamics. Results are presented from all three studies.
Microbial effects on colloidal agglomeration
Hersman, L.
1995-11-01
Colloidal particles are known to enhance the transport of radioactive metals through soil and rock systems. This study was performed to determine if a soil microorganism, isolated from the surface samples collected at Yucca Mountain, NV, could affect the colloidal properties of day particles. The agglomeration of a Wyoming bentonite clay in a sterile uninoculated microbial growth medium was compared to the agglomeration in the medium inoculated with a Pseudomonas sp. In a second experiment, microorganisms were cultured in the succinate medium for 50 h and removed by centrifugation. The agglomeration of the clay in this spent was compared to sterile uninoculated medium. In both experiments, the agglomeration of the clay was greater than that of the sterile, uninoculated control. Based on these results, which indicate that this microorganism enhanced the agglomeration of the bentonite clay, it is possible to say that in the presence of microorganisms colloidal movement through a rock matrix could be reduced because of an overall increase in the size of colloidal particle agglomerates. 32 refs.
Multigrid MALDI mass spectrometry imaging (mMALDI MSI).
Urbanek, Annett; Hölzer, Stefan; Knop, Katrin; Schubert, Ulrich S; von Eggeling, Ferdinand
2016-05-01
Matrix-assisted laser desorption/ionization mass spectrometry imaging (MALDI MSI) is an important technique for the spatially resolved molecular analysis of tissue sections. The selection of matrices influences the resulting mass spectra to a high degree. For extensive and simultaneous analysis, the application of different matrices to one tissue sample is desirable. To date, only a single matrix could be applied to a tissue section per experiment. However, repetitive removal of the matrix makes this approach time-consuming and damaging to tissue samples. To overcome these drawbacks, we developed a multigrid MALDI MSI technique (mMALDI MSI) that relies on automated inkjet printing to place differing matrices onto predefined dot grids. We used a cooled printhead to prevent cavitation of low viscosity solvents in the printhead nozzle. Improved spatial resolution of the dot grids was achieved by using a triple-pulse procedure that reduced droplet volume. The matrices can either be applied directly to the thaw-mounted tissue sample or by precoating the slide followed by mounting of the tissue sample. During the MALDI imaging process, we were able to precisely target different matrix point grids with the laser to simultaneously produce distinct mass spectra. Unlike the standard method, the prespotting approach optimizes the spectra quality, avoids analyte delocalization, and enables subsequent hematoxylin and eosin (H&E) staining. Graphical Abstract Scheme of the pre-spotted multigrid MALDI MSI workflow. PMID:27039200
Lazarov, R; Pasciak, J; Jones, J
2002-02-01
Construction, analysis and numerical testing of efficient solution techniques for solving elliptic PDEs that allow for parallel implementation have been the focus of the research. A number of discretization and solution methods for solving second order elliptic problems that include mortar and penalty approximations and domain decomposition methods for finite elements and finite volumes have been investigated and analyzed. Techniques for parallel domain decomposition algorithms in the framework of PETC and HYPRE have been studied and tested. Hierarchical parallel grid refinement and adaptive solution methods have been implemented and tested on various model problems. A parallel code implementing the mortar method with algebraically constructed multiplier spaces was developed.
A unified multigrid solver for the Navier-Stokes equations on mixed element meshes
NASA Technical Reports Server (NTRS)
Mavriplis, D. J.; Venkatakrishnan, V.
1995-01-01
A unified multigrid solution technique is presented for solving the Euler and Reynolds-averaged Navier-Stokes equations on unstructured meshes using mixed elements consisting of triangles and quadrilaterals in two dimensions, and of hexahedra, pyramids, prisms, and tetrahedra in three dimensions. While the use of mixed elements is by no means a novel idea, the contribution of the paper lies in the formulation of a complete solution technique which can handle structured grids, block structured grids, and unstructured grids of tetrahedra or mixed elements without any modification. This is achieved by discretizing the full Navier-Stokes equations on tetrahedral elements, and the thin layer version of these equations on other types of elements, while using a single edge-based data-structure to construct the discretization over all element types. An agglomeration multigrid algorithm, which naturally handles meshes of any types of elements, is employed to accelerate convergence. An automatic algorithm which reduces the complexity of a given triangular or tetrahedral mesh by merging candidate triangular or tetrahedral elements into quadrilateral or prismatic elements is also described. The gains in computational efficiency afforded by the use of non-simplicial meshes over fully tetrahedral meshes are demonstrated through several examples.
Multigrid with red black SOR revisited
Yavneh, I.
1994-12-31
Optimal relaxation parameters are obtained for red-black point Gauss-Seidel relaxation in multigrid solvers of a family of elliptic equations. The resulting relaxation schemes are found to retain high efficiency over an appreciable range of coefficients of the elliptic operator, yielding simple, inexpensive and fully parallelizable smoothers in many situations where more complicated and less cost-effective block-relaxation and/or partial coarsening are commonly used.
Development of a multigrid transonic potential flow code for cascades
NASA Technical Reports Server (NTRS)
Steinhoff, John
1992-01-01
Finite-volume methods for discretizing transonic potential flow equations have proven to be very flexible and accurate for both two and three dimensional problems. Since they only use local properties of the mapping, they allow decoupling of the grid generation from the rest of the problem. A very effective method for solving the discretized equations and converging to a solution is the multigrid-ADI technique. It has been successfully applied to airfoil problems where O type, C type and slit mappings have been used. Convergence rates for these cases are more than an order of magnitude faster than with relaxation techniques. In this report, we describe a method to extend the above methods, with the C type mappings, to airfoil cascade problems.
Kalchev, D.; Ketelsen, C.; Vassilevski, P. S.
2013-11-07
Our paper proposes an adaptive strategy for reusing a previously constructed coarse space by algebraic multigrid to construct a two-level solver for a problem with nearby characteristics. Furthermore, a main target application is the solution of the linear problems that appear throughout a sequence of Markov chain Monte Carlo simulations of subsurface flow with uncertain permeability field. We demonstrate the efficacy of the method with extensive set of numerical experiments.
Encapsulation of hazardous wastes into agglomerates
Guloy, A.
1992-01-28
The objective of this study was to investigate the feasibility of using the cementitious properties and agglomeration characteristics of coal conversion byproducts to encapsulate and immobilize hazardous waste materials. The intention was to establish an economical way of co-utilization and co-disposal of wastes. In addition, it may aid in the eradication of air pollution problems associated with the fine-powdery nature of fly ash. Encapsulation into agglomerates is a novel approach of treating toxic waste. Although encapsulation itself is not a new concept, existing methods employ high-cost resins that render them economically unfeasible. In this investigation, the toxic waste was contained in a concrete-like matrix whereby fly ash and other cementitious waste materials were utilized. The method incorporates the principles of solidification, stabilization and agglomeration. Another aspect of the study is the evaluation of the agglomeration as possible lightweight aggregates. Since fly ash is commercially used as an aggregate, it would be interesting to study the effect of incorporating toxic wastes in the strength development of the granules. In the investigation, the fly ash self-cementation process was applied to electroplating sludges as the toxic waste. The process hoped to provide a basis for delisting of the waste as hazardous and, thereby greatly minimize the cost of its disposal. Owing to the stringent regulatory requirements for hauling and disposal of hazardous waste, the cost of disposal is significant. The current practice for disposal is solidifying the waste with portland cement and dumping the hardened material in the landfill where the cost varies between $700--950/ton. Partially replacing portland cement with fly ash in concrete has proven beneficial, therefore applying the same principles in the treatment of toxic waste looked very promising.
A geometric multigrid Poisson solver for domains containing solid inclusions
NASA Astrophysics Data System (ADS)
Botto, Lorenzo
2013-03-01
A Cartesian grid method for the fast solution of the Poisson equation in three-dimensional domains with embedded solid inclusions is presented and its performance analyzed. The efficiency of the method, which assume Neumann conditions at the immersed boundaries, is comparable to that of a multigrid method for regular domains. The method is light in terms of memory usage, and easily adaptable to parallel architectures. Tests with random and ordered arrays of solid inclusions, including spheres and ellipsoids, demonstrate smooth convergence of the residual for small separation between the inclusion surfaces. This feature is important, for instance, in simulations of nearly-touching finite-size particles. The implementation of the method, “MG-Inc”, is available online. Catalogue identifier: AEOE_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEOE_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 19068 No. of bytes in distributed program, including test data, etc.: 215118 Distribution format: tar.gz Programming language: C++ (fully tested with GNU GCC compiler). Computer: Any machine supporting standard C++ compiler. Operating system: Any OS supporting standard C++ compiler. RAM: About 150MB for 1283 resolution Classification: 4.3. Nature of problem: Poisson equation in domains containing inclusions; Neumann boundary conditions at immersed boundaries. Solution method: Geometric multigrid with finite-volume discretization. Restrictions: Stair-case representation of the immersed boundaries. Running time: Typically a fraction of a minute for 1283 resolution.
Air agglomeration of hydrophobic particles
Drzymala, J.; Wheelock, T.D.
1995-12-31
The agglomeration of hydrophobic particles in an aqueous suspension was accomplished by introducing small amounts of air into the suspension while it was agitated vigorously. The extent of aggregation was proportional both to the air to solids ratio and to the hydrophobicity of the solids. For a given air/solids ratio, the extent of aggregation of different materials increased in the following order: graphite, gilsonite, coal coated with heptane, and Teflon. The structure of agglomerates produced from coarse Teflon particles differed noticeably from the structure of bubble-particle aggregates produced from smaller, less hydrophobic particles.
Fragmentation and restructuring of soft-agglomerates under shear.
Eggersdorfer, M L; Kadau, D; Herrmann, H J; Pratsinis, S E
2010-02-15
Soft-agglomerate restructuring, break-up (or fragmentation) and relaxation are studied in a simple shear flow by a discrete element method (DEM). The agglomerates, held together by van der Waals forces, rotate in the shear flow and are stretched into nearly linear structures (fractal dimension approaches unity) until they fracture at their weakest point resulting in lognormally-shaped fragment size distributions asymptotically. Individual fragments relax in the flow towards more compact agglomerates than the parent ones. The evolution of the average number of particles per fragment is described by generalized scaling laws between shear rate, onset (time-lag) of fragmentation, asymptotic fragment mass and size consistent with experimental and theoretical studies in the literature. The initial effective fractal dimension of the agglomerates influences the final one of the fragments. PMID:19948345
Zygarlicke, C.J.; Mann, M.D.; Laudal, D.L.; Miller, S.J.
1994-01-01
The Energy & Environmental Research Center (EERC) has been developing advanced indices that rank coals according to their fouling and slagging propensity in utility boilers. The indices are based on sophisticated analytical techniques for identifying and quantifying coal inorganics and are useful in predicting the effects of proposed operational changes on ash deposition in coal-fired boilers. These indices are intended to provide an economical way to reduce the amount of full-scale testing needed to determine the best means of minimizing ash-related problems. The successful design and operation of the fluidized-bed combustor requires the ability to control and mitigate ash-related problems. The major ash-related problems in FBC are agglomeration of bed material, ash deposition on heat-transfer surfaces, ash deposition on refractory and uncooled surfaces, corrosion, and erosion. The focus of the Development of Methods to Predict Agglomeration and Deposition in FBCs is on the agglomeration and deposition problems in atmospheric bubbling and circulating beds. The 1990 Clean Air Act Amendments require study of air toxic emissions from coal combustion systems. Since most of the toxic metals present in coal will be in particulate form, a high level of fine-particle control appears to be the best approach to achieving a high level of air toxics control. However, over 50% of mercury and a portion of selenium emissions are in vapor form and are not typically collected in particulate control devices. Therefore, the goal of this project is to develop methods that capture the vapor-phase metals while simultaneously achieving ultrahigh collection efficiency of particulate air toxics.
Multigrid Solution of the Navier-Stokes Equations at Low Speeds with Large Temperature Variations
NASA Technical Reports Server (NTRS)
Sockol, Peter M.
2002-01-01
Multigrid methods for the Navier-Stokes equations at low speeds and large temperature variations are investigated. The compressible equations with time-derivative preconditioning and preconditioned flux-difference splitting of the inviscid terms are used. Three implicit smoothers have been incorporated into a common multigrid procedure. Both full coarsening and semi-coarsening with directional fine-grid defect correction have been studied. The resulting methods have been tested on four 2D laminar problems over a range of Reynolds numbers on both uniform and highly stretched grids. Two of the three methods show efficient and robust performance over the entire range of conditions. In addition none of the methods have any difficulty with the large temperature variations.
A Pseudo-Temporal Multi-Grid Relaxation Scheme for Solving the Parabolized Navier-Stokes Equations
NASA Technical Reports Server (NTRS)
White, J. A.; Morrison, J. H.
1999-01-01
A multi-grid, flux-difference-split, finite-volume code, VULCAN, is presented for solving the elliptic and parabolized form of the equations governing three-dimensional, turbulent, calorically perfect and non-equilibrium chemically reacting flows. The space marching algorithms developed to improve convergence rate and or reduce computational cost are emphasized. The algorithms presented are extensions to the class of implicit pseudo-time iterative, upwind space-marching schemes. A full approximate storage, full multi-grid scheme is also described which is used to accelerate the convergence of a Gauss-Seidel relaxation method. The multi-grid algorithm is shown to significantly improve convergence on high aspect ratio grids.
A Pseubo-Temporal Multi-Grid Relaxation Scheme for Solving the Parabolized Navier-Stokes Equations
NASA Technical Reports Server (NTRS)
Morrison, J. H.; White, J. A.
1999-01-01
A multi-grid, flux-difference-split, finite-volume code, VULCAN, is presented for solving the elliptic and parabolized form of the equations governing three-dimensional, turbulent, calorically perfect and non-equilibrium chemically reacting flows. The space marching algorithms developed to improve convergence rate and or reduce computational cost are emphasized. The algorithms presented are extensions to the class of implicit pseudo-time iterative, upwind space-marching schemes. A full approximate storage, full multi-grid scheme is also described which is used to accelerate the convergence of a Gauss-Seidel relaxation method. The multi-grid algorithm is shown to significantly improve convergence on high aspect ratio grids.
Interpolation between Sobolev spaces in Lipschitz domains with an application to multigrid theory
Bramble, J.H. |
1995-10-01
In this paper the author describes an interpolation result for the Sobolev spaces H{sub 0}{sup S}({Omega}) where {Omega} is a bounded domain with a Lipschitz boundary. This result is applied to derive discrete norm estimates related to multilevel preconditioners and multigrid methods in the finite element method. The estimates are valid for operators of order 2m with Dirichlet boundary conditions. 11 refs.
Multigrid calculation of three-dimensional viscous cascade flows
NASA Technical Reports Server (NTRS)
Arnone, A.; Liou, M.-S.; Povinelli, L. A.
1991-01-01
A three-dimensional code for viscous cascade flow prediction has been developed. The space discretization uses a cell-centered scheme with eigenvalue scaling to weigh the artificial dissipation terms. Computational efficiency of a four-stage Runge-Kutta scheme is enhanced by using variable coefficients, implicit residual smoothing, and a full-multigrid method. The Baldwin-Lomax eddy-viscosity model is used for turbulence closure. A zonal, nonperiodic grid is used to minimize mesh distortion in and downstream of the throat region. Applications are presented for an annular vane with and without end wall contouring, and for a large-scale linear cascade. The calculation is validated by comparing with experiments and by studying grid dependency.
Multigrid calculation of three-dimensional viscous cascade flows
NASA Technical Reports Server (NTRS)
Arnone, A.; Liou, M.-S.; Povinelli, L. A.
1991-01-01
A 3-D code for viscous cascade flow prediction was developed. The space discretization uses a cell-centered scheme with eigenvalue scaling to weigh the artificial dissipation terms. Computational efficiency of a four stage Runge-Kutta scheme is enhanced by using variable coefficients, implicit residual smoothing, and a full multigrid method. The Baldwin-Lomax eddy viscosity model is used for turbulence closure. A zonal, nonperiodic grid is used to minimize mesh distortion in and downstream of the throat region. Applications are presented for an annular vane with and without end wall contouring, and for a large scale linear cascade. The calculation is validated by comparing with experiments and by studying grid dependency.
Design and implementation of parallel multigrid algorithms
NASA Technical Reports Server (NTRS)
Chan, Tony F.; Tuminaro, Ray S.
1988-01-01
Techniques for mapping multigrid algorithms to solve elliptic PDEs on hypercube parallel computers are described and demonstrated. The need for proper data mapping to minimize communication distances is stressed, and an execution-time model is developed to show how algorithm efficiency is affected by changes in the machine and algorithm parameters. Particular attention is then given to the case of coarse computational grids, which can lead to idle processors, load imbalances, and inefficient performance. It is shown that convergence can be improved by using idle processors to solve a new problem concurrently on the fine grid defined by a splitting.
Multigrid applied to singular perturbation problems
NASA Technical Reports Server (NTRS)
Kamowitz, David
1987-01-01
The solution of the singular perturbation problem by a multigrid algorithm is considered. Theoretical and experimental results for a number of different discretizations are presented. The theoretical and observed rates agree with the results developed in an earlier work of Kamowitz and Parter. In addition, the rate of convergence of the algorithm when the coarse grid operator is the natural finite difference analog of the fine grid operator is presented. This is in contrast to the case in the previous work where the Galerkin choice (I sup H sub h L sub h,I sup h sub H) was used for the coarse grid operators.
Multigrid Acceleration of Time-Accurate DNS of Compressible Turbulent Flow
NASA Technical Reports Server (NTRS)
Broeze, Jan; Geurts, Bernard; Kuerten, Hans; Streng, Martin
1996-01-01
An efficient scheme for the direct numerical simulation of 3D transitional and developed turbulent flow is presented. Explicit and implicit time integration schemes for the compressible Navier-Stokes equations are compared. The nonlinear system resulting from the implicit time discretization is solved with an iterative method and accelerated by the application of a multigrid technique. Since we use central spatial discretizations and no artificial dissipation is added to the equations, the smoothing method is less effective than in the more traditional use of multigrid in steady-state calculations. Therefore, a special prolongation method is needed in order to obtain an effective multigrid method. This simulation scheme was studied in detail for compressible flow over a flat plate. In the laminar regime and in the first stages of turbulent flow the implicit method provides a speed-up of a factor 2 relative to the explicit method on a relatively coarse grid. At increased resolution this speed-up is enhanced correspondingly.
Algebraic multigrid domain and range decomposition (AMG-DD / AMG-RD)*
Bank, R.; Falgout, R. D.; Jones, T.; Manteuffel, T. A.; McCormick, S. F.; Ruge, J. W.
2015-10-29
In modern large-scale supercomputing applications, algebraic multigrid (AMG) is a leading choice for solving matrix equations. However, the high cost of communication relative to that of computation is a concern for the scalability of traditional implementations of AMG on emerging architectures. This paper introduces two new algebraic multilevel algorithms, algebraic multigrid domain decomposition (AMG-DD) and algebraic multigrid range decomposition (AMG-RD), that replace traditional AMG V-cycles with a fully overlapping domain decomposition approach. While the methods introduced here are similar in spirit to the geometric methods developed by Brandt and Diskin [Multigrid solvers on decomposed domains, in Domain Decomposition Methods inmore » Science and Engineering, Contemp. Math. 157, AMS, Providence, RI, 1994, pp. 135--155], Mitchell [Electron. Trans. Numer. Anal., 6 (1997), pp. 224--233], and Bank and Holst [SIAM J. Sci. Comput., 22 (2000), pp. 1411--1443], they differ primarily in that they are purely algebraic: AMG-RD and AMG-DD trade communication for computation by forming global composite “grids” based only on the matrix, not the geometry. (As is the usual AMG convention, “grids” here should be taken only in the algebraic sense, regardless of whether or not it corresponds to any geometry.) Another important distinguishing feature of AMG-RD and AMG-DD is their novel residual communication process that enables effective parallel computation on composite grids, avoiding the all-to-all communication costs of the geometric methods. The main purpose of this paper is to study the potential of these two algebraic methods as possible alternatives to existing AMG approaches for future parallel machines. As a result, this paper develops some theoretical properties of these methods and reports on serial numerical tests of their convergence properties over a spectrum of problem parameters.« less
Algebraic multigrid domain and range decomposition (AMG-DD / AMG-RD)*
Bank, R.; Falgout, R. D.; Jones, T.; Manteuffel, T. A.; McCormick, S. F.; Ruge, J. W.
2015-10-29
In modern large-scale supercomputing applications, algebraic multigrid (AMG) is a leading choice for solving matrix equations. However, the high cost of communication relative to that of computation is a concern for the scalability of traditional implementations of AMG on emerging architectures. This paper introduces two new algebraic multilevel algorithms, algebraic multigrid domain decomposition (AMG-DD) and algebraic multigrid range decomposition (AMG-RD), that replace traditional AMG V-cycles with a fully overlapping domain decomposition approach. While the methods introduced here are similar in spirit to the geometric methods developed by Brandt and Diskin [Multigrid solvers on decomposed domains, in Domain Decomposition Methods in Science and Engineering, Contemp. Math. 157, AMS, Providence, RI, 1994, pp. 135--155], Mitchell [Electron. Trans. Numer. Anal., 6 (1997), pp. 224--233], and Bank and Holst [SIAM J. Sci. Comput., 22 (2000), pp. 1411--1443], they differ primarily in that they are purely algebraic: AMG-RD and AMG-DD trade communication for computation by forming global composite “grids” based only on the matrix, not the geometry. (As is the usual AMG convention, “grids” here should be taken only in the algebraic sense, regardless of whether or not it corresponds to any geometry.) Another important distinguishing feature of AMG-RD and AMG-DD is their novel residual communication process that enables effective parallel computation on composite grids, avoiding the all-to-all communication costs of the geometric methods. The main purpose of this paper is to study the potential of these two algebraic methods as possible alternatives to existing AMG approaches for future parallel machines. As a result, this paper develops some theoretical properties of these methods and reports on serial numerical tests of their convergence properties over a spectrum of problem parameters.
Low-rank coal oil agglomeration
Knudson, Curtis L.; Timpe, Ronald C.
1991-01-01
A low-rank coal oil agglomeration process. High mineral content, a high ash content subbituminous coals are effectively agglomerated with a bridging oil which is partially water soluble and capable of entering the pore structure, and usually coal derived.
Application of p-Multigrid to Discontinuous Galerkin Formulations of the Poisson Equation
NASA Technical Reports Server (NTRS)
Helenbrook, B. T.; Atkins, H. L.
2006-01-01
We investigate p-multigrid as a solution method for several different discontinuous Galerkin (DG) formulations of the Poisson equation. Different combinations of relaxation schemes and basis sets have been combined with the DG formulations to find the best performing combination. The damping factors of the schemes have been determined using Fourier analysis for both one and two-dimensional problems. One important finding is that when using DG formulations, the standard approach of forming the coarse p matrices separately for each level of multigrid is often unstable. To ensure stability the coarse p matrices must be constructed from the fine grid matrices using algebraic multigrid techniques. Of the relaxation schemes, we find that the combination of Jacobi relaxation with the spectral element basis is fairly effective. The results using this combination are p sensitive in both one and two dimensions, but reasonable convergence rates can still be achieved for moderate values of p and isotropic meshes. A competitive alternative is a block Gauss-Seidel relaxation. This actually out performs a more expensive line relaxation when the mesh is isotropic. When the mesh becomes highly anisotropic, the implicit line method and the Gauss-Seidel implicit line method are the only effective schemes. Adding the Gauss-Seidel terms to the implicit line method gives a significant improvement over the line relaxation method.
Multigrid acceleration and turbulence models for computations of 3D turbulent jets in crossflow
NASA Technical Reports Server (NTRS)
Demuren, A. O.
1991-01-01
A multigrid method is presented for the calculation of three-dimensional turbulent jets in crossflow. Turbulence closure is achieved with either the standard k-epsilon model or a Reynolds Stress Model (RSM). Multigrid acceleration enables convergence rates which are far superior to that for a single grid method. With the k-epsilon model the rate approaches that for laminar flow, but with RSM it is somewhat slower. The increased stiffness of the system of equations in the latter may be responsible. Computed results with both turbulence models are compared with experimental data for a pair of opposed jets in crossflow. Both models yield reasonable agreement with mean flow velocity but RSM yields better prediction of the Reynolds stresses.
Application of the multigrid solution technique to hypersonic entry vehicles
NASA Technical Reports Server (NTRS)
Greene, Francis A.
1993-01-01
A multigrid solution procedure has been incorporated in a version of the Langley Aerothermodynamic Upwind Relaxation Algorithm. The multigrid scheme is based on the Full Approximation Storage approach and uses Full Multigrid to obtain a well defined fine mesh starting solution. Predictions were obtained using standard transfer operators and a 'V-cycle' was used to control grid sequencing. Computed hypersonic flow solutions compared with experimental data for a 15 degree sphere cone, blended-wing body, and shuttle-like geometries are presented. It is shown that the algorithm accurately predicts heating rates, and when compared with the single grid algorithm computes solutions in one-third the computational time.
Agglomerate behaviour of fluticasone propionate within dry powder inhaler formulations.
Le, V N P; Robins, E; Flament, M P
2012-04-01
Due to their small size, the respirable drug particles tend to form agglomerates which prevent flowing and aerosolisation. A carrier is used to be mixed with drug in one hand to facilitate the powder flow during manufacturing, in other hand to help the fluidisation upon patient inhalation. Depending on drug concentration, drug agglomerates can be formed in the mixture. The aim of this work was to study the agglomeration behaviour of fluticasone propionate (FP) within interactive mixtures for inhalation. The agglomerate phenomenon of fluticasone propionate after mixing with different fractions of lactose without fine particles of lactose (smaller than 32 μm) was demonstrated by the optical microscopy observation. A technique measuring the FP size in the mixture was developed, based on laser diffraction method. The FP agglomerate sizes were found to be in a linear correlation with the pore size of the carrier powder bed (R(2)=0.9382). The latter depends on the particle size distribution of carrier. This founding can explain the role of carrier size in de-agglomeration of drug particles in the mixture. Furthermore, it gives more structural information of interactive mixture for inhalation that can be used in the investigation of aerosolisation mechanism of powder. According to the manufacturing history, different batches of FP show different agglomeration intensities which can be detected by Spraytec, a new laser diffraction method for measuring aerodynamic size. After mixing with a carrier, Lactohale LH200, the most cohesive batch of FP, generates a lower fine particle fraction. It can be explained by the fact that agglomerates of fluticasone propionate with very large size was detected in the mixtures. By using silica-gel beads as ball-milling agent during the mixing process, the FP agglomerate size decreases accordingly to the quantity of mixing aid. The homogeneity and the aerodynamic performance of the mixtures are improved. The mixing aid based on ball
Chen, Yunjie; Zhan, Tianming; Zhang, Ji
2016-01-01
We propose a novel segmentation method based on regional and nonlocal information to overcome the impact of image intensity inhomogeneities and noise in human brain magnetic resonance images. With the consideration of the spatial distribution of different tissues in brain images, our method does not need preestimation or precorrection procedures for intensity inhomogeneities and noise. A nonlocal information based Gaussian mixture model (NGMM) is proposed to reduce the effect of noise. To reduce the effect of intensity inhomogeneity, the multigrid nonlocal Gaussian mixture model (MNGMM) is proposed to segment brain MR images in each nonoverlapping multigrid generated by using a new multigrid generation method. Therefore the proposed model can simultaneously overcome the impact of noise and intensity inhomogeneity and automatically classify 2D and 3D MR data into tissues of white matter, gray matter, and cerebral spinal fluid. To maintain the statistical reliability and spatial continuity of the segmentation, a fusion strategy is adopted to integrate the clustering results from different grid. The experiments on synthetic and clinical brain MR images demonstrate the superior performance of the proposed model comparing with several state-of-the-art algorithms. PMID:27648448
Chen, Yunjie; Zhan, Tianming; Zhang, Ji; Wang, Hongyuan
2016-01-01
We propose a novel segmentation method based on regional and nonlocal information to overcome the impact of image intensity inhomogeneities and noise in human brain magnetic resonance images. With the consideration of the spatial distribution of different tissues in brain images, our method does not need preestimation or precorrection procedures for intensity inhomogeneities and noise. A nonlocal information based Gaussian mixture model (NGMM) is proposed to reduce the effect of noise. To reduce the effect of intensity inhomogeneity, the multigrid nonlocal Gaussian mixture model (MNGMM) is proposed to segment brain MR images in each nonoverlapping multigrid generated by using a new multigrid generation method. Therefore the proposed model can simultaneously overcome the impact of noise and intensity inhomogeneity and automatically classify 2D and 3D MR data into tissues of white matter, gray matter, and cerebral spinal fluid. To maintain the statistical reliability and spatial continuity of the segmentation, a fusion strategy is adopted to integrate the clustering results from different grid. The experiments on synthetic and clinical brain MR images demonstrate the superior performance of the proposed model comparing with several state-of-the-art algorithms. PMID:27648448
Multigrid for refined triangle meshes
Shapira, Yair
1997-02-01
A two-level preconditioning method for the solution of (locally) refined finite element schemes using triangle meshes is introduced. In the isotropic SPD case, it is shown that the condition number of the preconditioned stiffness matrix is bounded uniformly for all sufficiently regular triangulations. This is also verified numerically for an isotropic diffusion problem with highly discontinuous coefficients.
Three-dimensional multigrid algorithms for the flux-split Euler equations
NASA Technical Reports Server (NTRS)
Anderson, W. Kyle; Thomas, James L.; Whitfield, David L.
1988-01-01
The Full Approximation Scheme (FAS) multigrid method is applied to several implicit flux-split algorithms for solving the three-dimensional Euler equations in a body fitted coordinate system. Each of the splitting algorithms uses a variation of approximate factorization and is implemented in a finite volume formulation. The algorithms are all vectorizable with little or no scalar computation required. The flux vectors are split into upwind components using both the splittings of Steger-Warming and Van Leer. The stability and smoothing rate of each of the schemes are examined using a Fourier analysis of the complete system of equations. Results are presented for three-dimensional subsonic, transonic, and supersonic flows which demonstrate substantially improved convergence rates with the multigrid algorithm. The influence of using both a V-cycle and a W-cycle on the convergence is examined.
Kucukboyaci, Vefa; Haghighat, Alireza
2001-06-17
New angular multigrid formulations have been developed, including the Simplified Angular Multigrid (SAM), Nested Iteration (NI), and V-Cycle schemes, which are compatible with the parallel environment and the adaptive differencing strategy of the PENTRAN three-dimensional parallel S{sub N} code. Through use of the Fourier analysis method for an infinite, homogeneous medium, the effectiveness of the V-Cycle scheme was investigated for different problem parameters including scattering ratio, spatial differencing weights, quadrature order, and mesh size. The theoretical analysis revealed that the V-Cycle scheme is effective for a large range of scattering ratios and is insensitive to mesh size. The effectiveness of the new schemes was also investigated for practical shielding applications such as the Kobayashi benchmark problem and the boiling water reactor core shroud problem.
Design and implementation of a multigrid code for the Euler equations
NASA Technical Reports Server (NTRS)
Jespersen, D. C.
1983-01-01
The steady-state equations of inviscid fluid flow, the Euler equations, are a nonlinear nonelliptic system of equations admitting solutions with discontinuities (for example, shocks). The efficient numerical solution of these equations poses a strenuous challenge to multigrid methods. A multigrid code has been developed for the numerical solution of the Euler equations. In this paper some of the factors that had to be taken into account in the design and development of the code are reviewed. These factors include the importance of choosing an appropriate difference scheme, the usefulness of local mode analysis as a design tool, and the crucial question of how to treat the nonlinearity. Sample calculations of transonic flow about airfoils will be presented. No claim is made that the particular algorithm presented is optimal.
Multigrid iteration solution procedure for solving three-dimensional sets of coupled equations
Vondy, D.R.
1984-08-01
A procedure of iterative solution was coded in Fortran to apply the multigrid scheme of iteration to a set of coupled equations for three-dimensional problems. The incentive for this effort was to make available an implemented procedure that may be readily used as an alternative to overrelaxation, of special interest in applications where the latter is ineffective. The multigrid process was found to be effective, although noncompetitive with simple overrelaxation for simple, small problems. Absolute error level evaluation was used to support methods assessment. A code source listing is presented to allow ready application when the computer memory size is adequate, avoiding data transfer from auxiliary storage. Included are the capabilities for one-dimensional rebalance and a driver program illustrating use requirements. Feedback of additional experience from application is anticipated.
Microstickies agglomeration by electric field.
Du, Xiaotang Tony; Hsieh, Jeffery S
2016-01-01
Microstickies deposits on both paper machine and paper products when it agglomerates under step change in ionic strength, pH, temperature and chemical additives. These stickies increase the down time of the paper mill and decrease the quality of paper. The key property of microstickies is its smaller size, which leads to low removal efficiency and difficulties in measurement. Thus the increase of microstickies size help improve both removal efficiency and reduce measurement difficulty. In this paper, a new agglomeration technology based on electric field was investigated. The electric treatment could also increase the size of stickies particles by around 100 times. The synergetic effect between electric field treatment and detacky chemicals/dispersants, including polyvinyl alcohol, poly(diallylmethylammonium chloride) and lignosulfonate, was also studied. PMID:27332828
Coal beneficiation by gas agglomeration
Wheelock, Thomas D.; Meiyu, Shen
2003-10-14
Coal beneficiation is achieved by suspending coal fines in a colloidal suspension of microscopic gas bubbles in water under atmospheric conditions to form small agglomerates of the fines adhered by the gas bubbles. The agglomerates are separated, recovered and resuspended in water. Thereafter, the pressure on the suspension is increased above atmospheric to deagglomerate, since the gas bubbles are then re-dissolved in the water. During the deagglomeration step, the mineral matter is dispersed, and when the pressure is released, the coal portion of the deagglomerated gas-saturated water mixture reagglomerates, with the small bubbles now coming out of the solution. The reagglomerate can then be separated to provide purified coal fines without the mineral matter.
Wheelock, T.D.
1995-12-31
The preliminary laboratory-scale development of a gas-promoted, oil agglomeration process for cleaning coal advanced in three major research areas. One area of research resulted in the development of a method for measuring the rate of agglomeration of dilute particle suspensions and using the method to relate the rate of agglomeration of coal particles to various key parameters. A second area of research led to the development of a method for monitoring a batch agglomeration process by measuring changes in agitator torque. With this method it was possible to show that the agglomeration of a concentrated coal particle suspension is triggered by the introduction of a small amount of gas. The method was also used in conjunction with optical microscopy to study the mechanism of agglomeration. A third area of research led to the discovery that highly hydrophobic particles in an aqueous suspension can be agglomerated by air alone.
Agglomeration of food powder and applications.
Dhanalakshmi, K; Ghosal, S; Bhattacharya, S
2011-05-01
Agglomeration has many applications in food processing and major applications include easy flow table salt, dispersible milk powder and soup mix, instant chocolate mix, beverage powder, compacted cubes for nutritional-intervention program, health bars using expanded/puffed cereals, etc. The main purpose of agglomeration is to improve certain physical properties of food powders such as bulk density, flowability, dispersability, and stability. Agglomerated products are easy to use by the consumers and hence are preferred over the traditional non-agglomerated products that are usually non-flowable in nature. The properties of food agglomerates and the process of agglomeration like employing pressure, extrusion, rewetting, spray-bed drying, steam jet, heat/sintering, and binders have been reviewed. The physical and instant properties of agglomerated food products have also been discussed.
Implicit multigrid algorithms for the three-dimensional flux split Euler equations. Ph.D. Thesis
NASA Technical Reports Server (NTRS)
Anderson, W. K.
1986-01-01
The full approximation scheme multigrid method is applied to several implicit flux-split algorithms for solving the three-dimensional Euler equations in a body fitted coordinate system. Each uses a variation of approximate factorization and is implemented in a finite volume formulation. The algorithms are all vectorizable with little or no scalar computations required. The flux vectors are split into upwind components using both the splittings of Steger-Warming and Van Leer. Results comparing pressure distributions with experimental data using both splitting types are shown. The stability and smoothing rate of each of the schemes are examined using a Fourier analysis of the complete system of equations. Results are presented for three-dimensional subsonic, transonic, and supersonic flows which demonstrate substantially improved convergence rates with the multigrid algorithm. The influence of using both a V-cycle and a W-cycle on the convergence is examined. Using the multigrid method on both subsonic and transonic wing calculations, the final lift coefficient is obtained to within 0.1 percent of its final value in a few as 15 cycles for a mesh with over 210,000 points. A spectral radius of 0.89 is achieved for both subsonic and transonic flow over the ONERA M6 wing while a spectral radius of 0.83 is obtained for supersonic flow over an analytically defined forebody. Results compared with experiment for all cases show good agreement.
Development and scale-up of particle agglomeration processes for coal beneficiation
NASA Astrophysics Data System (ADS)
Shen, Meiyu
The development of two modified agglomeration processes for coal beneficiation is presented separately in Parts I and II of this dissertation. Part I is based on research which was conducted to study the mechanism and characteristics of a gas-promoted oil agglomeration process. Part II is based on research which was carried out to develop a newer and more innovative method for agglomerating coal particles with microscopic gas bubbles in aqueous suspensions. In Part I, the development of a gas-promoted oil agglomeration process for cleaning coal was carried out with scale model mixing systems in which aqueous suspensions of ultrafine coal particles were treated with a liquid hydrocarbon and a small amount of air. The resulting agglomerates were recovered by screening. During batch agglomeration tests the progress of agglomeration was monitored by observing changes in agitator torque in the case of concentrated suspension. A key parameter turned out to be the minimum time te required to produce compact spherical agglomerates. Other important parameters included the projected area mean particle diameter of the agglomerates recovered at the end of a test as well as the ash content and yield of agglomerates. Batch agglomeration tests were conducted with geometrically similar mixing tanks which ranged in volume from 0.346 to 11.07 liters. It was shown that gas bubbles trigger the process of agglomeration and participate in a very complex mechanism involving the interaction of particles, oil droplets, and gas bubbles. The process takes place in stages involving dispersion of oil and gas, flocculation, coagulation, and agglomerate building. Numerous agglomeration tests were conducted with two kinds of coal in concentrated suspensions to determine the important characteristics of the process and to study the effects of the following operating parameters: i-octane concentration, air concentration, particle concentration, tank diameter, impeller diameter, and impeller speed
Advanced physical fine coal cleaning spherical agglomeration. Final report
Not Available
1990-09-01
The project included process development, engineering, construction, and operation of a 1/3 tph proof-of-concept (POC) spherical agglomeration test module. The POC tests demonstrated that physical cleaning of ultrafine coal by agglomeration using heptane can achieve: (1) Pyritic sulfur reductions beyond that possible with conventional coal cleaning methods; (2) coal ash contents below those which can be obtained by conventional coal cleaning methods at comparable energy recoveries; (3) energy recoveries of 80 percent or greater measured against the raw coal energy content; (4) complete recovery of the heptane bridging liquid from the agglomerates; and (5) production of agglomerates with 3/8-inch size and less than 30 percent moisture. Test results met or exceeded all of the program objectives. Nominal 3/8-inch size agglomerates with less than 20 percent moisture were produced. The clean coal ash content varied between 1.5 to 5.5 percent by weight (dry basis) depending on feed coal type. Ash reductions of the run-of-mine (ROM) coal were 77 to 83 percent. ROM pyritic sulfur reductions varied from 86 to 90 percent for the three test coals, equating to total sulfur reductions of 47 to 72 percent.
Challenges of Algebraic Multigrid across Multicore Architectures
Baker, A H; Gamblin, T; Schulz, M; Yang, U M
2010-04-12
Algebraic multigrid (AMG) is a popular solver for large-scale scientific computing and an essential component of many simulation codes. AMG has shown to be extremely efficient on distributed-memory architectures. However, when executed on modern multicore architectures, we face new challenges that can significantly deteriorate AMG's performance. We examine its performance and scalability on three disparate multicore architectures: a cluster with four AMD Opteron Quad-core processors per node (Hera), a Cray XT5 with two AMD Opteron Hex-core processors per node (Jaguar), and an IBM BlueGene/P system with a single Quad-core processor (Intrepid). We discuss our experiences on these platforms and present results using both an MPI-only and a hybrid MPI/OpenMP model. We also discuss a set of techniques that helped to overcome the associated problems, including thread and process pinning and correct memory associations.
Distance-Two Interpolation for Parallel Algebraic Multigrid
De Sterck, H; Falgout, R; Nolting, J; Yang, U M
2007-05-08
Algebraic multigrid (AMG) is one of the most efficient and scalable parallel algorithms for solving sparse linear systems on unstructured grids. However, for large three-dimensional problems, the coarse grids that are normally used in AMG often lead to growing complexity in terms of memory use and execution time per AMG V-cycle. Sparser coarse grids, such as those obtained by the Parallel Modified Independent Set coarsening algorithm (PMIS) [7], remedy this complexity growth, but lead to non-scalable AMG convergence factors when traditional distance-one interpolation methods are used. In this paper we study the scalability of AMG methods that combine PMIS coarse grids with long distance interpolation methods. AMG performance and scalability is compared for previously introduced interpolation methods as well as new variants of them for a variety of relevant test problems on parallel computers. It is shown that the increased interpolation accuracy largely restores the scalability of AMG convergence factors for PMIS-coarsened grids, and in combination with complexity reducing methods, such as interpolation truncation, one obtains a class of parallel AMG methods that enjoy excellent scalability properties on large parallel computers.
Ewing, R.E.; Saevareid, O.; Shen, J.
1994-12-31
A multigrid algorithm for the cell-centered finite difference on equilateral triangular grids for solving second-order elliptic problems is proposed. This finite difference is a four-point star stencil in a two-dimensional domain and a five-point star stencil in a three dimensional domain. According to the authors analysis, the advantages of this finite difference are that it is an O(h{sup 2})-order accurate numerical scheme for both the solution and derivatives on equilateral triangular grids, the structure of the scheme is perhaps the simplest, and its corresponding multigrid algorithm is easily constructed with an optimal convergence rate. They are interested in relaxation of the equilateral triangular grid condition to certain general triangular grids and the application of this multigrid algorithm as a numerically reasonable preconditioner for the lowest-order Raviart-Thomas mixed triangular finite element method. Numerical test results are presented to demonstrate their analytical results and to investigate the applications of this multigrid algorithm on general triangular grids.
NASA Astrophysics Data System (ADS)
Pariona, Moisés Meza; de Oliveira, Fabiane; Teleginski, Viviane; Machado, Siliane; Pinto, Marcio Augusto Villela
2016-05-01
Al-1.5 wt% Fe alloy was irradiate by Yb-fiber laser beam using the laser surface remelting (LSR) technique, generating weld fillets that covered the whole surface of the sample. The laser-treatment showed to be an efficient technology for corrosion resistance improvements. In this study, the finite element method was used to simulate the solidification processes by LSR technique. The method Multigrid was employed in order to reduce the CPU time, which is important to the viability for industrial applications. Multigrid method is a technique very promising of optimization that reduced drastically the CPU time. The result was highly satisfactory, because the CPU time has fallen dramatically in comparison when it was not used Multigrid method. To validate the result of numerical simulation with the experimental result was done the microstructural characterization of laser-treated layer by the optical microscopy and SEM techniques and however, that both results showing be consistent.
Powder agglomeration in a microgravity environment
NASA Technical Reports Server (NTRS)
Cawley, James D.
1994-01-01
This is the final report for NASA Grant NAG3-755 entitled 'Powder Agglomeration in a Microgravity Environment.' The research program included both two types of numerical models and two types of experiments. The numerical modeling included the use of Monte Carlo type simulations of agglomerate growth including hydrodynamic screening and molecular dynamics type simulations of the rearrangement of particles within an agglomerate under a gravitational field. Experiments included direct observation of the agglomeration of submicron alumina and indirect observation, using small angle light scattering, of the agglomeration of colloidal silica and aluminum monohydroxide. In the former class of experiments, the powders were constrained to move on a two-dimensional surface oriented to minimize the effect of gravity. In the latter, some experiments involved mixture of suspensions containing particles of opposite charge which resulted in agglomeration on a very short time scale relative to settling under gravity.
Multigrid optimal mass transport for image registration and morphing
NASA Astrophysics Data System (ADS)
Rehman, Tauseef ur; Tannenbaum, Allen
2007-02-01
In this paper we present a computationally efficient Optimal Mass Transport algorithm. This method is based on the Monge-Kantorovich theory and is used for computing elastic registration and warping maps in image registration and morphing applications. This is a parameter free method which utilizes all of the grayscale data in an image pair in a symmetric fashion. No landmarks need to be specified for correspondence. In our work, we demonstrate significant improvement in computation time when our algorithm is applied as compared to the originally proposed method by Haker et al [1]. The original algorithm was based on a gradient descent method for removing the curl from an initial mass preserving map regarded as 2D vector field. This involves inverting the Laplacian in each iteration which is now computed using full multigrid technique resulting in an improvement in computational time by a factor of two. Greater improvement is achieved by decimating the curl in a multi-resolutional framework. The algorithm was applied to 2D short axis cardiac MRI images and brain MRI images for testing and comparison.
Ice slurry cooling research: Storage tank ice agglomeration and extraction
Kasza, K.; Hayashi, Kanetoshi
1999-08-01
A new facility has been built to conduct research and development on important issues related to implementing ice slurry cooling technology. Ongoing studies are generating important information on the factors that influence ice particle agglomeration in ice slurry storage tanks. The studies are also addressing the development of methods to minimize and monitor agglomeration and improve the efficiency and controllability of tank extraction of slurry for distribution to cooling loads. These engineering issues impede the utilization of the ice slurry cooling concept that has been under development by various groups.
Textbook Multigrid Efficiency for Computational Fluid Dynamics Simulations
NASA Technical Reports Server (NTRS)
Brandt, Achi; Thomas, James L.; Diskin, Boris
2001-01-01
Considerable progress over the past thirty years has been made in the development of large-scale computational fluid dynamics (CFD) solvers for the Euler and Navier-Stokes equations. Computations are used routinely to design the cruise shapes of transport aircraft through complex-geometry simulations involving the solution of 25-100 million equations; in this arena the number of wind-tunnel tests for a new design has been substantially reduced. However, simulations of the entire flight envelope of the vehicle, including maximum lift, buffet onset, flutter, and control effectiveness have not been as successful in eliminating the reliance on wind-tunnel testing. These simulations involve unsteady flows with more separation and stronger shock waves than at cruise. The main reasons limiting further inroads of CFD into the design process are: (1) the reliability of turbulence models; and (2) the time and expense of the numerical simulation. Because of the prohibitive resolution requirements of direct simulations at high Reynolds numbers, transition and turbulence modeling is expected to remain an issue for the near term. The focus of this paper addresses the latter problem by attempting to attain optimal efficiencies in solving the governing equations. Typically current CFD codes based on the use of multigrid acceleration techniques and multistage Runge-Kutta time-stepping schemes are able to converge lift and drag values for cruise configurations within approximately 1000 residual evaluations. An optimally convergent method is defined as having textbook multigrid efficiency (TME), meaning the solutions to the governing system of equations are attained in a computational work which is a small (less than 10) multiple of the operation count in the discretized system of equations (residual equations). In this paper, a distributed relaxation approach to achieving TME for Reynolds-averaged Navier-Stokes (RNAS) equations are discussed along with the foundations that form the
Mapping robust parallel multigrid algorithms to scalable memory architectures
NASA Technical Reports Server (NTRS)
Overman, Andrea; Vanrosendale, John
1993-01-01
The convergence rate of standard multigrid algorithms degenerates on problems with stretched grids or anisotropic operators. The usual cure for this is the use of line or plane relaxation. However, multigrid algorithms based on line and plane relaxation have limited and awkward parallelism and are quite difficult to map effectively to highly parallel architectures. Newer multigrid algorithms that overcome anisotropy through the use of multiple coarse grids rather than relaxation are better suited to massively parallel architectures because they require only simple point-relaxation smoothers. In this paper, we look at the parallel implementation of a V-cycle multiple semicoarsened grid (MSG) algorithm on distributed-memory architectures such as the Intel iPSC/860 and Paragon computers. The MSG algorithms provide two levels of parallelism: parallelism within the relaxation or interpolation on each grid and across the grids on each multigrid level. Both levels of parallelism must be exploited to map these algorithms effectively to parallel architectures. This paper describes a mapping of an MSG algorithm to distributed-memory architectures that demonstrates how both levels of parallelism can be exploited. The result is a robust and effective multigrid algorithm for distributed-memory machines.
Mapping robust parallel multigrid algorithms to scalable memory architectures
NASA Technical Reports Server (NTRS)
Overman, Andrea; Vanrosendale, John
1993-01-01
The convergence rate of standard multigrid algorithms degenerates on problems with stretched grids or anisotropic operators. The usual cure for this is the use of line or plane relaxation. However, multigrid algorithms based on line and plane relaxation have limited and awkward parallelism and are quite difficult to map effectively to highly parallel architectures. Newer multigrid algorithms that overcome anisotropy through the use of multiple coarse grids rather than line relaxation are better suited to massively parallel architectures because they require only simple point-relaxation smoothers. The parallel implementation of a V-cycle multiple semi-coarsened grid (MSG) algorithm or distributed-memory architectures such as the Intel iPSC/860 and Paragon computers is addressed. The MSG algorithms provide two levels of parallelism: parallelism within the relaxation or interpolation on each grid and across the grids on each multigrid level. Both levels of parallelism must be exploited to map these algorithms effectively to parallel architectures. A mapping of an MSG algorithm to distributed-memory architectures that demonstrate how both levels of parallelism can be exploited is described. The results is a robust and effective multigrid algorithm for distributed-memory machines.
NASA Technical Reports Server (NTRS)
Yokota, Jeffrey W.
1988-01-01
An LU implicit multigrid algorithm is developed to calculate 3-D compressible viscous flows. This scheme solves the full 3-D Reynolds-Averaged Navier-Stokes equation with a two-equation kappa-epsilon model of turbulence. The flow equations are integrated by an efficient, diagonally inverted, LU implicit multigrid scheme while the kappa-epsilon equations are solved, uncoupled from the flow equations, by a block LU implicit algorithm. The flow equations are solved within the framework of the multigrid method using a four-grid level W-cycle, while the kappa-epsilon equations are iterated only on the finest grid. This treatment of the Reynolds-Averaged Navier-Stokes equations proves to be an efficient method for calculating 3-D compressible viscous flows.
Multilevel methods for elliptic problems on unstructured grids
NASA Technical Reports Server (NTRS)
Chan, Tony F.; Go, Susie; Zikatanov, Ludmil
1997-01-01
Multilevel methods on unstructured grids for elliptic problems are reviewed. The advantages of these techniques are the flexible approximation of the boundaries of complicated physical domains and the ability to adapt the grid to the resolution of fine scaled structures. Multilevel methods, which include multigrid methods and domain decomposition methods, depend on the correct splitting of appropriate finite element spaces. The standard splittings used in the structured grid case cannot be directly extended to unstructured grids due to their requirement for a hierarchical grid structure. Issues related to the application of multilevel methods to unstructured grids are discussed, including how the coarse spaces and transfer operators are defined and how different types of boundary conditions are treated. An obvious way to generate a coarse mesh is to regrid the physical domain several times. Several alternatives are proposed and discussed: node nested coarse spaces, agglomerated coarse spaces and algebraically generated coarse spaces.
Low-rank coal oil agglomeration
Knudson, C.L.; Timpe, R.C.
1991-07-16
A low-rank coal oil agglomeration process is described. High mineral content, a high ash content subbituminous coals are effectively agglomerated with a bridging oil which is partially water soluble and capable of entering the pore structure, and is usually coal-derived.
Analysis of multigrid algorithms for nonsymmetric and indefinite elliptic problems
Bramble, J.H.; Pasciak, J.E.; Xu, J.
1988-10-01
We prove some new estimates for the convergence of multigrid algorithms applied to nonsymmetric and indefinite elliptic boundary value problems. We provide results for the so-called 'symmetric' multigrid schemes. We show that for the variable V-script-cycle and the W-script-cycle schemes, multigrid algorithms with any amount of smoothing on the finest grid converge at a rate that is independent of the number of levels or unknowns, provided that the initial grid is sufficiently fine. We show that the V-script-cycle algorithm also converges (under appropriate assumptions on the coarsest grid) but at a rate which may deteriorate as the number of levels increases. This deterioration for the V-script-cycle may occur even in the case of full elliptic regularity. Finally, the results of numerical experiments are given which illustrate the convergence behavior suggested by the theory.
Transonic Drag Prediction Using an Unstructured Multigrid Solver
NASA Technical Reports Server (NTRS)
Mavriplis, D. J.; Levy, David W.
2001-01-01
This paper summarizes the results obtained with the NSU-3D unstructured multigrid solver for the AIAA Drag Prediction Workshop held in Anaheim, CA, June 2001. The test case for the workshop consists of a wing-body configuration at transonic flow conditions. Flow analyses for a complete test matrix of lift coefficient values and Mach numbers at a constant Reynolds number are performed, thus producing a set of drag polars and drag rise curves which are compared with experimental data. Results were obtained independently by both authors using an identical baseline grid and different refined grids. Most cases were run in parallel on commodity cluster-type machines while the largest cases were run on an SGI Origin machine using 128 processors. The objective of this paper is to study the accuracy of the subject unstructured grid solver for predicting drag in the transonic cruise regime, to assess the efficiency of the method in terms of convergence, cpu time, and memory, and to determine the effects of grid resolution on this predictive ability and its computational efficiency. A good predictive ability is demonstrated over a wide range of conditions, although accuracy was found to degrade for cases at higher Mach numbers and lift values where increasing amounts of flow separation occur. The ability to rapidly compute large numbers of cases at varying flow conditions using an unstructured solver on inexpensive clusters of commodity computers is also demonstrated.
Non-Galerkin Coarse Grids for Algebraic Multigrid
Falgout, Robert D.; Schroder, Jacob B.
2014-06-26
Algebraic multigrid (AMG) is a popular and effective solver for systems of linear equations that arise from discretized partial differential equations. And while AMG has been effectively implemented on large scale parallel machines, challenges remain, especially when moving to exascale. Particularly, stencil sizes (the number of nonzeros in a row) tend to increase further down in the coarse grid hierarchy, and this growth leads to more communication. Therefore, as problem size increases and the number of levels in the hierarchy grows, the overall efficiency of the parallel AMG method decreases, sometimes dramatically. This growth in stencil size is due to the standard Galerkin coarse grid operator, $P^T A P$, where $P$ is the prolongation (i.e., interpolation) operator. For example, the coarse grid stencil size for a simple three-dimensional (3D) seven-point finite differencing approximation to diffusion can increase into the thousands on present day machines, causing an associated increase in communication costs. We therefore consider algebraically truncating coarse grid stencils to obtain a non-Galerkin coarse grid. First, the sparsity pattern of the non-Galerkin coarse grid is determined by employing a heuristic minimal “safe” pattern together with strength-of-connection ideas. Second, the nonzero entries are determined by collapsing the stencils in the Galerkin operator using traditional AMG techniques. The result is a reduction in coarse grid stencil size, overall operator complexity, and parallel AMG solve phase times.
NASA Technical Reports Server (NTRS)
Elmiligui, Alaa; Cannizzaro, Frank; Melson, N. D.
1991-01-01
A general multiblock method for the solution of the three-dimensional, unsteady, compressible, thin-layer Navier-Stokes equations has been developed. The convective and pressure terms are spatially discretized using Roe's flux differencing technique while the viscous terms are centrally differenced. An explicit Runge-Kutta method is used to advance the solution in time. Local time stepping, adaptive implicit residual smoothing, and the Full Approximation Storage (FAS) multigrid scheme are added to the explicit time stepping scheme to accelerate convergence to steady state. Results for three-dimensional test cases are presented and discussed.
Engineering development of selective agglomeration. Final report
Not Available
1993-04-01
This report presents the findings of the project entitled ``Engineering Development of Selective Agglomeration.`` The purpose is to develop selective agglomeration technology to a commercially acceptable level by 1993. Engineering development included bench-scale process development, component development adaptation or modification of existing unit operations, proof-of-concept (POC) module design, fabrication, testing, data evaluation, and conceptual design of a commercial facility. The information obtained during POC operation resulted in a technical and economic design base sufficient to support construction and operation of a commercial plant. Throughout this project performance targets for the engineering development of selective agglomeration process were to achieve 85% or greater Btu recovery at 85% or greater pyritic sulfur rejection (PSR). Additional objectives included producing a final clean-coal product with an ash content of 6% or less which is suitable for conventional coal handling systems. The selective agglomeration process, as applied to coal cleaning, is based on differences in the surface chemistry of coal and its associated impurities. Coal particles are hydrophobic (i.e., repel water) while the majority of its impurities are hydrophilic (i.e., stabilized in water). During selective agglomeration, a liquid (the agglomerant) that is immiscible with water is introduced into a coal-water slurry and agitated to disperse it in the slurry, thereby allowing it to come into contact with all particles in the slurry. The coal particles, due to their hydrophobic nature, are attracted to the agglomerant phase. The hydrophilic mineral impurities remain in the water phase. Continued agitation of the agglomerant-coated coal particles causes them to coalesce to form agglomerates. Once the agglomerates are formed, they are separated from the mineral matter-bearing aqueous phase by subsequent processing steps.
Coarse-grid selection for parallel algebraic multigrid
Cleary, A. J., LLNL
1998-06-01
The need to solve linear systems arising from problems posed on extremely large, unstructured grids has sparked great interest in parallelizing algebraic multigrid (AMG) To date, however, no parallel AMG algorithms exist We introduce a parallel algorithm for the selection of coarse-grid points, a crucial component of AMG, based on modifications of certain paallel independent set algorithms and the application of heuristics designed to insure the quality of the coarse grids A prototype serial version of the algorithm is implemented, and tests are conducted to determine its effect on multigrid convergence, and AMG complexity
Light extinction at agglomerates of spheres--a practical test on the submicroscale.
Kätzel, Uwe; Gruy, Frederic; Babick, Frank; Klöden, Wolfgang
2005-09-01
Today's theories applied to the inversion of measurement data from optical measurement devices are restricted to single spherical particles. However, particles formed in industrial processes such as precipitation and crystallization are often nonspherical or agglomerates. Theoretical approaches to describe the optical behavior of such particle systems have already been proposed. The verification of these theories has mostly been done using microwave scattering experiments with agglomerates in the millimeter range. This paper provides a first but surely not all-embracing practical test for a general extension of the Mie theory to agglomerates of submicroscale spheres. For the sake of simplicity and from practical viewpoints of online-sensor development only light extinction of an agglomerated suspension has been examined. The required rigid agglomerates have been produced using a spray-drying method that generates particles with a much higher mechanical stability than can be obtained by the usual procedures. Subsequent fractionation of the suspension delivers systems with only a limited number of agglomerate configurations. Extinction measurements at multiple wavelengths using dynamic extinction spectroscopy have been conducted to determine the extinction cross section of the agglomerated dispersions. These data are compared with computations of agglomerates scattering.
Ruge, J.; Li, Y.; McCormick, S.F.
1994-12-31
The formulation and time discretization of problems in meteorology are often tailored to the type of efficient solvers available for use on the discrete problems obtained. A common procedure is to formulate the problem so that a constant (or latitude-dependent) coefficient Poisson-like equation results at each time step, which is then solved using spectral methods. This both limits the scope of problems that can be handled and requires linearization by forward extrapolation of nonlinear terms, which, in turn, requires filtering to control noise. Multigrid methods do not suffer these limitations, and can be applied directly to systems of nonlinear equations with variable coefficients. Here, a global barotropic semi-Lagrangian model, developed by the authors, is presented which results in a system of three coupled nonlinear equations to be solved at each time step. A multigrid method for the solution of these equations is described, and results are presented.
Modeling of particle agglomeration in nanofluids
Krishna, K. Hari; Neti, S.; Oztekin, A.; Mohapatra, S.
2015-03-07
Agglomeration strongly influences the stability or shelf life of nanofluid. The present computational and experimental study investigates the rate of agglomeration quantitatively. Agglomeration in nanofluids is attributed to the net effect of various inter-particle interaction forces. For the nanofluid considered here, a net inter-particle force depends on the particle size, volume fraction, pH, and electrolyte concentration. A solution of the discretized and coupled population balance equations can yield particle sizes as a function of time. Nanofluid prepared here consists of alumina nanoparticles with the average particle size of 150 nm dispersed in de-ionized water. As the pH of the colloid was moved towards the isoelectric point of alumina nanofluids, the rate of increase of average particle size increased with time due to lower net positive charge on particles. The rate at which the average particle size is increased is predicted and measured for different electrolyte concentration and volume fraction. The higher rate of agglomeration is attributed to the decrease in the electrostatic double layer repulsion forces. The rate of agglomeration decreases due to increase in the size of nano-particle clusters thus approaching zero rate of agglomeration when all the clusters are nearly uniform in size. Predicted rates of agglomeration agree adequate enough with the measured values; validating the mathematical model and numerical approach is employed.
Shapes of agglomerates in plasma etching reactors
Huang, F.Y.; Kushner, M.J.
1997-05-01
Dust particle contamination of wafers in reactive ion etching (RIE) plasma tools is a continuing concern in the microelectronics industry. It is common to find that particles collected on surfaces or downstream of the etch chamber are agglomerates of smaller monodisperse spherical particles. The shapes of the agglomerates vary from compact, high fractal dimension structures to filamentary, low fractal dimension structures. These shapes are important with respect to the transport of particles in RIE tools under the influence electrostatic and ion drag forces, and the possible generation of polarization forces. A molecular dynamics simulation has been developed to investigate the shapes of agglomerates in plasma etching reactors. We find that filamentary, low fractal dimension structures are generally produced by smaller ({lt}100s nm) particles in low powered plasmas where the kinetic energy of primary particles is insufficient to overcome the larger Coulomb repulsion of a compact agglomerate. This is analogous to the diffusive regime in neutral agglomeration. Large particles in high powered plasmas generally produce compact agglomerates of high fractal dimension, analogous to ballistic agglomeration of neutrals. {copyright} {ital 1997 American Institute of Physics.}
Multigrid TVD-type scheme for computing inviscid and viscous flows
NASA Astrophysics Data System (ADS)
Wiedermann, Alexander; Iwamoto, Junjiro
1994-06-01
A numerical scheme for the computation of steady-state transonic flow fields is presented, which is based on a total variation diminishing (TVD) approach. Various kinds of the anti-diffusive flux terms have been considered, and their effect on the computed results investigated. The time-dependent governing equations are given in a conservative formulation and solved by a hybrid multistage Runge-Kutta scheme. To obtain an improved convergence rate a multigrid procedure has been added to the scheme. The time-marching method presented has been verified by inviscid and viscous two-dimensional flow-field computations.
Adaptive parallel multigrid for Euler and incompressible Navier-Stokes equations
Trottenberg, U.; Oosterlee, K.; Ritzdorf, H.
1996-12-31
The combination of (1) very efficient solution methods (Multigrid), (2) adaptivity, and (3) parallelism (distributed memory) clearly is absolutely necessary for future oriented numerics but still regarded as extremely difficult or even unsolved. We show that very nice results can be obtained for real life problems. Our approach is straightforward (based on {open_quotes}MLAT{close_quotes}). But, of course, reasonable refinement and load-balancing strategies have to be used. Our examples are 2D, but 3D is on the way.
The development of an algebraic multigrid algorithm for symmetric positive definite linear systems
Vanek, P.; Mandel, J.; Brezina, M.
1996-12-31
An algebraic multigrid algorithm for symmetric, positive definite linear systems is developed based on the concept of prolongation by smoothed aggregation. Coarse levels are generated automatically. We present a set of requirements motivated heuristically by a convergence theory. The algorithm then attempts to satisfy the requirements. Input to the method are the coefficient matrix and zero energy modes, which are determined from nodal coordinates and knowledge of the differential equation. Efficiency of the resulting algorithm is demonstrated by computational results on real world problems from solid elasticity, plate blending, and shells.
Multigrid Computations of 3-D Incompressible Internal and External Viscous Rotating Flows
NASA Technical Reports Server (NTRS)
Sheng, Chunhua; Taylor, Lafayette K.; Chen, Jen-Ping; Jiang, Min-Yee; Whitfield, David L.
1996-01-01
This report presents multigrid methods for solving the 3-D incompressible viscous rotating flows in a NASA low-speed centrifugal compressor and a marine propeller 4119. Numerical formulations are given in both the rotating reference frame and the absolute frame. Comparisons are made for the accuracy, efficiency, and robustness between the steady-state scheme and the time-accurate scheme for simulating viscous rotating flows for complex internal and external flow applications. Prospects for further increase in efficiency and accuracy of unsteady time-accurate computations are discussed.
Fast multigrid-based computation of the induced electric field for transcranial magnetic stimulation
NASA Astrophysics Data System (ADS)
Laakso, Ilkka; Hirata, Akimasa
2012-12-01
In transcranial magnetic stimulation (TMS), the distribution of the induced electric field, and the affected brain areas, depends on the position of the stimulation coil and the individual geometry of the head and brain. The distribution of the induced electric field in realistic anatomies can be modelled using computational methods. However, existing computational methods for accurately determining the induced electric field in realistic anatomical models have suffered from long computation times, typically in the range of tens of minutes or longer. This paper presents a matrix-free implementation of the finite-element method with a geometric multigrid method that can potentially reduce the computation time to several seconds or less even when using an ordinary computer. The performance of the method is studied by computing the induced electric field in two anatomically realistic models. An idealized two-loop coil is used as the stimulating coil. Multiple computational grid resolutions ranging from 2 to 0.25 mm are used. The results show that, for macroscopic modelling of the electric field in an anatomically realistic model, computational grid resolutions of 1 mm or 2 mm appear to provide good numerical accuracy compared to higher resolutions. The multigrid iteration typically converges in less than ten iterations independent of the grid resolution. Even without parallelization, each iteration takes about 1.0 s or 0.1 s for the 1 and 2 mm resolutions, respectively. This suggests that calculating the electric field with sufficient accuracy in real time is feasible.
Agglomeration of microparticles in complex plasmas
Du, Cheng-Ran; Thomas, Hubertus M.; Ivlev, Alexei V.; Konopka, Uwe; Morfill, Gregor E.
2010-11-15
Agglomeration of highly charged microparticles was observed and studied in complex plasma experiments carried out in a capacitively coupled rf discharge. The agglomeration was caused by strong waves triggered in a particle cloud by decreasing neutral gas pressure. Using a high-speed camera during this unstable regime, it was possible to resolve the motion of individual microparticles and to show that the relative velocities of some particles were sufficiently high to overcome the mutual Coulomb repulsion and hence to result in agglomeration. After stabilizing the cloud again through the increase of the pressure, we were able to observe the aggregates directly with a long-distance microscope. We show that the agglomeration rate deduced from our experiments is in good agreement with theoretical estimates. In addition, we briefly discuss the mechanisms that can provide binding of highly charged microparticles in a plasma.
Advances in food powder agglomeration engineering.
Cuq, B; Gaiani, C; Turchiuli, C; Galet, L; Scher, J; Jeantet, R; Mandato, S; Petit, J; Murrieta-Pazos, I; Barkouti, A; Schuck, P; Rondet, E; Delalonde, M; Dumoulin, E; Delaplace, G; Ruiz, T
2013-01-01
Food powders are used in everyday life in many ways and offer technological solutions to the problem of food production. The natural origin of food powders, diversity in their chemical composition, variability of the raw materials, heterogeneity of the native structures, and physicochemical reactivity under hydrothermal stresses contribute to the complexity in their behavior. Food powder agglomeration has recently been considered according to a multiscale approach, which is followed in the chapter layout: (i) at the particle scale, by a presentation of particle properties and surface reactivity in connection with the agglomeration mechanisms, (ii) at the mechanisms scale, by describing the structuration dynamics of agglomerates, (iii) at the process scale, by a presentation of agglomeration technologies and sensors and by studying the stress transmission mode in the powder bed, and finally (iv) by an integration of the acquired knowledge, thanks to a dimensional analysis carried out at each scale.
Chekli, L; Roy, M; Tijing, L D; Donner, E; Lombi, E; Shon, H K
2015-08-15
Titanium dioxide nanoparticles (TiO2 NPs) are currently one of the most prolifically used nanomaterials, resulting in an increasing likelihood of release to the environment. This is of concern as the potential toxicity of TiO2 NPs has been investigated in several recent studies. Research into their fate and behaviour once entering the environment is urgently needed to support risk assessment and policy development. In this study, we used a multi-method approach combining light scattering and field-flow fractionation techniques to assess both the aggregation behaviour and aggregate structure of TiO2 NPs in different river waters. Results showed that both the aggregate size and surface-adsorbed dissolved organic matter (DOM) were strongly related to the initial DOM concentration of the tested waters (i.e. R(2) > 0.90) suggesting that aggregation of TiO2 NPs is controlled by the presence and concentration of DOM. The conformation of the formed aggregates was also found to be strongly related to the surface-adsorbed DOM (i.e. R(2) > 0.95) with increasing surface-adsorbed DOM leading to more compact structures. Finally, the concentration of TiO2 NPs remaining in the supernatant after sedimentation of the larger aggregates was found to decrease proportionally with both increasing IS and decreasing DOM concentration, resulting in more than 95% sedimentation in the highest IS sample.
A uHPLC-MS mathematical modeling approach to dry powder inhaler single agglomerate analysis.
Pennington, Justin; Lena, John; Medendorp, Joseph; Ewing, Gary
2011-10-01
Demonstration of content uniformity (CU) is critical toward the successful development of dry powder inhalers (DPIs). Methods for unit dose CU determination for DPI products are well-established within the field of respiratory science. Recent advances in the area include a uHPLC-MS method for high-throughput uniformity analysis, which allows for a greater understanding of blending operations as the industry transitions to a quality-by-design approach to development. Further enhancements to this uHPLC-MS method now enable it to determine CU and sample weight at the single agglomerate level, which is roughly 50× smaller than a unit dose. When coupled with optical microscopy-based agglomerate sizing, the enhanced uHPLC-MS method can also predict the density and porosity of individual agglomerates. Expanding analytical capabilities to the single agglomerate level provides greater insights and confidence in the DPI manufacturing process.
FAS multigrid calculations of three dimensional flow using non-staggered grids
NASA Technical Reports Server (NTRS)
Matovic, D.; Pollard, A.; Becker, H. A.; Grandmaison, E. W.
1993-01-01
Grid staggering is a well known remedy for the problem of velocity/pressure coupling in incompressible flow calculations. Numerous inconveniences occur, however, when staggered grids are implemented, particularly when a general-purpose code, capable of handling irregular three-dimensional domains, is sought. In several non-staggered grid numerical procedures proposed in the literature, the velocity/pressure coupling is achieved by either pressure or velocity (momentum) averaging. This approach is not convenient for simultaneous (block) solvers that are preferred when using multigrid methods. A new method is introduced in this paper that is based upon non-staggered grid formulation with a set of virtual cell face velocities used for pressure/velocity coupling. Instead of pressure or velocity averaging, a momentum balance at the cell face is used as a link between the momentum and mass balance constraints. The numerical stencil is limited to 9 nodes (in 2D) or 27 nodes (in 3D), both during the smoothing and inter-grid transfer, which is a convenient feature when a block point solver is applied. The results for a lid-driven cavity and a cube in a lid-driven cavity are presented and compared to staggered grid calculations using the same multigrid algorithm. The method is shown to be stable and produce a smooth (wiggle-free) pressure field.
Maghsoodi, M; Tajalli Bakhsh, A S
2011-06-01
Spherical crystallization (SC) of carbamazepine (CBZ) was carried out for preparation of the agglomerates using the solvent change method. The potential of the intraagglomerate addition of sodium starch glycolate (SSG) as a disintegrant agent and povidone (PVP) as a hydrophilic polymer was also evaluated. The process of SC involved recrystallization of CBZ and its simultaneous agglomeration with additives. An ethanol:isopropyl acetate:water system was used where isopropyl acetate acted as a bridging liquid and ethanol and water as good and bad solvents, respectively. The agglomerates were characterized by differential scanning calorimetry (DSC), powder X-ray diffraction (XRPD), and Scanning electron microscopy and were evaluated for yield, flowability, disintegration time and drug release. CBZ agglomerates exhibited significantly improved micromeritic properties as well as dissolution behavior in comparison to conventional drug crystals. The dissolution rate of drug from agglomerates was enhanced by inclusion of SSG, while addition of PVP to CBZ/SSG agglomerates led to reduction in the release rate of CBZ even below that of the conventional drug crystals. SC process can be considered as a suitable alternative to conventional granulation process to obtain agglomerates of CBZ with excipients with improved micromeritic properties and modified dissolution rate. PMID:20175665
Solving Upwind-Biased Discretizations. 2; Multigrid Solver Using Semicoarsening
NASA Technical Reports Server (NTRS)
Diskin, Boris
1999-01-01
This paper studies a novel multigrid approach to the solution for a second order upwind biased discretization of the convection equation in two dimensions. This approach is based on semi-coarsening and well balanced explicit correction terms added to coarse-grid operators to maintain on coarse-grid the same cross-characteristic interaction as on the target (fine) grid. Colored relaxation schemes are used on all the levels allowing a very efficient parallel implementation. The results of the numerical tests can be summarized as follows: 1) The residual asymptotic convergence rate of the proposed V(0, 2) multigrid cycle is about 3 per cycle. This convergence rate far surpasses the theoretical limit (4/3) predicted for standard multigrid algorithms using full coarsening. The reported efficiency does not deteriorate with increasing the cycle, depth (number of levels) and/or refining the target-grid mesh spacing. 2) The full multi-grid algorithm (FMG) with two V(0, 2) cycles on the target grid and just one V(0, 2) cycle on all the coarse grids always provides an approximate solution with the algebraic error less than the discretization error. Estimates of the total work in the FMG algorithm are ranged between 18 and 30 minimal work units (depending on the target (discretizatioin). Thus, the overall efficiency of the FMG solver closely approaches (if does not achieve) the goal of the textbook multigrid efficiency. 3) A novel approach to deriving a discrete solution approximating the true continuous solution with a relative accuracy given in advance is developed. An adaptive multigrid algorithm (AMA) using comparison of the solutions on two successive target grids to estimate the accuracy of the current target-grid solution is defined. A desired relative accuracy is accepted as an input parameter. The final target grid on which this accuracy can be achieved is chosen automatically in the solution process. the actual relative accuracy of the discrete solution approximation
Kinetic energy density and agglomerate abrasion rate during blending of agglomerates into powders.
Willemsz, Tofan A; Hooijmaijers, Ricardo; Rubingh, Carina M; Tran, Thanh N; Frijlink, Henderik W; Vromans, Herman; van der Voort Maarschalk, Kees
2012-01-23
Problems related to the blending of a cohesive powder with a free flowing bulk powder are frequently encountered in the pharmaceutical industry. The cohesive powder often forms lumps or agglomerates which are not dispersed during the mixing process and are therefore detrimental to blend uniformity. Achieving sufficient blend uniformity requires that the blending conditions are able to break up agglomerates, which is often an abrasion process. This study was based on the assumption that the abrasion rate of agglomerates determines the required blending time. It is shown that the kinetic energy density of the moving powder bed is a relevant parameter which correlates with the abrasion rate of agglomerates. However, aspects related to the strength of agglomerates should also be considered. For this reason the Stokes abrasion number (St(Abr)) has been defined. This parameter describes the ratio between the kinetic energy density of the moving powder bed and the work of fracture of the agglomerate. The St(Abr) number is shown to predict the abrasion potential of agglomerates in the dry-mixing process. It appeared possible to include effects of filler particle size and impeller rotational rate into this concept. A clear relationship between abrasion rate of agglomerates and the value of St(Abr) was demonstrated.
Agglomeration and defluidization in FBC of biomass fuels -- Mechanisms and measures for prevention
Nordin, A.; Oehman, M.; Skrifvars, B.J.; Hupa, M.
1996-12-31
The use of biomass fuels in fluidized bed combustion (FBC) and gasification (FBG) is becoming more important because of the environmental benefits associated with these fuel and processes. However, severe bed agglomeration and defluidization have been reported due to the special ash forming constituents of some biomass fuels. Previous results have indicated that this could possibly be prevented by intelligent fuel mixing. In the present work the mechanisms of bed agglomeration using two different biomass fuels as well as the mechanism of the prevention of agglomeration by co-combustion with coal (50/50 %{sub w}) were studied. Several repeated combustion tests with the two biomass fuels, alone (Lucerne and olive flesh), all resulted in agglomeration and defluidization of the bed within less than 30 minutes. By controlled defluidization experiments the initial cohesion temperatures for the two fuels were determined to be as low as 670 C and 940 C, respectively. However, by fuel mixing the initial agglomeration temperature increased to 950 C and more than 1050 C, respectively. When co-combusted with coal during ten hour extended runs, no agglomeration was observed for either of the two fuel mixtures. The agglomeration temperatures were compared with results from a laboratory method, based on compression strength measurements of ash pellets, and results from chemical equilibrium calculations. Samples of bed materials, collected throughout the experimental runs, as well as the produced agglomerated beds, were analyzed using SEM EDS and X-ray diffraction. The results showed that loss of fluidization resulted from formation of molten phases coating the bed materials; a salt melt in the case of Lucerne and a silicate melt in the case of the olive fuel. By fuel mixing, the in-bed ash composition is altered, conferring higher melting temperatures, and thereby agglomeration and defluidization can be prevented.
Physical properties of soils in Rostov agglomeration
NASA Astrophysics Data System (ADS)
Gorbov, S. N.; Bezuglova, O. S.; Abrosimov, K. N.; Skvortsova, E. B.; Tagiverdiev, S. S.; Morozov, I. V.
2016-08-01
Physical properties of natural and anthropogenically transformed soils of Rostov agglomeration were examined. The data obtained by conventional methods and new approaches to the study of soil physical properties (in particular, tomographic study of soil monoliths) were used for comparing the soils of different functional zones of the urban area. For urban territories in the steppe zone, a comparison of humus-accumulative horizons (A, Asod, Ap, and buried [A] horizons) made it possible to trace tendencies of changes in surface soils under different anthropogenic impacts and in the buried and sealed soils. The microtomographic study demonstrated differences in the bulk density and aggregation of urban soils from different functional zones. The A horizon in the forest-park zone is characterized by good aggregation and high porosity, whereas buried humus-accumulative horizons of anthropogenically transformed soils are characterized by poor aggregation and low porosity. The traditional parameters of soil structure and texture also proved to be informative for the identification of urban pedogenesis.
Higher-order ice-sheet modelling accelerated by multigrid on graphics cards
NASA Astrophysics Data System (ADS)
Brædstrup, Christian; Egholm, David
2013-04-01
Higher-order ice flow modelling is a very computer intensive process owing primarily to the nonlinear influence of the horizontal stress coupling. When applied for simulating long-term glacial landscape evolution, the ice-sheet models must consider very long time series, while both high temporal and spatial resolution is needed to resolve small effects. The use of higher-order and full stokes models have therefore seen very limited usage in this field. However, recent advances in graphics card (GPU) technology for high performance computing have proven extremely efficient in accelerating many large-scale scientific computations. The general purpose GPU (GPGPU) technology is cheap, has a low power consumption and fits into a normal desktop computer. It could therefore provide a powerful tool for many glaciologists working on ice flow models. Our current research focuses on utilising the GPU as a tool in ice-sheet and glacier modelling. To this extent we have implemented the Integrated Second-Order Shallow Ice Approximation (iSOSIA) equations on the device using the finite difference method. To accelerate the computations, the GPU solver uses a non-linear Red-Black Gauss-Seidel iterator coupled with a Full Approximation Scheme (FAS) multigrid setup to further aid convergence. The GPU finite difference implementation provides the inherent parallelization that scales from hundreds to several thousands of cores on newer cards. We demonstrate the efficiency of the GPU multigrid solver using benchmark experiments.
Multitasked embedded multigrid for three-dimensional flow simulation. Final report
Johnson, G.M.; Swisshelm, J.M.; Pryor, D.V.; Ziebarth, J.P.
1986-06-01
This project explored fast algorithms for Euler and Navier-Stokes simulations. A particular issue pursued under the grant was the integration of an explicit three dimensional flow solver, embedded mesh refinements, a model equation hierarchy, multiple grid acceleration and extensive rectorization and multi tasking. Several papers were produced during this effort including such titles as Multitasked embedded multigrid for three-dimensional flow simulation and Multigrid approaches to the Euler equations. An efficient algorithm designed to be used for Navier-Stokes simulations of complex flows over complete configurations is described. The algorithm incorporates a number of elements, including an explicit three-dimensional flow solver, embedded mesh refinements, a model equation hierarchy ranging from the Euler equations through the full Navier-Stokes equations, multiple-grid convergence acceleration and extensive vectorization and multitasking for efficient execution on parallel-processing supercomputers. Results are presented for a preliminary trial of the method on a problem representative of turbomachinery applications. Based on this performance data, it is estimated that a mature implementation of the algorithm will yield overall speedups ranging as high as 100.
Linear Multigrid Techniques in Self-consistent Electronic Structure Calculations
Fattebert, J-L
2000-05-23
Ab initio DFT electronic structure calculations involve an iterative process to solve the Kohn-Sham equations for an Hamiltonian depending on the electronic density. We discretize these equations on a grid by finite differences. Trial eigenfunctions are improved at each step of the algorithm using multigrid techniques to efficiently reduce the error at all length scale, until self-consistency is achieved. In this paper we focus on an iterative eigensolver based on the idea of inexact inverse iteration, using multigrid as a preconditioner. We also discuss how this technique can be used for electrons described by general non-orthogonal wave functions, and how that leads to a linear scaling with the system size for the computational cost of the most expensive parts of the algorithm.
Scaling Algebraic Multigrid Solvers: On the Road to Exascale
Baker, A H; Falgout, R D; Gamblin, T; Kolev, T; Schulz, M; Yang, U M
2010-12-12
Algebraic Multigrid (AMG) solvers are an essential component of many large-scale scientific simulation codes. Their continued numerical scalability and efficient implementation is critical for preparing these codes for exascale. Our experiences on modern multi-core machines show that significant challenges must be addressed for AMG to perform well on such machines. We discuss our experiences and describe the techniques we have used to overcome scalability challenges for AMG on hybrid architectures in preparation for exascale.
Implicit method for the computation of unsteady flows on unstructured grids
NASA Technical Reports Server (NTRS)
Venkatakrishnan, V.; Mavriplis, D. J.
1995-01-01
An implicit method for the computation of unsteady flows on unstructured grids is presented. Following a finite difference approximation for the time derivative, the resulting nonlinear system of equations is solved at each time step by using an agglomeration multigrid procedure. The method allows for arbitrarily large time steps and is efficient in terms of computational effort and storage. Inviscid and viscous unsteady flows are computed to validate the procedure. The issue of the mass matrix which arises with vertex-centered finite volume schemes is addressed. The present formulation allows the mass matrix to be inverted indirectly. A mesh point movement and reconnection procedure is described that allows the grids to evolve with the motion of bodies. As an example of flow over bodies in relative motion, flow over a multi-element airfoil system undergoing deployment is computed.
Implicit method for the computation of unsteady flows on unstructured grids
Venkatakrishnan, V.; Mavriplis, D.J.
1996-09-01
An implicit method for the computation of unsteady flows on unstructured grids is presented. Following a finite difference approximation for the time derivative, the resulting nonlinear system of equations is solved at each time step by using an agglomeration multigrid procedure. The method allows for arbitrarily large time steps and is efficient in terms of computational effort and storage. Inviscid and viscous unsteady flows are computed to validate the procedure. The issue of the mass matrix which arises with vertex-centered finite volume schemes is addressed. The present formulation allows the mass matrix to be inverted indirectly. A mesh point movement and reconnection procedure is described that allows the grids to evolve with the motion of bodies. As an example of flow over bodies in relative motion, flow over a multi-element airfoil system undergoing deployment is computed. 48 refs., 24 figs.
Bipolar charged aerosol agglomeration and collection by a two-zone agglomerator.
Xiang, X D; Chen, B Z; Colbeck, I
2001-07-01
In older to collect fine particles more efficiently, a new-type electrostatic agglomerator with two zones was developed. The distinguishing feature of this electrostatic agglomerator is that the particles are bipolarly charged and coagulated in the same alternating electric field simultaneously. The silica flour with 2 microns mass median diameter and the smoke from burning wood powder were used as test aerosol. The comparison experimental results have shown that when the mean electric field is 4 kV/cm the collection efficiency of the new electrostatic agglomerator was 98.2% for silica flour and 67.4% for wood powder smoke. Under the same experimental condition, the collection efficiency of the electrostatic agglomerator with three zones was 97.4% for collecting silica flour and the collection efficiency of the electrostatic precipitator was 56.3% for wood powder smoke.
The analysis of multigrid algorithms for pseudodifferential operators of order minus one
Bramble, J.H.; Leyk, Z.; Pasciak, J.E. ||
1994-10-01
Multigrid algorithms are developed to solve the discrete systems approximating the solutions of operator equations involving pseudodifferential operators of order minus one. Classical multigrid theory deals with the case of differential operators of positive order. The pseudodifferential operator gives rise to a coercive form on H{sup {minus}1/2}({Omega}). Effective multigrid algorithms are developed for this problem. These algorithms are novel in that they use the inner product on H{sup {minus}1}({Omega}) as a base inner product for the multigrid development. The authors show that the resulting rate of iterative convergence can, at worst, depend linearly on the number of levels in these novel multigrid algorithms. In addition, it is shown that the convergence rate is independent of the number of levels (and unknowns) in the case of a pseudodifferential operator defined by a single-layer potential. Finally, the results of numerical experiments illustrating the theory are presented. 19 refs., 1 fig., 2 tabs.
Laakso, Ilkka; Hirata, Akimasa
2012-12-01
In transcranial magnetic stimulation (TMS), the distribution of the induced electric field, and the affected brain areas, depends on the position of the stimulation coil and the individual geometry of the head and brain. The distribution of the induced electric field in realistic anatomies can be modelled using computational methods. However, existing computational methods for accurately determining the induced electric field in realistic anatomical models have suffered from long computation times, typically in the range of tens of minutes or longer. This paper presents a matrix-free implementation of the finite-element method with a geometric multigrid method that can potentially reduce the computation time to several seconds or less even when using an ordinary computer. The performance of the method is studied by computing the induced electric field in two anatomically realistic models. An idealized two-loop coil is used as the stimulating coil. Multiple computational grid resolutions ranging from 2 to 0.25 mm are used. The results show that, for macroscopic modelling of the electric field in an anatomically realistic model, computational grid resolutions of 1 mm or 2 mm appear to provide good numerical accuracy compared to higher resolutions. The multigrid iteration typically converges in less than ten iterations independent of the grid resolution. Even without parallelization, each iteration takes about 1.0 s or 0.1 s for the 1 and 2 mm resolutions, respectively. This suggests that calculating the electric field with sufficient accuracy in real time is feasible.
NASA Technical Reports Server (NTRS)
Woods, Claudia M.; Brewe, David E.
1988-01-01
A numerical solution to a theoretical model of vapor cavitation in a dynamically loaded journal bearing is developed utilizing a multigrid iteration technique. The method is compared with a noniterative approach in terms of computational time and accuracy. The computational model is based on the Elrod algorithm, a control volume approach to the Reynolds equation which mimics the Jakobsson-Floberg and Olsson cavitation theory. Besides accounting for a moving cavitation boundary and conservation of mass at the boundary, it also conserves mass within the cavitated region via a smeared mass or striated flow extending to both surfaces in the film gap. The mixed nature of the equations (parabolic in the full film zone and hyperbolic in the cavitated zone) coupled with the dynamic aspects of the problem create interesting difficulties for the present solution approach. Emphasis is placed on the methods found to eliminate solution instabilities. Excellent results are obtained for both accuracy and reduction of computational time.
NASA Technical Reports Server (NTRS)
Woods, C. M.; Brewe, D. E.
1989-01-01
A numerical solution to a theoretical model of vapor cavitation in a dynamically loaded journal bearing is developed utilizing a multigrid iteration technique. The method is compared with a noniterative approach in terms of computational time and accuracy. The computational model is based on the Elrod algorithm, a control volume approach to the Reynolds equation which mimics the Jakobsson-Floberg and Olsson cavitation theory. Besides accounting for a moving cavitation boundary and conservation of mass at the boundary, it also conserves mass within the cavitated region via a smeared mass or striated flow extending to both surfaces in the film gap. The mixed nature of the equations (parabolic in the full film zone and hyperbolic in the cavitated zone) coupled with the dynamic aspects of the problem create interesting difficulties for the present solution approach. Emphasis is placed on the methods found to eliminate solution instabilities. Excellent results are obtained for both accuracy and reduction of computational time.
Color image segmentation by the vector-valued Allen-Cahn phase-field model: a multigrid solution.
Kay, David A; Tomasi, Alessandro
2009-10-01
We present an efficient numerical solution of a PDE-driven model for color image segmentation and give numerical examples of the results. The method combines the vector-valued Allen-Cahn phase field equation with initial data fitting terms with prescribed interface width and fidelity constants. Efficient numerical solution is achieved using a multigrid splitting of a finite element space, thereby producing an efficient and robust method for the segmentation of large images. We also present the use of adaptive mesh refinement to further speed up the segmentation process.
Multigrid computations of unsteady rotor-stator interaction using the Navier-Stokes equations
Arnone, A.; Sestini, A.; Pacciani, R.
1995-12-01
A Navier-Stokes time-accurate solver has been extended to the analysis of unsteady rotor-stator interaction. In the proposed method, a fully-implicit time discretization is used to remove stability limitations. A four-stage Runge-Kutta scheme is used in conjunction with several accelerating techniques typical of steady-state solvers, instead of traditional time-expensive factorizations. Those accelerating strategies include local time stepping, residual smoothing, and multigrid. Direct interpolation of the conservative variables is used to handle the interfaces between blade rows. Two-dimensional viscous calculations of unsteady rotor-stator interaction in a modern gas turbine stage are presented to check for the capability of the procedure.
A quadtree-adaptive multigrid solver for the Serre-Green-Naghdi equations
NASA Astrophysics Data System (ADS)
Popinet, Stéphane
2015-12-01
The Serre-Green-Naghdi (SGN) equations, also known as the fully-nonlinear Boussinesq wave equations, accurately describe the behaviour of dispersive shoaling water waves. This article presents and validates a novel combination of methods for the numerical approximation of solutions to the SGN equations. The approach preserves the robustness of the original finite-volume Saint-Venant solver, in particular for the treatment of wetting/drying and equilibrium states. The linear system of coupled vector equations governing the dispersive SGN momentum sources is solved simply and efficiently using a generic multigrid solver. This approach generalises automatically to adaptive quadtree meshes. Adaptive mesh refinement is shown to provide orders-of-magnitude gains in speed and memory when applied to the dispersive propagation of waves during the Tohoku tsunami. The source code, test cases and examples are freely available.
Implicit/Multigrid Algorithms for Incompressible Turbulent Flows on Unstructured Grids
NASA Technical Reports Server (NTRS)
Anderson, W. Kyle; Rausch, Russ D.; Bonhaus, Daryl L.
1997-01-01
An implicit code for computing inviscid and viscous incompressible flows on unstructured grids is described. The foundation of the code is a backward Euler time discretization for which the linear system is approximately solved at each time step with either a point implicit method or a preconditioned Generalized Minimal Residual (GMRES) technique. For the GMRES calculations, several techniques are investigated for forming the matrix-vector product. Convergence acceleration is achieved through a multigrid scheme that uses non-nested coarse grids that are generated using a technique described in the present paper. Convergence characteristics are investigated and results are compared with an exact solution for the inviscid flow over a four-element airfoil. Viscous results, which are compared with experimental data, include the turbulent flow over a NACA 4412 airfoil, a three-element airfoil for which Mach number effects are investigated, and three-dimensional flow over a wing with a partial-span flap.
Fast multigrid solution of the advection problem with closed characteristics
Yavneh, I.; Venner, C.H.; Brandt, A.
1996-12-31
The numerical solution of the advection-diffusion problem in the inviscid limit with closed characteristics is studied as a prelude to an efficient high Reynolds-number flow solver. It is demonstrated by a heuristic analysis and numerical calculations that using upstream discretization with downstream relaxation-ordering and appropriate residual weighting in a simple multigrid V cycle produces an efficient solution process. We also derive upstream finite-difference approximations to the advection operator, whose truncation terms approximate {open_quotes}physical{close_quotes} (Laplacian) viscosity, thus avoiding spurious solutions to the homogeneous problem when the artificial diffusivity dominates the physical viscosity.
Development of a Gas-Promoted Oil Agglomeration Process
C. Nelson; F. Zhang; J. Drzymala; M. Shen; R. Abbott; T. D. Wheelock
1997-11-01
The preliminary laboratory-scale development of a gas-promoted, oil agglomeration process for cleaning coal was carried out with scale model mixing systems in which aqueous suspensions of ultrafine coal particles were treated with a liquid hydrocarbon and a small amount of air. The resulting agglomerates were recovered by screening. During a batch agglomeration test the progress of agglomeration was monitored by observing changes in agitator torque in the case of concentrated suspensions or by observing changes in turbidity in the case of dilute suspensions. Dilute suspensions were employed for investigating the kinetics of agglomeration, whereas concentrated suspensions were used for determining parameters that characterize the process of agglomeration. A key parameter turned out to be the minimum time te required to produce compact spherical agglomerates. Other important parameters included the projected area mean particle diameter of the agglomerates recovered at the end of a test as well as the ash content and yield of agglomerates. Batch agglomeration tests were conducted with geometrically similar mixing tanks which ranged in volume from 0.346 to 11.07 liters. Each tank was enclosed to control the amount of air present. A variable speed agitator fitted with a six blade turbine impeller was used for agitation. Tests were conducted with moderately hydrophobic Pittsburgh No. 8 coal and with more hydrophobic Upper Freeport coal using either n-heptane, i-octane, or hexadecane as an agglomerant.
NASA Astrophysics Data System (ADS)
Bauer, Petr; Klement, Vladimír; Oberhuber, Tomáš; Žabka, Vítězslav
2016-03-01
We present a complete GPU implementation of a geometric multigrid solver for the numerical solution of the Navier-Stokes equations for incompressible flow. The approximate solution is constructed on a two-dimensional unstructured triangular mesh. The problem is discretized by means of the mixed finite element method with semi-implicit timestepping. The linear saddle-point problem arising from the scheme is solved by the geometric multigrid method with a Vanka-type smoother. The parallel solver is based on the red-black coloring of the mesh triangles. We achieved a speed-up of 11 compared to a parallel (4 threads) code based on OpenMP and 19 compared to a sequential code.
Transport and Deposition of Welding Fume Agglomerates in a Realistic Human Nasal Airway.
Tian, Lin; Inthavong, Kiao; Lidén, Göran; Shang, Yidan; Tu, Jiyuan
2016-07-01
Welding fume is a complex mixture containing ultra-fine particles in the nanometer range. Rather than being in the form of a singular sphere, due to the high particle concentration, welding fume particles agglomerate into long straight chains, branches, or other forms of compact shapes. Understanding the transport and deposition of these nano-agglomerates in human respiratory systems is of great interest as welding fumes are a known health hazard. The neurotoxin manganese (Mn) is a common element in welding fumes. Particulate Mn, either as soluble salts or oxides, that has deposited on the olfactory mucosa in human nasal airway is transported along the olfactory nerve to the olfactory bulb within the brain. If this Mn is further transported to the basal ganglia of the brain, it could accumulate at the part of the brain that is the focal point of its neurotoxicity. Accounting for various dynamic shape factors due to particle agglomeration, the current computational study is focused on the exposure route, the deposition pattern, and the deposition efficiency of the inhaled welding fume particles in a realistic human nasal cavity. Particular attention is given to the deposition pattern and deposition efficiency of inhaled welding fume agglomerates in the nasal olfactory region. For particles in the nanoscale, molecular diffusion is the dominant transport mechanism. Therefore, Brownian diffusion, hydrodynamic drag, Saffman lift force, and gravitational force are included in the model study. The deposition efficiencies for single spherical particles, two kinds of agglomerates of primary particles, two-dimensional planar and straight chains, are investigated for a range of primary particle sizes and a range of number of primary particles per agglomerate. A small fraction of the inhaled welding fume agglomerates is deposited on the olfactory mucosa, approximately in the range 0.1-1%, and depends on particle size and morphology. The strong size dependence of the deposition
Ayhan, F.D.
2009-11-15
The aim of this study was to investigate desulfurization and de-ashing of a mixture of subbituminous coal and gangue minerals by the agglomeration method. For this purpose, experimental studies were conducted on a mixture containing subbituminous coal, pyrite, quartz and calcite. The effects of some parameters that markedly influence the effectiveness of selective oil agglomeration, such as solid concentration, pH, bridging liquid type and concentration, and depressant type and amount, were investigated. Agglomeration results showed that the usage of various depressants (Na{sub 2}SiO{sub 3}, FeCl3, corn starch, wheat starch) in the agglomeration medium has a positive effect on the reduction of ash and total sulfur content of agglomerates. It was found that an agglomerate product containing 3.03% total sulfur and 25.01% ash with a total sulfur reduction of 56.71% was obtained from a feed that contained 7% total sulfur and 43.58% ash when FeCl{sub 3} was used in the agglomeration medium.
Domain decomposition multigrid for unstructured grids
Shapira, Yair
1997-01-01
A two-level preconditioning method for the solution of elliptic boundary value problems using finite element schemes on possibly unstructured meshes is introduced. It is based on a domain decomposition and a Galerkin scheme for the coarse level vertex unknowns. For both the implementation and the analysis, it is not required that the curves of discontinuity in the coefficients of the PDE match the interfaces between subdomains. Generalizations to nonmatching or overlapping grids are made.
Identification of micro parameters for discrete element simulation of agglomerates
NASA Astrophysics Data System (ADS)
Palis, Stefan; Antonyuk, Sergiy; Dosta, Maksym; Heinrich, Stefan
2013-06-01
The mechanical behaviour of solid particles like agglomerates, granules or crystals strongly depends on their micro structure, e.g. structural defects and porosity. In order to model the mechanical behaviour of these inhomogeneous media the discrete element method has been proven to be an appropriate tool. The model parameters used are typically micro parameters like bond stiffness, particle-particle contact stiffness, strength of the bonds. Due to the lack of general methods for a direct micro parameter determination, normally laborious parameter adaptation has to be done in order to fit experiment and simulation. In this contribution a systematic and automatic way for parameter adaptation using real experiments is proposed. Due to the fact, that discrete element models are typically systems of differential equations of very high order, gradient based methods are not suitable. Hence, the focus will be on derivative free methods.
Chemiluminescence in the Agglomeration of Metal Clusters
König; Rabin; Schulze; Ertl
1996-11-22
The agglomeration of copper or silver atoms in a matrix of noble gas atoms to form small clusters may be accompanied by the emission of visible light. Spectral analysis reveals the intermediate formation of electronically excited atoms and dimers as the source of the chemiluminescence. A mechanism is proposed, according to which the gain in binding energy upon cluster formation may even lead to the ejection of excited fragments as a result of unstable intermediate configurations. A similar concept was introduced in the field of nuclear reactions by Niels Bohr 60 years ago.
Agglomeration defects on irradiated carbon nanotubes
Steini Moura, Cassio; Balzaretti, Naira Maria; Amaral, Livio; Gribel Lacerda, Rodrigo; Pimenta, Marcos A.
2012-03-15
Aligned carbon nanotubes (CNT) were irradiated in the longitudinal and perpendicular directions, with low energy carbon and helium ions in order to observe the formation of defects in the atomic structure. Analysis through Raman spectroscopy and scanning electron microscopy indicated bundle rupture and ion track formation on nanotube bundles. Aligned CNT presented a kind of defect comprising ravine formation and tube agglomeration on top of the substrate. The latter structure is possibly caused by static charge accumulation induced by the incoming ions. Fluence plays a role on the short range order. Higher fluence irradiation transforms CNT into amorphous carbon nanowires.
Efficient Implementation of Multigrid Solvers on Message-Passing Parrallel Systems
NASA Technical Reports Server (NTRS)
Lou, John
1994-01-01
We discuss our implementation strategies for finite difference multigrid partial differential equation (PDE) solvers on message-passing systems. Our target parallel architecture is Intel parallel computers: the Delta and Paragon system.
Multifrequency scanning probe microscopy study of nanodiamond agglomerates
NASA Astrophysics Data System (ADS)
Aravind, Vasudeva; Lippold, Stephen; Li, Qian; Strelcov, Evgheny; Okatan, Baris; Legum, Benjamin; Kalinin, Sergei; Clarion University Team; Oak Ridge National Laboratory Team
Due to their rich surface chemistry and excellent mechanical properties and non-toxic nature, nanodiamond particles have found applications such as biomedicine, tribology and lubrication, targeted drug delivery systems, tissue scaffolds and surgical implants. Although single nanodiamond particles have diameters about 4-5nm, they tend to form agglomerates. While these agglomerates can be useful for some purposes, many applications of nanodiamonds require single particle, disaggregated nanodiamonds. This work is oriented towards studying forces and interactions that contribute to agglomeration in nanodiamonds. In this work, using multifrequency scanning probe microscopy techniques, we show that agglomerate sizes can vary between 50-100nm in raw nanodiamonds. Extremeties of particles and Interfaces between agglomerates show dissipative forces with scanning probe microscope tip, indicating agglomerates could act as points of increased adhesion, thus reducing lubricating efficiency when nanodiamonds are used as lubricant additives. This research was conducted at the Center for Nanophase Materials Sciences, which is a DOE Office of Science User Facility.
MULTIGRID FOR THE MORTAR FINITE ELEMENT METHOD. (R825207)
The perspectives, information and conclusions conveyed in research project abstracts, progress reports, final reports, journal abstracts and journal publications convey the viewpoints of the principal investigator and may not represent the views and policies of ORD and EPA. Concl...
MULTIGRID HOMOGENIZATION OF HETEROGENEOUS POROUS MEDIA
Dendy, J.E.; Moulton, J.D.
2000-10-01
This is the final report of a three-year, Laboratory-Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL); this report, however, reports on only two years research, since this project was terminated at the end of two years in response to the reduction in funding for the LDRD Program at LANL. The numerical simulation of flow through heterogeneous porous media has become a vital tool in forecasting reservoir performance, analyzing groundwater supply and predicting the subsurface flow of contaminants. Consequently, the computational efficiency and accuracy of these simulations is paramount. However, the parameters of the underlying mathematical models (e.g., permeability, conductivity) typically exhibit severe variations over a range of significantly different length scales. Thus the numerical treatment of these problems relies on a homogenization or upscaling procedure to define an approximate coarse-scale problem that adequately captures the influence of the fine-scale structure, with a resultant compromise between the competing objectives of computational efficiency and numerical accuracy. For homogenization in models of flow through heterogeneous porous media, We have developed new, efficient, numerical, multilevel methods, that offer a significant improvement in the compromise between accuracy and efficiency. We recently combined this approach with the work of Dvorak to compute bounded estimates of the homogenized permeability for such flows and demonstrated the effectiveness of this new algorithm with numerical examples.
Direct preparation of spherically agglomerated salicylic acid crystals during crystallization.
Kawashima, Y; Okumura, M; Takenaka, H; Kojima, A
1984-11-01
Needle-like salicylic acid crystals were transformed into a spherically shaped dense form during crystallization by the spherical crystallization technique. Agitation of a mixture of ethanol-water-chloroform containing salicylic acid yielded spherically agglomerated salicylic acid crystals. The crystallinity of the agglomerated salicylic acid the amount of ethanol in the solvent mixture was decreased. The wettability of the agglomerated crystals increased when the amount of ethanol in the solvent mixture was decreased, and this enhanced the dissolution rate of the crystals. The remarkable improvements in the flow and packing of the agglomerated crystals enabled the direct compression of the crystals.
Modeling of crushed ore agglomeration for heap leach operations
NASA Astrophysics Data System (ADS)
Dhawan, Nikhil
The focus of this dissertation is modeling of the evolution of size distribution in batch agglomeration drum. There has been no successful work on modeling of crushed ore agglomeration although the framework for population balance modeling of pelletization and granulation is readily available. In this study three different batch agglomeration drums were used to study the agglomeration kinetics of copper, gold and nickel ores. The agglomerate size distribution is inherently subject to random fluctuation due the very nature of the process. Yet, with careful experimentation and size analysis the evolution of size distribution can be followed. The population balance model employing the random coalesce model with a constant rate kernel was shown to work well in a micro and lab scale agglomerator experiments. In small drums agglomerates begin to break in a short time, whereas the growth is uniform in the lab scale drum. The experimental agglomerate size distributions exhibit self-preserving size spectra which confirms the applicability of coalescence rate based model. The same spectra became a useful fact for predicting the size distribution with an empirical model. Since moisture is a principal variable, the absolute deviation from optimum moisture was used as the primary variable in the empirical model. Having established a model for the size distribution, the next step was to delve into the internal constituents of each agglomerate size class. To this end, an experimental scheme known as dip test was devised. The outcome of the test was the size distribution of progeny particles which make up a given size class of agglomerate. The progeny size distribution was analyzed with a model that partitions the particles into a host and guest category. The ensuing partition coefficient is a valuable in determining how a particle in a size class participates in larger agglomerates. This dissertation lays out the fundamentals for applying the population balance concept to batch
Adaptive multigrid domain decomposition solutions for viscous interacting flows
NASA Technical Reports Server (NTRS)
Rubin, Stanley G.; Srinivasan, Kumar
1992-01-01
Several viscous incompressible flows with strong pressure interaction and/or axial flow reversal are considered with an adaptive multigrid domain decomposition procedure. Specific examples include the triple deck structure surrounding the trailing edge of a flat plate, the flow recirculation in a trough geometry, and the flow in a rearward facing step channel. For the latter case, there are multiple recirculation zones, of different character, for laminar and turbulent flow conditions. A pressure-based form of flux-vector splitting is applied to the Navier-Stokes equations, which are represented by an implicit lowest-order reduced Navier-Stokes (RNS) system and a purely diffusive, higher-order, deferred-corrector. A trapezoidal or box-like form of discretization insures that all mass conservation properties are satisfied at interfacial and outflow boundaries, even for this primitive-variable, non-staggered grid computation.
Pauli-Bruns, Anette; Knop, Klaus; Lippold, Bernhard C
2010-03-01
The one-step preparation of sustained release matrix pellets, using a melting procedure in a fluidized bed apparatus, was tested in a 2(3) full factorial design of experiments, using microcrystalline wax as lipophilic binder, theophylline as model drug and talc as additional matrix forming agent. The three influence parameters were (A) size of binder particles, (B) fraction of theophylline in solid particles and (C) fraction of microcrystalline wax in formulation. The response variables were agglomerate size and size distribution, dissolution time, agglomerate crush resistance, sphericity, yield and porosity. Nearly spherical pellets comprising a smooth, closed surface could be obtained with the used method, exhibiting the hollow core typical for the immersion and layering mechanism. The reproducibility was very good concerning all responses. The size of agglomerates is proportional to the size of the binder particles, which serve as cores for pellet formation in the molten state in the fluidized bed. Additionally, the agglomerate size is influenced by the volume of the solid particles in relation to the binder particles, with more solid particles leading to larger agglomerates and vice versa. Dissolution times vary in a very wide range, resulting from the interplay between amount of drug in relation to the meltable matrix substance microcrystalline wax and the non-meltable matrix substance talc. The change of binder particle size does not lead to a structural change of the matrix; both dissolution times and porosity are not significantly altered. Agglomerate crush resistance is low due to the hollow core of the pellets. However, it is significantly increased if the volume fraction of microcrystalline wax in the matrix is high, which means that the matrix is mechanically better stabilized. A theoretical model has been established to quantitatively explain agglomerate growth and very good accordance of the full particle size distributions between predicted and
NASA Astrophysics Data System (ADS)
Kojima, A.; Hanada, M.; Tobari, H.; Nishikiori, R.; Hiratsuka, J.; Kashiwagi, M.; Umeda, N.; Yoshida, M.; Ichikawa, M.; Watanabe, K.; Yamano, Y.; Grisham, L. R.
2016-02-01
Design techniques for the vacuum insulation have been developed in order to realize a reliable voltage holding capability of multi-aperture multi-grid (MAMuG) accelerators for fusion application. In this method, the nested multi-stage configuration of the MAMuG accelerator can be uniquely designed to satisfy the target voltage within given boundary conditions. The evaluation of the voltage holding capabilities of each acceleration stages was based on the previous experimental results about the area effect and the multi-aperture effect. Since the multi-grid effect was found to be the extension of the area effect by the total facing area this time, the total voltage holding capability of the multi-stage can be estimated from that per single stage by assuming the stage with the highest electric field, the total facing area, and the total apertures. By applying these consideration, the analysis on the 3-stage MAMuG accelerator for JT-60SA agreed well with the past gap-scan experiments with an accuracy of less than 10% variation, which demonstrated the high reliability to design MAMuG accelerators and also multi-stage high voltage bushings.
Kojima, A; Hanada, M; Tobari, H; Nishikiori, R; Hiratsuka, J; Kashiwagi, M; Umeda, N; Yoshida, M; Ichikawa, M; Watanabe, K; Yamano, Y; Grisham, L R
2016-02-01
Design techniques for the vacuum insulation have been developed in order to realize a reliable voltage holding capability of multi-aperture multi-grid (MAMuG) accelerators for fusion application. In this method, the nested multi-stage configuration of the MAMuG accelerator can be uniquely designed to satisfy the target voltage within given boundary conditions. The evaluation of the voltage holding capabilities of each acceleration stages was based on the previous experimental results about the area effect and the multi-aperture effect. Since the multi-grid effect was found to be the extension of the area effect by the total facing area this time, the total voltage holding capability of the multi-stage can be estimated from that per single stage by assuming the stage with the highest electric field, the total facing area, and the total apertures. By applying these consideration, the analysis on the 3-stage MAMuG accelerator for JT-60SA agreed well with the past gap-scan experiments with an accuracy of less than 10% variation, which demonstrated the high reliability to design MAMuG accelerators and also multi-stage high voltage bushings.
Kojima, A; Hanada, M; Tobari, H; Nishikiori, R; Hiratsuka, J; Kashiwagi, M; Umeda, N; Yoshida, M; Ichikawa, M; Watanabe, K; Yamano, Y; Grisham, L R
2016-02-01
Design techniques for the vacuum insulation have been developed in order to realize a reliable voltage holding capability of multi-aperture multi-grid (MAMuG) accelerators for fusion application. In this method, the nested multi-stage configuration of the MAMuG accelerator can be uniquely designed to satisfy the target voltage within given boundary conditions. The evaluation of the voltage holding capabilities of each acceleration stages was based on the previous experimental results about the area effect and the multi-aperture effect. Since the multi-grid effect was found to be the extension of the area effect by the total facing area this time, the total voltage holding capability of the multi-stage can be estimated from that per single stage by assuming the stage with the highest electric field, the total facing area, and the total apertures. By applying these consideration, the analysis on the 3-stage MAMuG accelerator for JT-60SA agreed well with the past gap-scan experiments with an accuracy of less than 10% variation, which demonstrated the high reliability to design MAMuG accelerators and also multi-stage high voltage bushings. PMID:26932032
Molecular dynamics study of self-agglomeration of charged fullerenes in solvents.
Banerjee, Soumik
2013-01-28
The agglomeration of fullerenes in solvents is an important phenomenon that is relevant to controlled synthesis of fullerene-based nanowires as well as fullerene-based composites. The molecular aggregation in solvents depends on the atomistic interactions of fullerene with the solvent and is made complicated by the fact that fullerenes accrue negative surface charges when present in solvents such as water. In the present work, we simulated fullerenes of varying size and shape (C60, C180, C240, and C540) with and without surface charges in polar protic (water), polar aprotic (acetone), and nonpolar (toluene) solvents using molecular dynamics method. Our results demonstrate that uncharged fullerenes form agglomerates in polar solvents such as water and acetone and remain relatively dispersed in nonpolar toluene. The presence of surface charge significantly reduces agglomerate size in water and acetone. Additionally, the relative influence of surface charge on fullerene agglomeration depends on the size and geometry of the fullerene with larger fullerenes forming relatively smaller agglomerates. We evaluated the diffusion coefficients of solvent molecules within the solvation shell of fullerenes and observed that they are much lower than the bulk solvent and are strongly associated with the fullerenes as seen in the corresponding radial distribution functions. To correlate agglomerate size with the binding energy between fullerenes, we evaluated the potential of mean force between fullerenes in each solvent. Consistent with the solubility of fullerenes, binding energy between fullerenes is the greatest in water followed by acetone and toluene. The presence of charge decreases the binding energy of fullerenes in water and thus results in dispersed fullerenes.
Molecular dynamics study of self-agglomeration of charged fullerenes in solvents
NASA Astrophysics Data System (ADS)
Banerjee, Soumik
2013-01-01
The agglomeration of fullerenes in solvents is an important phenomenon that is relevant to controlled synthesis of fullerene-based nanowires as well as fullerene-based composites. The molecular aggregation in solvents depends on the atomistic interactions of fullerene with the solvent and is made complicated by the fact that fullerenes accrue negative surface charges when present in solvents such as water. In the present work, we simulated fullerenes of varying size and shape (C60, C180, C240, and C540) with and without surface charges in polar protic (water), polar aprotic (acetone), and nonpolar (toluene) solvents using molecular dynamics method. Our results demonstrate that uncharged fullerenes form agglomerates in polar solvents such as water and acetone and remain relatively dispersed in nonpolar toluene. The presence of surface charge significantly reduces agglomerate size in water and acetone. Additionally, the relative influence of surface charge on fullerene agglomeration depends on the size and geometry of the fullerene with larger fullerenes forming relatively smaller agglomerates. We evaluated the diffusion coefficients of solvent molecules within the solvation shell of fullerenes and observed that they are much lower than the bulk solvent and are strongly associated with the fullerenes as seen in the corresponding radial distribution functions. To correlate agglomerate size with the binding energy between fullerenes, we evaluated the potential of mean force between fullerenes in each solvent. Consistent with the solubility of fullerenes, binding energy between fullerenes is the greatest in water followed by acetone and toluene. The presence of charge decreases the binding energy of fullerenes in water and thus results in dispersed fullerenes.
Molecular dynamics study of self-agglomeration of charged fullerenes in solvents.
Banerjee, Soumik
2013-01-28
The agglomeration of fullerenes in solvents is an important phenomenon that is relevant to controlled synthesis of fullerene-based nanowires as well as fullerene-based composites. The molecular aggregation in solvents depends on the atomistic interactions of fullerene with the solvent and is made complicated by the fact that fullerenes accrue negative surface charges when present in solvents such as water. In the present work, we simulated fullerenes of varying size and shape (C60, C180, C240, and C540) with and without surface charges in polar protic (water), polar aprotic (acetone), and nonpolar (toluene) solvents using molecular dynamics method. Our results demonstrate that uncharged fullerenes form agglomerates in polar solvents such as water and acetone and remain relatively dispersed in nonpolar toluene. The presence of surface charge significantly reduces agglomerate size in water and acetone. Additionally, the relative influence of surface charge on fullerene agglomeration depends on the size and geometry of the fullerene with larger fullerenes forming relatively smaller agglomerates. We evaluated the diffusion coefficients of solvent molecules within the solvation shell of fullerenes and observed that they are much lower than the bulk solvent and are strongly associated with the fullerenes as seen in the corresponding radial distribution functions. To correlate agglomerate size with the binding energy between fullerenes, we evaluated the potential of mean force between fullerenes in each solvent. Consistent with the solubility of fullerenes, binding energy between fullerenes is the greatest in water followed by acetone and toluene. The presence of charge decreases the binding energy of fullerenes in water and thus results in dispersed fullerenes. PMID:23387595
Wheelock, T.D.
1994-10-01
During the first year of the project two model mixing systems, which differed in size but were similar in design, were constructed and tested. The systems were equipped for measuring agitator speed and torque and for measuring the turbidity of coal particle suspensions undergoing agglomeration. Preliminary measurements of aqueous suspensions of coal particles showed that the Beer-Lambert law applies to such suspensions at least for low concentrations. Therefore, the measured turbidity can be used as an indicator of particle concentration and a means for monitoring the progress of oil agglomeration. However, the method is not applicable for large particle concentrations so a different technique was tested for monitoring the agglomeration of large concentrations. This technique involves measuring agitator torque and observing changes in torque while agitator speed is held constant. The results of preliminary tests of the technique were encouraging. In these tests significant changes in agitator torque were observed when particle agglomeration took place as long as solids concentration of 25 w/v % or more were utilized. A number of agglomeration tests were conducted using either one or the other of the two monitoring techniques. Both methods showed that even very small amounts of air can promote the oil agglomeration of coal particles suspended in water. Even the amount of air dissolved in water at room temperature and pressure can affect the process providing the air is displaced from the solution by a slightly soluble agglomerant such as heptane. The apparent rate of agglomeration was observed to increase as more air was introduced and also as agitator speed was increased.
Pulse combusted acoustic agglomeration apparatus and process
Mansour, Momtaz N.; Chandran, Ravi
1994-01-01
An improved apparatus and process for removal of particulates entrained in a gas stream are provided. The removal process employs a pulse combustor to provide an acoustic pressure wave to acoustically enhance agglomeration of particulates which may be collected and removed using a conventional separation apparatus. The apparatus may be employed as a direct fired system for improved operation of gas-operated equipment such as a gas turbine, or may, alternatively, be employed as an add-on subsystem for combustion exhaust clean-up. Additionally, added particulates may include a sorbent for effecting sorption of other contaminants such as sulfur. Various other particulates for contaminant removal may also be introduced into the system as exemplified by alkali-gettering agents.
Pulse combusted acoustic agglomeration apparatus and process
Mansour, Momtaz N.
1993-01-01
An improved apparatus and process for removal of particulates entrained in a gas stream are provided. The removal process employs a pulse combustor to provide an acoustic pressure wave to acoustically enhance bimodal agglomeration of particulates which may be collected and removed using a conventional separation apparatus. A particulate having a size different from the size of the particulate in the gas stream to be cleaned is introduced into the system to effectuate the bimodal process. The apparatus may be employed as a direct fired system for improved operation of gas-operated equipment such as a gas turbine, or may, alternatively, be employed as an add-on subsystem for combustion exhaust clean-up. Additionally, the added particulate may be a sorbent for effecting sorption of other contaminants such as sulfur. Various other particulates for contaminant removal may also be introduced into the system as exemplified by alkali-gettering agents.
Innovations in thermoelectric materials research: Compound agglomeration, testing and preselection
NASA Astrophysics Data System (ADS)
Lopez de Cardenas, Hugo Francisco Lopez
Thermoelectric materials have the capacity to convert a temperature differential into electrical power and vice versa. They will represent the next revolution in alternative energies once their efficiencies are enhanced so they can complement other forms of green energies that depend on sources other than a temperature differential. Progress in materials science depends on the ability to discover new materials to eventually understand them and to finally improve their properties. The work presented here is aimed at dynamizing the screening of materials of thermoelectric interest. The results of this project will enable: theoretical preselection of thermoelectric compounds based on their bandgap and a rapid agglomeration method that does not require melting or sintering. A special interest will be given to Iodine-doped TiSe2 that generated extraordinary results and a new set of equations are proposed to accurately describe the dependence of the power factor and the figure of merit on the intrinsic properties of the materials.
Development of a Gas-Promoted Oil Agglomeration Process
M. Shen; T. D. Wheelock
1998-10-30
Further agglomeration tests were conducted in a series of tests designed to determine the effects of various parameters on the size and structure of the agglomerates formed, the rate of agglomeration, coal recovery, and ash rejection. For this series of tests, finely ground Pittsburgh No. 8 coal has been agglomerated with i-octane in a closed mixing system with a controlled amount of air present to promote particle agglomeration. The present results provide further evidence of the role played by air. As the concentration of air in the system was increased from 4.5 to 18 v/w% based on the weight of coal, coal recovery and ash rejection both increased. The results also show that coal recovery and ash rejection were improved by increasing agitator speed. On the other hand, coal recovery was not affected by a change in solids concentration from 20 to 30 w/w%.
Bed material agglomeration during fluidized bed combustion. Final report
Brown, R.C.; Dawson, M.R.; Smeenk, J.L.
1996-01-01
The purpose of this project is to determine the physical and chemical reactions which lead to the undesired agglomeration of bed material during fluidized bed combustion of coal and to relate these reactions to specific causes. A survey of agglomeration and deposit formation in industrial fluidized bed combustors (FBCs) indicate that at least five boilers were experiencing some form of bed material agglomeration. Deposit formation was reported at nine sites with deposits most commonly at coal feed locations and in cyclones. Other deposit locations included side walls and return loops. Three general types of mineralogic reactions were observed to occur in the agglomerates and deposits. Although alkalies may play a role with some {open_quotes}high alkali{close_quotes} lignites, we found agglomeration was initiated due to fluxing reactions between iron (II) from pyrites and aluminosilicates from clays. This is indicated by the high amounts of iron, silica, and alumina in the agglomerates and the mineralogy of the agglomerates. Agglomeration likely originated in the dense phase of the FBC bed within the volatile plume which forms when coal is introduced to the boiler. Secondary mineral reactions appear to occur after the agglomerates have formed and tend to strengthen the agglomerates. When calcium is present in high amounts, most of the minerals in the resulting deposits are in the melilite group (gehlenite, melilite, and akermanite) and pyroxene group (diopside and augite). During these solid-phase reactions, the temperature of formation of the melilite minerals can be lowered by a reduction of the partial pressure of CO{sub 2} (Diopside + Calcite {r_arrow}Akermanite).
NASA Astrophysics Data System (ADS)
Choi, Young Joon; Djilali, Ned
2016-01-01
Colloidal agglomeration of nanoparticles in shear flow is investigated by solving the fluid-particle and particle-particle interactions in a 2D system. We use an extended finite element method in which the dynamics of the particles is solved in a fully coupled manner with the flow, allowing an accurate description of the fluid-particle interfaces without the need of boundary-fitted meshes or of empirical correlations to account for the hydrodynamic interactions between the particles. Adaptive local mesh refinement using a grid deformation method is incorporated with the fluid-structure interaction algorithm, and the particle-particle interaction at the microscopic level is modeled using the Lennard-Jones potential. Motivated by the process used in fabricating fuel cell catalysts from a colloidal ink, the model is applied to investigate agglomeration of colloidal particles under external shear flow in a sliding bi-periodic Lees-Edwards frame with varying shear rates and particle fraction ratios. Both external shear and particle fraction are found to have a crucial impact on the structure formation of colloidal particles in a suspension. Segregation intensity and graph theory are used to analyze the underlying agglomeration patterns and structures, and three agglomeration regimes are identified.
Operational source receptor calculations for large agglomerations
NASA Astrophysics Data System (ADS)
Gauss, Michael; Shamsudheen, Semeena V.; Valdebenito, Alvaro; Pommier, Matthieu; Schulz, Michael
2016-04-01
For Air quality policy an important question is how much of the air pollution within an urbanized region can be attributed to local sources and how much of it is imported through long-range transport. This is critical information for a correct assessment of the effectiveness of potential emission measures. The ratio between indigenous and long-range transported air pollution for a given region depends on its geographic location, the size of its area, the strength and spatial distribution of emission sources, the time of the year, but also - very strongly - on the current meteorological conditions, which change from day to day and thus make it important to provide such calculations in near-real-time to support short-term legislation. Similarly, long-term analysis over longer periods (e.g. one year), or of specific air quality episodes in the past, can help to scientifically underpin multi-regional agreements and long-term legislation. Within the European MACC projects (Monitoring Atmospheric Composition and Climate) and the transition to the operational CAMS service (Copernicus Atmosphere Monitoring Service) the computationally efficient EMEP MSC-W air quality model has been applied with detailed emission data, comprehensive calculations of chemistry and microphysics, driven by high quality meteorological forecast data (up to 96-hour forecasts), to provide source-receptor calculations on a regular basis in forecast mode. In its current state, the product allows the user to choose among different regions and regulatory pollutants (e.g. ozone and PM) to assess the effectiveness of fictive emission reductions in air pollutant emissions that are implemented immediately, either within the agglomeration or outside. The effects are visualized as bar charts, showing resulting changes in air pollution levels within the agglomeration as a function of time (hourly resolution, 0 to 4 days into the future). The bar charts not only allow assessing the effects of emission
Not Available
1992-12-31
A major concern with the utilization of coal in directly fired gas turbines is the control of particulate emissions and reduction of sulfur dioxide, and alkali vapor from combustion of coal, upstream of the gas turbine. Much research and development has been sponsored on methods for particulate emissions control and the direct injection of calcium-based sorbents to reduce SO{sub 2} emission levels. The results of this research and development indicate that both acoustic agglomeration of particulates and direct injection of sorbents have the potential to become a significant emissions control strategy. The Sonic Enhanced Ash Agglomeration and Sulfur Capture program focuses upon the application of an MTCI proprietary invention (Invention Disclosure filed) for simultaneously enhancing sulfur capture and particulate agglomeration of the combustor effluent. This application can be adapted as either a ``hot flue gas cleanup`` subsystem for the current concepts for combustor islands or as an alternative primary pulse combustor island in which slagging, sulfur capture, particulate agglomeration and control, and alkali gettering as well as NO{sub x} control processes become an integral part of the pulse combustion process.
Fragmentation and bond strength of airborne diesel soot agglomerates
Rothenbacher, Sonja; Messerer, Armin; Kasper, Gerhard
2008-01-01
Background The potential of diesel soot aerosol particles to break up into smaller units under mechanical stress was investigated by a direct impaction technique which measures the degree of fragmentation of individual agglomerates vs. impact energy. Diesel aerosol was generated by an idling diesel engine used for passenger vehicles. Both the aerosol emitted directly and aerosol that had undergone additional growth by Brownian coagulation ("aging") was investigated. Optionally a thermo-desoption technique at 280°C was used to remove all high-volatility and the majority of low-volatility HC adsorbates from the aerosol before aging. Results It was found that the primary soot agglomerates emitted directly from the engine could not be fragmented at all. Soot agglomerates permitted to grow additionally by Brownian coagulation of the primary emitted particles could be fragmented to a maximum of 75% and 60% respectively, depending on whether adsorbates were removed from their surface prior to aging or not. At most, these aged agglomerates could be broken down to roughly the size of the agglomerates from the primary emission. The energy required for a 50% fragmentation probability of all bonds within an agglomerate was reduced by roughly a factor of 2 when aging "dry" agglomerates. Average bond energies derived from the data were 0.52*10-16 and 1.2*10-16 J, respectively. This is about 2 orders of magnitude higher than estimates for pure van-der-Waals agglomerates, but agrees quite well with other observations. Conclusion Although direct conclusions regarding the behavior of inhaled diesel aerosol in contact with body fluids cannot be drawn from such measurements, the results imply that highly agglomerated soot aerosol particles are unlikely to break up into units smaller than roughly the size distribution emitted as tail pipe soot. PMID:18533015
NASA Astrophysics Data System (ADS)
Zohdi, T. I.
2016-03-01
In industry, particle-laden fluids, such as particle-functionalized inks, are constructed by adding fine-scale particles to a liquid solution, in order to achieve desired overall properties in both liquid and (cured) solid states. However, oftentimes undesirable particulate agglomerations arise due to some form of mutual-attraction stemming from near-field forces, stray electrostatic charges, process ionization and mechanical adhesion. For proper operation of industrial processes involving particle-laden fluids, it is important to carefully breakup and disperse these agglomerations. One approach is to target high-frequency acoustical pressure-pulses to breakup such agglomerations. The objective of this paper is to develop a computational model and corresponding solution algorithm to enable rapid simulation of the effect of acoustical pulses on an agglomeration composed of a collection of discrete particles. Because of the complex agglomeration microstructure, containing gaps and interfaces, this type of system is extremely difficult to mesh and simulate using continuum-based methods, such as the finite difference time domain or the finite element method. Accordingly, a computationally-amenable discrete element/discrete ray model is developed which captures the primary physical events in this process, such as the reflection and absorption of acoustical energy, and the induced forces on the particulate microstructure. The approach utilizes a staggered, iterative solution scheme to calculate the power transfer from the acoustical pulse to the particles and the subsequent changes (breakup) of the pulse due to the particles. Three-dimensional examples are provided to illustrate the approach.
Agglomeration of proteins in acoustically levitated droplets.
Delissen, Friedmar; Leiterer, Jork; Bienert, Ralf; Emmerling, Franziska; Thünemann, Andreas F
2008-09-01
An ultrasonic trap (acoustic levitator) was used as an analytical tool to allow container-free handling of proteins in small sample volumes. This trap was combined for the first time with synchrotron small-angle X-ray scattering (SAXS) for structure analysis of biological macromolecules in a solution. The microfocus beamline at BESSY was used as a source of intense X-ray radiation. Apoferritin (APO) was used as a model protein, and its aggregation behavior in a levitator was followed from a diluted solution to the solid state. Different stages of APO agglomeration were observed without solid container walls, which may influence aggregation behavior and produce a parasitic scattering background. Starting with a volume of 5 microL we analyzed the concentration dependence of APO structure factors in the range from 5 to 1,200 mg/mL (solid protein). The solution was stirred automatically due to convection inside the droplet caused by the ultrasonic field. SAXS data recording of APO was performed in time intervals of 60 s during an aggregation experiment of 30 to 60 min. PMID:18607573
Review of ash agglomeration in fluidized bed gasifiers
Matulevicius, E.S.; Golan, L.P.
1984-07-01
The purpose of this study is to review the data and mathematical models which describe the phenomena involved in the agglomeration of ash in fluidized bed coal gasifiers (FBG). Besides highlighting the data and theoretical models, this review lists areas where there is a lack of information regarding the actual mechanisms of agglomeration. Also, potential areas for further work are outlined. The work is directed at developing models of agglomeration which could be included in computer codes describing fluidized bed gasifier phenomena, e.g., FLAG and CHEMFLUB which have been developed for the US Department of Energy. 134 references, 24 figures, 13 tables.
Multistage Schemes with Multigrid for Euler and Navier-Strokes Equations: Components and Analysis
NASA Technical Reports Server (NTRS)
Swanson, R. C.; Turkel, Eli
1997-01-01
A class of explicit multistage time-stepping schemes with centered spatial differencing and multigrids are considered for the compressible Euler and Navier-Stokes equations. These schemes are the basis for a family of computer programs (flow codes with multigrid (FLOMG) series) currently used to solve a wide range of fluid dynamics problems, including internal and external flows. In this paper, the components of these multistage time-stepping schemes are defined, discussed, and in many cases analyzed to provide additional insight into their behavior. Special emphasis is given to numerical dissipation, stability of Runge-Kutta schemes, and the convergence acceleration techniques of multigrid and implicit residual smoothing. Both the Baldwin and Lomax algebraic equilibrium model and the Johnson and King one-half equation nonequilibrium model are used to establish turbulence closure. Implementation of these models is described.
Optimization of refractive liquid crystal lenses using an efficient multigrid simulation.
Milton, Harry; Brimicombe, Paul; Morgan, Philip; Gleeson, Helen; Clamp, John
2012-05-01
A multigrid computational model has been developed to assess the performance of refractive liquid crystal lenses, which is up to 40 times faster than previous techniques. Using this model, the optimum geometries producing an ideal parabolic voltage distribution were deduced for refractive liquid crystal lenses with diameters from 1 to 9 mm. The ratio of insulation thickness to lens diameter was determined to be 1:2 for small diameter lenses, tending to 1:3 for larger lenses. The model is used to propose a new method of lens operation with lower operating voltages needed to induce specific optical powers. The operating voltages are calculated for the induction of optical powers between + 1.00 D and + 3.00 D in a 3 mm diameter lens, with the speed of the simulation facilitating the optimization of the refractive index profile. We demonstrate that the relationship between additional applied voltage and optical power is approximately linear for optical powers under + 3.00 D. The versatility of the computational simulation has also been demonstrated by modeling of in-plane electrode liquid crystal devices.
Multigrid solution of incompressible turbulent flows by using two-equation turbulence models
Zheng, X.; Liu, C.; Sung, C.H.
1996-12-31
Most of practical flows are turbulent. From the interest of engineering applications, simulation of realistic flows is usually done through solution of Reynolds-averaged Navier-Stokes equations and turbulence model equations. It has been widely accepted that turbulence modeling plays a very important role in numerical simulation of practical flow problem, particularly when the accuracy is of great concern. Among the most used turbulence models today, two-equation models appear to be favored for the reason that they are more general than algebraic models and affordable with current available computer resources. However, investigators using two-equation models seem to have been more concerned with the solution of N-S equations. Less attention is paid to the solution method for the turbulence model equations. In most cases, the turbulence model equations are loosely coupled with N-S equations, multigrid acceleration is only applied to the solution of N-S equations due to perhaps the fact the turbulence model equations are source-term dominant and very stiff in sublayer region.
A fast multigrid-based electromagnetic eigensolver for curved metal boundaries on the Yee mesh
Bauer, Carl A.; Werner, Gregory R.; Cary, John R.
2013-10-15
For embedded boundary electromagnetics using the Dey–Mittra (Dey and Mittra, 1997) [1] algorithm, a special grad–div matrix constructed in this work allows use of multigrid methods for efficient inversion of Maxwell’s curl–curl matrix. Efficient curl–curl inversions are demonstrated within a shift-and-invert Krylov-subspace eigensolver (open-sourced at ([ofortt]https://github.com/bauerca/maxwell[cfortt])) on the spherical cavity and the 9-cell TESLA superconducting accelerator cavity. The accuracy of the Dey–Mittra algorithm is also examined: frequencies converge with second-order error, and surface fields are found to converge with nearly second-order error. In agreement with previous work (Nieter et al., 2009) [2], neglecting some boundary-cut cell faces (as is required in the time domain for numerical stability) reduces frequency convergence to first-order and surface-field convergence to zeroth-order (i.e. surface fields do not converge). Additionally and importantly, neglecting faces can reduce accuracy by an order of magnitude at low resolutions.
An Adaptive Multigrid Algorithm for Simulating Solid Tumor Growth Using Mixture Models
Wise, S.M.; Lowengrub, J.S.; Cristini, V.
2010-01-01
In this paper we give the details of the numerical solution of a three-dimensional multispecies diffuse interface model of tumor growth, which was derived in (Wise et al., J. Theor. Biol. 253 (2008)) and used to study the development of glioma in (Frieboes et al., NeuroImage 37 (2007) and tumor invasion in (Bearer et al., Cancer Research, 69 (2009)) and (Frieboes et al., J. Theor. Biol. 264 (2010)). The model has a thermodynamic basis, is related to recently developed mixture models, and is capable of providing a detailed description of tumor progression. It utilizes a diffuse interface approach, whereby sharp tumor boundaries are replaced by narrow transition layers that arise due to differential adhesive forces among the cell-species. The model consists of fourth-order nonlinear advection-reaction-diffusion equations (of Cahn-Hilliard-type) for the cell-species coupled with reaction-diffusion equations for the substrate components. Numerical solution of the model is challenging because the equations are coupled, highly nonlinear, and numerically stiff. In this paper we describe a fully adaptive, nonlinear multigrid/finite difference method for efficiently solving the equations. We demonstrate the convergence of the algorithm and we present simulations of tumor growth in 2D and 3D that demonstrate the capabilities of the algorithm in accurately and efficiently simulating the progression of tumors with complex morphologies. PMID:21076663
An Adaptive Multigrid Algorithm for Simulating Solid Tumor Growth Using Mixture Models.
Wise, S M; Lowengrub, J S; Cristini, V
2011-01-01
In this paper we give the details of the numerical solution of a three-dimensional multispecies diffuse interface model of tumor growth, which was derived in (Wise et al., J. Theor. Biol. 253 (2008)) and used to study the development of glioma in (Frieboes et al., NeuroImage 37 (2007) and tumor invasion in (Bearer et al., Cancer Research, 69 (2009)) and (Frieboes et al., J. Theor. Biol. 264 (2010)). The model has a thermodynamic basis, is related to recently developed mixture models, and is capable of providing a detailed description of tumor progression. It utilizes a diffuse interface approach, whereby sharp tumor boundaries are replaced by narrow transition layers that arise due to differential adhesive forces among the cell-species. The model consists of fourth-order nonlinear advection-reaction-diffusion equations (of Cahn-Hilliard-type) for the cell-species coupled with reaction-diffusion equations for the substrate components. Numerical solution of the model is challenging because the equations are coupled, highly nonlinear, and numerically stiff. In this paper we describe a fully adaptive, nonlinear multigrid/finite difference method for efficiently solving the equations. We demonstrate the convergence of the algorithm and we present simulations of tumor growth in 2D and 3D that demonstrate the capabilities of the algorithm in accurately and efficiently simulating the progression of tumors with complex morphologies. PMID:21076663
Development of an explicit multiblock/multigrid flow solver for viscous flows in complex geometries
NASA Technical Reports Server (NTRS)
Steinthorsson, E.; Liou, M. S.; Povinelli, L. A.
1993-01-01
A new computer program is being developed for doing accurate simulations of compressible viscous flows in complex geometries. The code employs the full compressible Navier-Stokes equations. The eddy viscosity model of Baldwin and Lomax is used to model the effects of turbulence on the flow. A cell centered finite volume discretization is used for all terms in the governing equations. The Advection Upwind Splitting Method (AUSM) is used to compute the inviscid fluxes, while central differencing is used for the diffusive fluxes. A four-stage Runge-Kutta time integration scheme is used to march solutions to steady state, while convergence is enhanced by a multigrid scheme, local time-stepping, and implicit residual smoothing. To enable simulations of flows in complex geometries, the code uses composite structured grid systems where all grid lines are continuous at block boundaries (multiblock grids). Example results shown are a flow in a linear cascade, a flow around a circular pin extending between the main walls in a high aspect-ratio channel, and a flow of air in a radial turbine coolant passage.
A fast multigrid-based electromagnetic eigensolver for curved metal boundaries on the Yee mesh
NASA Astrophysics Data System (ADS)
Bauer, Carl A.; Werner, Gregory R.; Cary, John R.
2013-10-01
For embedded boundary electromagnetics using the Dey-Mittra (Dey and Mittra, 1997) [1] algorithm, a special grad-div matrix constructed in this work allows use of multigrid methods for efficient inversion of Maxwell's curl-curl matrix. Efficient curl-curl inversions are demonstrated within a shift-and-invert Krylov-subspace eigensolver (open-sourced at [ofortt]https://github.com/bauerca/maxwell[cfortt]) on the spherical cavity and the 9-cell TESLA superconducting accelerator cavity. The accuracy of the Dey-Mittra algorithm is also examined: frequencies converge with second-order error, and surface fields are found to converge with nearly second-order error. In agreement with previous work (Nieter et al., 2009) [2], neglecting some boundary-cut cell faces (as is required in the time domain for numerical stability) reduces frequency convergence to first-order and surface-field convergence to zeroth-order (i.e. surface fields do not converge). Additionally and importantly, neglecting faces can reduce accuracy by an order of magnitude at low resolutions.
Transport and Deposition of Welding Fume Agglomerates in a Realistic Human Nasal Airway.
Tian, Lin; Inthavong, Kiao; Lidén, Göran; Shang, Yidan; Tu, Jiyuan
2016-07-01
Welding fume is a complex mixture containing ultra-fine particles in the nanometer range. Rather than being in the form of a singular sphere, due to the high particle concentration, welding fume particles agglomerate into long straight chains, branches, or other forms of compact shapes. Understanding the transport and deposition of these nano-agglomerates in human respiratory systems is of great interest as welding fumes are a known health hazard. The neurotoxin manganese (Mn) is a common element in welding fumes. Particulate Mn, either as soluble salts or oxides, that has deposited on the olfactory mucosa in human nasal airway is transported along the olfactory nerve to the olfactory bulb within the brain. If this Mn is further transported to the basal ganglia of the brain, it could accumulate at the part of the brain that is the focal point of its neurotoxicity. Accounting for various dynamic shape factors due to particle agglomeration, the current computational study is focused on the exposure route, the deposition pattern, and the deposition efficiency of the inhaled welding fume particles in a realistic human nasal cavity. Particular attention is given to the deposition pattern and deposition efficiency of inhaled welding fume agglomerates in the nasal olfactory region. For particles in the nanoscale, molecular diffusion is the dominant transport mechanism. Therefore, Brownian diffusion, hydrodynamic drag, Saffman lift force, and gravitational force are included in the model study. The deposition efficiencies for single spherical particles, two kinds of agglomerates of primary particles, two-dimensional planar and straight chains, are investigated for a range of primary particle sizes and a range of number of primary particles per agglomerate. A small fraction of the inhaled welding fume agglomerates is deposited on the olfactory mucosa, approximately in the range 0.1-1%, and depends on particle size and morphology. The strong size dependence of the deposition
NASA Astrophysics Data System (ADS)
1985-08-01
The design specifications for the HTHP AA Facility are listed. The facility is an open-loop, air flow system with subsystems and components to provide the high temperature, high pressure, residence time, dust loading and acoustic irradiation to simulate the aerosol and Hot Gas Cleanup (HGCU) AA system of a Pressurized Fluid Bed Combustor (PFBC), Combined Cycle Power Plant. Data sampling, instrumentation, and automatic controls and data analysis systems are also provided. This test plan describes the testing to be done on the high temperature, high pressure acoustic agglomerator (HTHP AA) at Pen State University's High Intensity Acoustic Laboratory.
Vectorizable multigrid algorithms for transonic flow calculations. M.S. Thesis
NASA Technical Reports Server (NTRS)
Melson, N. D.
1985-01-01
The analysis and incorporation into a multigrid scheme of several vectorizable algorithms are discussed. Von Neumann analyses of vertical line, horizontal line, and alternating direction ZEBRA algorithms were performed; and the results were used to predict their multigrid damping rates. The algorithms were then successfully implemented in a transonic conservative full-potential computer program. The convergence acceleration effect of multiple grids is shown and the convergence rates of the vectorizable algorithms are compared to the convergence rates of standard successive line overrelaxation (SLOR) algorithms.
A multigrid solver for semi-implicit global shallow-water models
NASA Technical Reports Server (NTRS)
Barros, Saulo R. M.; Dee, Dick P.; Dickstein, Flavio
1990-01-01
A multigrid solver is developed for the discretized two-dimensional elliptic equation on the sphere that arises from a semiimplicit time discretization of the global shallow-water equations. Different formulations of the semiimplicit scheme result in variable-coefficient Helmholtz-type equations for which no fast direct solvers are available. The efficiency of the multigrid solver is optimal, in the sense that the total operation count is proportional to the number of unknowns. Numerical experiments using initial data derived from actual 300-mb height and wind velocity fields indicate that the present model has very good accuracy and stability properties.
NASA Technical Reports Server (NTRS)
Thompson, C. P.; Leaf, G. K.; Vanrosendale, J.
1991-01-01
An algorithm is described for the solution of the laminar, incompressible Navier-Stokes equations. The basic algorithm is a multigrid based on a robust, box-based smoothing step. Its most important feature is the incorporation of automatic, dynamic mesh refinement. This algorithm supports generalized simple domains. The program is based on a standard staggered-grid formulation of the Navier-Stokes equations for robustness and efficiency. Special grid transfer operators were introduced at grid interfaces in the multigrid algorithm to ensure discrete mass conservation. Results are presented for three models: the driven-cavity, a backward-facing step, and a sudden expansion/contraction.
A multigrid algorithm for the cell-centered finite difference scheme
NASA Technical Reports Server (NTRS)
Ewing, Richard E.; Shen, Jian
1993-01-01
In this article, we discuss a non-variational V-cycle multigrid algorithm based on the cell-centered finite difference scheme for solving a second-order elliptic problem with discontinuous coefficients. Due to the poor approximation property of piecewise constant spaces and the non-variational nature of our scheme, one step of symmetric linear smoothing in our V-cycle multigrid scheme may fail to be a contraction. Again, because of the simple structure of the piecewise constant spaces, prolongation and restriction are trivial; we save significant computation time with very promising computational results.
NASA Technical Reports Server (NTRS)
Bates, J. R.; Semazzi, F. H. M.; Higgins, R. W.; Barros, Saulo R. M.
1990-01-01
A vector semi-Lagrangian semi-implicit two-time-level finite-difference integration scheme for the shallow water equations on the sphere is presented. A C-grid is used for the spatial differencing. The trajectory-centered discretization of the momentum equation in vector form eliminates pole problems and, at comparable cost, gives greater accuracy than a previous semi-Lagrangian finite-difference scheme which used a rotated spherical coordinate system. In terms of the insensitivity of the results to increasing timestep, the new scheme is as successful as recent spectral semi-Lagrangian schemes. In addition, the use of a multigrid method for solving the elliptic equation for the geopotential allows efficient integration with an operation count which, at high resolution, is of lower order than in the case of the spectral models. The properties of the new scheme should allow finite-difference models to compete with spectral models more effectively than has previously been possible.
Column oil agglomeration of fly ash with ultrasonics
Gray, M.L.; Champagne, K.J.; Soong, Y.; Finseth, D.H.
1999-07-01
A promising oil agglomeration process has been developed for the beneficiation of fly ash using a six-foot agglomeration column. Carbon concentrates have been separated from fly ash with yields greater than 60 % and purities of 55 to 74 %. The parameters examined in the study include ultrasonic exposure, pulse rate, frequency, agitation speed, and blade configuration. The effects of the experimental variables on the quality of separation are discussed.
Acoustic agglomeration of power plant fly ash. Final report
Reethof, G.; McDaniel, O.H.
1982-01-01
The work has shown that acoustic agglomeration at practical acoustic intensities and frequencies is technically and most likely economically viable. The following studies were performed with the listed results: The physics of acoustic agglomeration is complex particularly at the needed high acoustic intensities in the range of 150 to 160 dB and frequencies in the 2500 Hz range. The analytical model which we developed, although not including nonlinear acoustic efforts, agreed with the trends observed. We concentrated our efforts on clarifying the impact of high acoustic intensities on the generation of turbulence. Results from a special set of tests show that although some acoustically generated turbulence of sorts exists in the 150 to 170 dB range with acoustic streaming present, such turbulence will not be a significant factor in acoustic agglomeration compared to the dominant effect of the acoustic velocities at the fundamental frequency and its harmonics. Studies of the robustness of the agglomerated particles using the Anderson Mark III impactor as the source of the shear stresses on the particles show that the agglomerates should be able to withstand the rigors of flow through commercial cyclones without significant break-up. We designed and developed a 700/sup 0/F tubular agglomerator of 8'' internal diameter. The electrically heated system functioned well and provided very encouraging agglomeration results at acoustic levels in the 150 to 160 dB and 2000 to 3000 Hz ranges. We confirmed earlier results that an optimum frequency exists at about 2500 Hz and that larger dust loadings will give better results. Studies of the absorption of acoustic energy by various common gases as a function of temperature and humidity showed the need to pursue such an investigation for flue gas constituents in order to provide necessary data for the design of agglomerators. 65 references, 56 figures, 4 tables.
Low-rank coal oil agglomeration product and process
Knudson, Curtis L.; Timpe, Ronald C.; Potas, Todd A.; DeWall, Raymond A.; Musich, Mark A.
1992-01-01
A selectively-sized, raw, low-rank coal is processed to produce a low ash and relative water-free agglomerate with an enhanced heating value and a hardness sufficient to produce a non-decrepitating, shippable fuel. The low-rank coal is treated, under high shear conditions, in the first stage to cause ash reduction and subsequent surface modification which is necessary to facilitate agglomerate formation. In the second stage the treated low-rank coal is contacted with bridging and binding oils under low shear conditions to produce agglomerates of selected size. The bridging and binding oils may be coal or petroleum derived. The process incorporates a thermal deoiling step whereby the bridging oil may be completely or partially recovered from the agglomerate; whereas, partial recovery of the bridging oil functions to leave as an agglomerate binder, the heavy constituents of the bridging oil. The recovered oil is suitable for recycling to the agglomeration step or can serve as a value-added product.
Low-rank coal oil agglomeration product and process
Knudson, C.L.; Timpe, R.C.; Potas, T.A.; DeWall, R.A.; Musich, M.A.
1992-11-10
A selectively-sized, raw, low-rank coal is processed to produce a low ash and relative water-free agglomerate with an enhanced heating value and a hardness sufficient to produce a non-degradable, shippable fuel. The low-rank coal is treated, under high shear conditions, in the first stage to cause ash reduction and subsequent surface modification which is necessary to facilitate agglomerate formation. In the second stage the treated low-rank coal is contacted with bridging and binding oils under low shear conditions to produce agglomerates of selected size. The bridging and binding oils may be coal or petroleum derived. The process incorporates a thermal deoiling step whereby the bridging oil may be completely or partially recovered from the agglomerate; whereas, partial recovery of the bridging oil functions to leave as an agglomerate binder, the heavy constituents of the bridging oil. The recovered oil is suitable for recycling to the agglomeration step or can serve as a value-added product.
Iterative methods for elliptic finite element equations on general meshes
NASA Technical Reports Server (NTRS)
Nicolaides, R. A.; Choudhury, Shenaz
1986-01-01
Iterative methods for arbitrary mesh discretizations of elliptic partial differential equations are surveyed. The methods discussed are preconditioned conjugate gradients, algebraic multigrid, deflated conjugate gradients, an element-by-element techniques, and domain decomposition. Computational results are included.
Detwiler, R.L.; Mehl, S.; Rajaram, H.; Cheung, W.W.
2002-01-01
Numerical solution of large-scale ground water flow and transport problems is often constrained by the convergence behavior of the iterative solvers used to solve the resulting systems of equations. We demonstrate the ability of an algebraic multigrid algorithm (AMG) to efficiently solve the large, sparse systems of equations that result from computational models of ground water flow and transport in large and complex domains. Unlike geometric multigrid methods, this algorithm is applicable to problems in complex flow geometries, such as those encountered in pore-scale modeling of two-phase flow and transport. We integrated AMG into MODFLOW 2000 to compare two- and three-dimensional flow simulations using AMG to simulations using PCG2, a preconditioned conjugate gradient solver that uses the modified incomplete Cholesky preconditioner and is included with MODFLOW 2000. CPU times required for convergence with AMG were up to 140 times faster than those for PCG2. The cost of this increased speed was up to a nine-fold increase in required random access memory (RAM) for the three-dimensional problems and up to a four-fold increase in required RAM for the two-dimensional problems. We also compared two-dimensional numerical simulations of steady-state transport using AMG and the generalized minimum residual method with an incomplete LU-decomposition preconditioner. For these transport simulations, AMG yielded increased speeds of up to 17 times with only a 20% increase in required RAM. The ability of AMG to solve flow and transport problems in large, complex flow systems and its ready availability make it an ideal solver for use in both field-scale and pore-scale modeling.
Gravitational agglomeration of post-HCDA LMFBR nonspherical aerosols
NASA Astrophysics Data System (ADS)
Tuttle, R. F.
1980-12-01
A theoretical investigation of collisional dynamics of two particle interactions in a gravitational field is reported. This research is unique in that it is the first attempt at modeling the hydrodynamic interactions between a nonspherical particle and a spherical particle undergoing gravitational collisions in an LMFBR environment. Basic definitions and expressions are developed for nonspherical particles and related to spherical particles by means of shape factors. Using volume equivalent diameter as the defining length in the gravitational collision kernel, the aerodynamic shape factor, k, the density correction factor, alpha, and the gravitational collision shape factor, beta, are used to correct the collision kernel for the case of collisions between aerosol agglomerates. The Navier-Stokes equation in oblate spheroidal coordinates is solved to model a nonspherical particle and then the dynamic equations for two particle motions are developed. A computer program NGCEFF is constructed, the Navier-Stokes equation is solved by the finite difference method, and the dynamical equations are solved by Gear's method. It is concluded that the aerosol gravitational collision shape factor can be determined by further theoretical work based on the concepts and methods developed in this dissertation.
NASA Technical Reports Server (NTRS)
Liu, Chao-Qun; Shan, H.; Jiang, L.
1999-01-01
Numerical investigation of flow separation over a NACA 0012 airfoil at large angles of attack has been carried out. The numerical calculation is performed by solving the full Navier-Stokes equations in generalized curvilinear coordinates. The second-order LU-SGS implicit scheme is applied for time integration. This scheme requires no tridiagonal inversion and is capable of being completely vectorized, provided the corresponding Jacobian matrices are properly selected. A fourth-order centered compact scheme is used for spatial derivatives. In order to reduce numerical oscillation, a sixth-order implicit filter is employed. Non-reflecting boundary conditions are imposed at the far-field and outlet boundaries to avoid possible non-physical wave reflection. Complex flow separation and vortex shedding phenomenon have been observed and discussed.
NASA Astrophysics Data System (ADS)
Wang, Lu; Zhang, Guo-Hua; Wang, Jing-Song; Chou, Kuo-Chih
2016-08-01
An agglomeration of the furnace charge always takes place during the oxidation roasting process of molybdenite concentrate (with the main component of MoS2) in multiple hearth furnaces, which greatly affects the production process and furnace service life. In the present work, a preliminary study about the influence of various components on the agglomeration phenomenon of pure MoS2 have been carried out. The results show that reaction temperature, impurity content, and air flow rate have significant effects on the agglomeration extent. Meanwhile, the impurity type added into the pure MoS2 plays a crucial role. It was found that CaO and MgO have a stronger sulfur-fixing effect and that the desulphurization of the roasted product was uncompleted. It was also concluded that the agglomeration is due to the formation of low-melting-point eutectics, including that between MoO3 and impurities and that between MoO3 and Mo4O11. It is suggested that decreasing the impurities contents, especially K, Cu, Pb, and Fe, is an effective method for reducing the extent of agglomeration.
Colloidal stability of coal-simulated suspensions in selective agglomeration
Schurger, M.L.
1989-01-01
A coal suspension was simulated by using graphite to simulate the carbonaceous fraction and kaolinite clay to simulate the ash fraction. Separate studies on each material established their response to additions of oxidized pyrite (ferrous sulfate) and a humic acid simulate (salicylic acid) in terms of zeta potentials profiles with pH and Ionic strength. Concentrations of iron and salicylic acid evaluated were 4.5 {times} 10{sup {minus}3} M and 2.0 {times} 10{sup {minus}4} M, respectively. The zeta potentials profiles of graphite, clay and hexadecane were negative throughout the pH ranges studied. The addition of iron lowered the zeta potentials all of the suspensions under all pH and ionic strength conditions. Salicylic acid decreased the graphite and hexadecane zeta potentials but had no effect on the clay zeta potential profiles. Agglomeration of graphite with bridging liquid shows distinct time dependent rate mechanisms, a initial growth of graphite agglomerates followed by consolidation phase. Graphite agglomeration was rapid with the maximum amount of agglomerate volume growth occurring in under 2-4 minutes. Agglomeration in the first two minutes was characterized by a 1st order rate mechanism. The presence of either Iron and salicylic acid generally improved the first order rates. The addition of clay also improved the first order rates except in the presence of salicylic acid. Heteroagglomeration of graphite with clay was found by hydrodynamic arguments to be unfavored. A multicomponent population balance model which had been developed for evaluating collision efficiencies of coal, ash and pyrite selective agglomeration was evaluated to explain these results. The growth and consolidation characteristics of graphite agglomeration for the experimental conditions examined herein revealed the limitations of such as model for this application.
Effect of Drying Phase on the Agglomerates Prepared by Spherical Crystallization
Maghsoodi, Maryam; Yari, Zahra
2015-01-01
In this paper, differences in porosity, compressive strength and tablet- forming ability of carbamazepine crystals agglomerated under similar condition, but subjected to different drying temperatures are reported. The agglomerates were prepared by spherical crystallization method and thereafter dried without agitation at different temperature. An increased drying temperature did not affect the shape and structure texture of dried particles and did not cause them to fracture. Drying of particles at higher temperature suppressed the particle contraction as a consequence of fast evaporation and hence produced particles of larger mean diameter, higher porosity and thus lower compressive strength than those dried at lower temperature. Through a relationship with particle porosity, the drying rate also affected the ability of particles to form tablets. PMID:25561911
Multivariate analysis applied to agglomerated macrobenthic data from an unpolluted estuary.
Conde, Anxo; Novais, Júlio M; Domínguez, Jorge
2013-01-01
We agglomerated species into higher taxonomic aggregations and functional groups to analyse environmental gradients in an unpolluted estuary. We then applied non-metric Multidimensional Scaling and Redundancy Analysis (RDA) for ordination of the agglomerated data matrices. The correlation between the ordinations produced by both methods was generally high. However, the performance of the RDA models depended on the data matrix used to fit the model. As a result, salinity and total nitrogen were only found significant when aggregated data matrices were used rather than species data matrix. We used the results to select a RDA model that explained a higher percentage of variance in the species data set than the parsimonious model. We conclude that the use of aggregated matrices may be considered complementary to the use of species data to obtain a broader insight into the distribution of macrobenthic assemblages in relation to environmental gradients. PMID:23684322
Theranostic potential of gold nanoparticle-protein agglomerates.
Sanpui, Pallab; Paul, Anumita; Chattopadhyay, Arun
2015-11-28
Owing to the ever-increasing applications, glittered with astonishing success of gold nanoparticles (Au NPs) in biomedical research as diagnostic and therapeutic agents, the study of Au NP-protein interaction seems critical for maximizing their theranostic efficiency, and thus demands comprehensive understanding. The mutual interaction of Au NPs and proteins at physiological conditions may result in the aggregation of protein, which can ultimately lead to the formation of Au NP-protein agglomerates. In the present article, we try to appreciate the plausible steps involved in the Au NP-induced aggregation of proteins and also the importance of the proteins' three-dimensional structures in the process. The Au NP-protein agglomerates can potentially be exploited for efficient loading and subsequent release of various therapeutically important molecules, including anticancer drugs, with the unique opportunity of incorporating hydrophilic as well as hydrophobic drugs in the same nanocarrier system. Moreover, the Au NP-protein agglomerates can act as 'self-diagnostic' systems, allowing investigation of the conformational state of the associated protein(s) as well as the protein-protein or protein-Au NP interaction within the agglomerates. Furthermore, the potential of these Au NP-protein agglomerates as a novel platform for multifunctional theranostic application along with exciting future-possibilities is highlighted here. PMID:26508277
Theranostic potential of gold nanoparticle-protein agglomerates
NASA Astrophysics Data System (ADS)
Sanpui, Pallab; Paul, Anumita; Chattopadhyay, Arun
2015-11-01
Owing to the ever-increasing applications, glittered with astonishing success of gold nanoparticles (Au NPs) in biomedical research as diagnostic and therapeutic agents, the study of Au NP-protein interaction seems critical for maximizing their theranostic efficiency, and thus demands comprehensive understanding. The mutual interaction of Au NPs and proteins at physiological conditions may result in the aggregation of protein, which can ultimately lead to the formation of Au NP-protein agglomerates. In the present article, we try to appreciate the plausible steps involved in the Au NP-induced aggregation of proteins and also the importance of the proteins' three-dimensional structures in the process. The Au NP-protein agglomerates can potentially be exploited for efficient loading and subsequent release of various therapeutically important molecules, including anticancer drugs, with the unique opportunity of incorporating hydrophilic as well as hydrophobic drugs in the same nanocarrier system. Moreover, the Au NP-protein agglomerates can act as `self-diagnostic' systems, allowing investigation of the conformational state of the associated protein(s) as well as the protein-protein or protein-Au NP interaction within the agglomerates. Furthermore, the potential of these Au NP-protein agglomerates as a novel platform for multifunctional theranostic application along with exciting future-possibilities is highlighted here.
Acoustic agglomeration of fine particles based on a high intensity acoustical resonator
NASA Astrophysics Data System (ADS)
Zhao, Yun; Zeng, Xinwu; Tian, Zhangfu
2015-10-01
Acoustic agglomeration (AA) is considered to be a promising method for reducing the air pollution caused by fine aerosol particles. Removal efficiency and energy consuming are primary parameters and generally have a conflict with each other for the industry applications. It was proved that removal efficiency is increased with sound intensity and optimal frequency is presented for certain polydisperse aerosol. As a result, a high efficiency and low energy cost removal system was constructed using acoustical resonance. High intensity standing wave is generated by a tube system with abrupt section driven by four loudspeakers. Numerical model of the tube system was built base on the finite element method, and the resonance condition and SPL increase were confirmd. Extensive tests were carried out to investigate the acoustic field in the agglomeration chamber. Removal efficiency of fine particles was tested by the comparison of filter paper mass and particle size distribution at different operating conditions including sound pressure level (SPL), and frequency. The experimental study has demonstrated that agglomeration increases with sound pressure level. Sound pressure level in the agglomeration chamber is between 145 dB and 165 dB from 500 Hz to 2 kHz. The resonance frequency can be predicted with the quarter tube theory. Sound pressure level gain of more than 10 dB is gained at resonance frequency. With the help of high intensity sound waves, fine particles are reduced greatly, and the AA effect is enhanced at high SPL condition. The optimal frequency is 1.1kHz for aerosol generated by coal ash. In the resonace tube, higher resonance frequencies are not the integral multiplies of the first one. As a result, Strong nonlinearity is avoided by the dissonant characteristic and shock wave is not found in the testing results. The mechanism and testing system can be used effectively in industrial processes in the future.
Basic principles and mechanisms of selective oil agglomeration
Wheelock, T.D.; Drzymala, J.; Allen, R.W.; Hu, Y.-C.; Tyson, D.; Xiaoping, Qiu; Lessa, A.
1990-01-01
Numerous measurements of the heat of immersion of coal were conducting using several different particle size fractions of No. 2 Gas Seam coal from Raleigh County, West Virginia. The heat of immersion was determined in water, methanol, heptane, hexadecane and neohexane (2,2-dimethybutane). A comparison of the results with those determined previously for Illinois No. 6 coal is discussed. A number of potential pyrite depressants for use in oil agglomeration of coal were screened by testing the response of sulfidized mineral pyrite to agglomeration with heptane in the presence of the potential depressant. The following were tested; sodium dithionite, sodium thiosulfate, ferrous sulfate, ferric sulfate, titanous chloride, hydrogen peroxide, Oxone (a form of potassium monopersulfate), pyrogallol, quebracho (colloidal dispersant derived from tree bark), milk whey, and several organic thiols. Ferric chloride was applied to mixtures of Upper Freeport coal and sulfidized mineral pyrite before subjecting the mixtures to agglomeration with heptane. 7 refs., 23 figs., 3 tabs.
A pocket model for aluminum agglomeration in composite propellants
NASA Technical Reports Server (NTRS)
Cohen, N. S.
1981-01-01
This paper presents a model for the purpose of estimating the fraction of aluminum powder that will form agglomerates at the surface of deflagrating composite propellants. The basic idea is that the fraction agglomerated depends upon the amount of aluminum that melts within effective binder pocket volumes framed by oxidizer particles. The effective pocket depends upon the ability of ammonium perchlorate modals to encapsulate the aluminum and provide a local temperature sufficient to ignite the aluminum. Model results are discussed in the light of data showing effects of propellant formulation variables and pressure.
Helgeson, Zach L; Jenkins, Jed S; Abraham, John P; Sparrow, Ephraim M
2011-01-01
Background: The transport of particles in surrogate and actual arterial geometries has been investigated synergistically by experimentation and numerical simulation. The motivating application for this work is orbital atherectomy which spawns a particle cloud in the process of debulking plaque from arterial walls. Methods: Paired simulations and experiments were performed to prove the capability of the simulation model to predict both fluid and particle motions in branched arterial geometries. The verified model was then employed to predict the pattern of fluid flow in an actual multi-branched arterial geometry, including the flowrates passing through each of the individual branches. These predictions are in very good agreement with experimental data. Focus was then shifted to the issues of particle agglomeration within the flowing fluid and particle accumulation on the vessel walls. Once again, a synergistic approach was used. Flow visualization was employed to track the particle motions and to identify possible particle agglomeration within the fluid. Results and Conclusions: Accumulation of particles on walls was identified by measuring size distributions of effluent and residue within the artery. Scanning Electron Microscopy (SEM) evaluation showed evidence of a size-based sorting as the particles passed through vessels. It was found that plaque-facsimile particles resisted particle-particle agglomeration. They also did not accumulate to the wall of the facsimile artery. In addition, simulations showed that if particle-wall accumulation were to occur, it would be limited to very small regions in the artery branches. PMID:21643425
2013-01-01
Background The exact role of primary nanoparticle (NP) size and their degree of agglomeration in aerosols on the determination of pulmonary effects is still poorly understood. Smaller NP are thought to have greater biological reactivity, but their level of agglomeration in an aerosol may also have an impact on pulmonary response. The aim of this study was to investigate the role of primary NP size and the agglomeration state in aerosols, using well-characterized TiO2 NP, on their relative pulmonary toxicity, through inflammatory, cytotoxic and oxidative stress effects in Fisher 344 male rats. Methods Three different sizes of TiO2 NP, i.e., 5, 10–30 or 50 nm, were inhaled as small (SA) (< 100 nm) or large agglomerates (LA) (> 100 nm) at 20 mg/m3 for 6 hours. Results Compared to the controls, bronchoalveolar lavage fluids (BALF) showed that LA aerosols induced an acute inflammatory response, characterized by a significant increase in the number of neutrophils, while SA aerosols produced significant oxidative stress damages and cytotoxicity. Data also demonstrate that for an agglomeration state smaller than 100 nm, the 5 nm particles caused a significant increase in cytotoxic effects compared to controls (assessed by an increase in LDH activity), while oxidative damage measured by 8-isoprostane concentration was less when compared to 10–30 and 50 nm particles. In both SA and LA aerosols, the 10–30 nm TiO2 NP size induced the most pronounced pro-inflammatory effects compared to controls. Conclusions Overall, this study showed that initial NP size and agglomeration state are key determinants of nano-TiO2 lung inflammatory reaction, cytotoxic and oxidative stress induced effects. PMID:24090040
Investigation of spherical oil agglomeration properties of celestite.
Cebeci, Yakup; Sönmez, Ibrahim
2004-05-01
In this study, concentration of celestite particles was investigated by using oil agglomeration. For this purpose, effects of operating parameters were investigated, and zeta potential measurements and Fourier transform infrared spectrophotometry (FTIR) analyses have also been carried out. In the experiments, effects of operating parameters such as pH, stirring speed, amount of Na oleate as a anionic type collector and kerosene as a bridging liquid, solid ratio, agglomeration time, collector stirring time, conditioning time, and amount of EDTA were investigated to obtain optimum conditions. Zeta potential measurements were carried out for various pH values and amounts of Na oleate. FTIR analyses were investigated to determine the adsorption type of Na oleate on celestite surface. By evaluation of the experimental results, optimum oil agglomeration conditions of celestite were determined as follows: pH 7, stirring speed 1500 rpm, amount of kerosene 100 l/t, amount of Na oleate 10 kg/t, solid ratio 5 wt%, conditioning time 5 min, collector stirring time 1 min, agglomeration time 5 min, and amount of EDTA 1.0 kg/t. In the optimum conditions, celestite was concentrated with recovery of 89.47 wt%.
Universities' Entrepreneurial Performance: The Role of Agglomeration Economies
ERIC Educational Resources Information Center
Chen, Ping Penny
2011-01-01
In spite of the extensive research on universities' entrepreneurship, whether research strength fosters or dampens their entrepreneurial performance remains controversial. Much research claims an influential role of research universities in regional economy, however, little has been said about what a part that the agglomeration economies may play…
Engineering development of selective agglomeration. Site closeout report
Not Available
1993-04-01
The Selective Agglomeration POC facility consisted of a coal crushing and grinding circuit, followed by an agglomeration circuit and product dewatering. (A plot plan of the facility is shown in Figure 1-2.) The coal crushing and grinding system consisted of a hammermill coal crusher, weigh-belt feeder, two ball mills (primary and secondary), and necessary hoppers, pumps, and conveyors. The mills were capable of providing coal over a range of grinds from a d{sub 50} of 125 to 25 microns. Slurry discharged from the ball mills was pumped to the agglomeration circuit. The agglomeration circuit began with a high-shear mixer, where diesel was added to the slurry to begin the formation of microagglomerates. The high-shear mixer was followed by two stages of conventional flotation cells for microagglomerate recovery. The second-stage-flotation-cell product was pumped to either a rotary-drum vacuum filter or a high-G centrifuge for dewatering. The dewatered product was then convoyed to the product pad from which dump trucks were used to transfer it to the utility plant located next to the facility. Plant tailings were pumped to the water clarifier for thickening and then dewatered in plate-and-frame filter presses. These dewatered tailings were also removed to the utility via dump truck. Clarified water (thickener overflow) was recycled to the process via a head tank.
Multigrid-based grid-adaptive solution of the Navier-Stokes equations
NASA Astrophysics Data System (ADS)
Michelsen, Jess
A finite volume scheme for solution of the incompressible Navier-Stokes equations in two dimensions and axisymmetry is described. Solutions are obtained on nonorthogonal, solution adaptive BFC grids, based on the Brackbill-Saltzman generator. Adaptivity is achieved by the use of a single control function based on the local kinetic energy production. Nonstaggered allocation of pressure and Cartesian velocity components avoids the introduction of curvature terms associated with the use of a grid-direction vector-base. A special interpolation of the pressure correction equation in the SIMPLE algorithm ensures firm coupling between velocity and pressure field. Steady-state solutions are accelerated by a full approximation multigrid scheme working on the decoupled grid-flow problem, while an algebraic multigrid scheme is employed for the pressure correction equation.
A multigrid approach to the global stability of swept attachment-line boundary layers
NASA Astrophysics Data System (ADS)
Meneghello, Gianluca; Schmid, Peter; Huerre, Patrick
2011-11-01
A novel numerical approach to global stability analysis is presented. A multigrid framework is leveraged in order to achieve a high computational efficiency for both the base flow and eigenvalue/eigenmode computations. The base flow is obtained as the solution of the non-linear, steady-state Navier-Stokes equations at a computational cost of nearly O (n) , where n denotes the number of degrees of freedom. The eigenvectors are obtained using the same multigrid solver, coupled to an iterative shift-invert Arnoldi algorithm. The global stability analysis of the incompressible, viscous flow near the attachment line of a swept wing is then examined for a range of Reynolds numbers up to 10000. Different families of global modes are identified together with the dominant physical mechanisms underlying the perturbation dynamics in the vicinity of the swept attachment line. Financial support from Airbus and the French National Center for Scientific Research (CNRS) is gratefully acknowledged.
A Parallel Multigrid Solver for Viscous Flows on Anisotropic Structured Grids
NASA Technical Reports Server (NTRS)
Prieto, Manuel; Montero, Ruben S.; Llorente, Ignacio M.; Bushnell, Dennis M. (Technical Monitor)
2001-01-01
This paper presents an efficient parallel multigrid solver for speeding up the computation of a 3-D model that treats the flow of a viscous fluid over a flat plate. The main interest of this simulation lies in exhibiting some basic difficulties that prevent optimal multigrid efficiencies from being achieved. As the computing platform, we have used Coral, a Beowulf-class system based on Intel Pentium processors and equipped with GigaNet cLAN and switched Fast Ethernet networks. Our study not only examines the scalability of the solver but also includes a performance evaluation of Coral where the investigated solver has been used to compare several of its design choices, namely, the interconnection network (GigaNet versus switched Fast-Ethernet) and the node configuration (dual nodes versus single nodes). As a reference, the performance results have been compared with those obtained with the NAS-MG benchmark.
Allahham, Ayman; Stewart, Peter J; Das, Shyamal C
2013-11-30
Influence of ternary, poorly water-soluble components on the agglomerate strength of cohesive indomethacin mixtures during dissolution was studied to explore the relationship between agglomerate strength and extent of de-agglomeration and dissolution of indomethacin (Ind). Dissolution profiles of Ind from 20% Ind-lactose binary mixtures, and ternary mixtures containing additional dibasic calcium phosphate (1% or 10%; DCP), calcium sulphate (10%) and talc (10%) were determined. Agglomerate strength distributions were estimated by Monte Carlo simulation of particle size, work of cohesion and packing fraction distributions. The agglomerate strength of Ind decreased from 1.19 MPa for the binary Ind mixture to 0.84 MPa for 1DCP:20Ind mixture and to 0.42 MPa for 1DCP:2Ind mixture. Both extent of de-agglomeration, demonstrated by the concentration of the dispersed indomethacin distribution, and extent of dispersion, demonstrated by the particle size of the dispersed indomethacin, were in descending order of 1DCP:2Ind>1DCP:20Ind>binary Ind. The addition of calcium sulphate dihydrate and talc also reduced the agglomerate strength and improved de-agglomeration and dispersion of indomethacin. While not definitively causal, the improved de-agglomeration and dispersion of a poorly water soluble drug by poorly water soluble components was related to the agglomerate strength of the cohesive matrix during dissolution.
Method of producing non-agglomerating submicron size particles
Bourne, Roy S.; Eichman, Clarence C.; Welbon, William W.
1989-01-01
Submicron size particles are produced by using a sputtering process to deposit particles into a liquid. The liquid is processed to recover the particles therefrom, and the particles have sizes in the range of twenty to two hundred Angstroms. Either metallic or non-metallic particles can be produced, and the metallic particles can be used in "metallic inks".
Chander, S.; Hogg, R.
1995-07-01
The development of practical technologies for the deep cleaning of coal has been seriously hampered by the problems of carrying out efficient coal/mineral separations at the very fine sizes (often finer than 10 mm) needed to achieve adequate liberation of the mineral matter from the coal matrix. It is generally recognized that surface-based separation processes such as froth flotation or selective agglomeration offer considerable potential for such applications but there remain many problems in obtaining the required selectivity with acceptable recovery of combustible matter. In froth flotation, selectivity is substantially reduced at fine sizes due, primarily, to overloading of the froth phase which leads to excessive carryover of water and entrained mineral matter. Oil agglomeration, on the other hand, can provide good selectivity at low levels of oil addition but the agglomerates tend to be too fragile for separation by the screening methods normally used. The addition of larger amounts of oil can yield large, strong agglomerates which are easily separated but the selectivity is reduced and reagent costs can become excessive.
Santos, R M; Vilaverde, C; Cunha, E; Paiva, M C; Covas, J A
2016-01-01
A one-step melt-mixing method is proposed to study dispersion and re-agglomeration phenomena of the as-received and functionalized graphite nanoplates in polypropylene melts. Graphite nanoplates were chemically modified via 1,3-dipolar cycloaddition of an azomethine ylide and then grafted with polypropylene-graft-maleic anhydride. The effect of surface functionalization on the dispersion kinetics, nanoparticle re-agglomeration and interface bonding with the polymer is investigated. Nanocomposites with 2 or 10 wt% of as-received and functionalized graphite nanoplates were prepared in a small-scale prototype mixer coupled to a capillary rheometer. Samples were collected along the flow axis and characterized by optical microscopy, scanning electron microscopy and electrical conductivity measurements. The as-received graphite nanoplates tend to re-agglomerate upon stress relaxation of the polymer melt. The covalent attachment of a polymer to the nanoparticle surface enhances the stability of dispersion, delaying the re-agglomeration. Surface modification also improves interfacial interactions and the resulting composites presented improved electrical conductivity. PMID:26439171
NASA Technical Reports Server (NTRS)
Ku, Hwar-Ching; Ramaswamy, Bala
1993-01-01
The new multigrid (or adaptive) pseudospectral element method was carried out for the solution of incompressible flow in terms of primitive variable formulation. The desired features of the proposed method include the following: (1) the ability to treat complex geometry; (2) high resolution adapted in the interesting areas; (3) requires minimal working space; and (4) effective in a multiprocessing environment. The approach for flow problems, complex geometry or not, is to first divide the computational domain into a number of fine-grid and coarse-grid subdomains with the inter-overlapping area. Next, it is necessary to implement the Schwarz alternating procedure (SAP) to exchange the data among subdomains, where the coarse-grid correction is used to remove the high frequency error that occurs when the data interpolation from the fine-grid subdomain to the coarse-grid subdomain is conducted. The strategy behind the coarse-grid correction is to adopt the operator of the divergence of the velocity field, which intrinsically links the pressure equation, into this process. The solution of each subdomain can be efficiently solved by the direct (or iterative) eigenfunction expansion technique with the least storage requirement, i.e. O(N(exp 3)) in 3-D and O(N(exp 2)) in 2-D. Numerical results of both driven cavity and jet flow will be presented in the paper to account for the versatility of the proposed method.
Effect of Agglomeration on the Toxicity of Nano-sized Carbon Black in Sprague-Dawley Rats
Kang, Mingu; Han, Jeong-Hee; Yang, Jeong-Sun
2012-01-01
Objectives Recent studies have shown that nano-sized carbon black is more toxic than large respirable carbon black because of its higher surface area. However, it is not clear if carbon black made larger by agglomeration demonstrates decreased toxicity. The purpose of this study was to verify if agglomeration affects the toxicity of carbon black using three differently prepared nano-sized carbon black aerosols in nose-only inhalation chambers for 13 weeks. Methods Printex 90 was selected as a representative nano-sized carbon black. To generate aerosols of three different types of agglomerates, Printex 90 was dispersed in distilled water by three different methods: vortex, vortex+sonication, and vortex+sonication with dispersion in a stabilizer. Then, the three differently prepared solutions were aerosolized through venturi nozzles. Male Sprague-Dawley rats were exposed to Printex 90 aerosols in a nose-only exposure chamber for 6 h/d, 5 d/wk for 13 weeks at a concentration of approximately 9 mg/m3. Results Numbers of total cells in the bronchoalveolar lavage (BAL) fluid, macrophages, and polymorphonuclear leukocytes were increased and carbon black masses were clearly seen in BAL cells and lung tissues of rats exposed to Printex 90. However, few differences were found between the three differently agglomerated aerosols. In addition, there were no significant differences in other parameters, such as body weight, lung function or cytokine levels in BAL fluid following carbon black exposure. Conclusions Only mild to moderate respiratory effects were found in rats exposed to nano-sized carbon black at 9 mg/m3 for 13 weeks. Agglomeration did not affect the toxicity of nano-sized carbon particles. PMID:23106037
Preventing ash agglomeration during gasification of high-sodium lignite
Robert S. Dahlin; Johnny R. Dorminey; WanWang Peng; Roxann F. Leonard; Pannalal Vimalchand
2009-01-15
Various additives were evaluated to assess their ability to prevent ash agglomeration during the gasification of high-sodium lignite. Additives that showed promise in simple muffle furnace tests included meta-kaolin, vermiculite, two types of silica fume, and one type of bauxite. Additives that were tested and rejected included dolomite, calcite, sand flour, kaolinite, fine kaolin, and calcined bauxite. Based on the muffle furnace test results, the meta-kaolin was selected for a follow-on demonstration in a pilot-scale coal gasifier. Pilot-scale testing showed that the addition of coarse (minus 14-mesh, 920-{mu}m mean size) meta-kaolin at a feed rate roughly equivalent to the ash content of the lignite (10 wt %) successfully prevented agglomeration and deposition problems during gasification of high-sodium lignite at a maximum operating temperature of 927{sup o}C (1700{sup o}F). 13 refs., 24 figs., 1 tab.
Engineering development of selective agglomeration: Trace element removal study
Not Available
1993-09-01
Southern Company Services, Inc., (SCS) was contracted in 1989 by the US Department of Energy (DOE) to develop a commercially acceptable selective agglomeration technology to enhance the use of high-sulfur coals by 1993. The project scope involved development of a bench-scale process and components, as well as the design, testing, and evaluation of a proof-of-concept (POC) facility. To that end, a two-ton-per-hour facility was constructed and tested near Wilsonville, Alabama. Although it was not the primary focus of the test program, SCS also measured the ability of selective agglomeration to remove trace elements from coal. This document describes the results of that program.
Functionally graded porous scaffolds made of Ti-based agglomerates.
Nazari, Keivan A; Hilditch, Tim; Dargusch, Matthew S; Nouri, Alireza
2016-10-01
Mono- and double-layer porous scaffolds were successfully fabricated using ball-milled agglomerates of Ti and Ti-10Nb-3Mo alloy. For selectively controlling the level of porosity and pore size, the agglomerates were sieved into two different size fractions of 100-300μm and 300-500μm. Compressive mechanical properties were measured on a series of cylindrical sintered compacts with different ratios of solid core diameter to porous layer width. The graded porous scaffolds exhibited stress-strain curves typical for metallic foams with a defined plateau region after yielding. The compressive strengths and elastic moduli ranged from 300 to 700MPa and 14 to 55GPa, respectively, depending on the core diameter and the material used. The obtained properties make these materials suitable for load-bearing implant applications.
Soot oxidation and agglomeration modeling in a microgravity diffusion flame
Ezekoye, O.A.; Zhang, Z.
1997-07-01
The global evolution of a microgravity diffusion flame is detailed. Gas species evolution is computed using a reduced finite rate chemical mechanism. Soot evolution is computed using various combinations of existing soot mechanisms. Radiative transfer is coupled to the soot and gas phase chemistry processes using a P1 spherical harmonics radiation model. The soot agglomeration model was examined to note the dependence of soot growth and oxidation processes on soot surface area predictions. For limiting cases where agglomeration was excluded from the soot evolution model, soot primary particle sizes and number concentrations were calculated, and the number of primary particles per aggregate was inferred. These computations are compared with experimental results for microgravity and nonbuoyant flame conditions.
Vectorized image segmentation via trixel agglomeration
Prasad, Lakshman; Skourikhine, Alexei N.
2006-10-24
A computer implemented method transforms an image comprised of pixels into a vectorized image specified by a plurality of polygons that can be subsequently used to aid in image processing and understanding. The pixelated image is processed to extract edge pixels that separate different colors and a constrained Delaunay triangulation of the edge pixels forms a plurality of triangles having edges that cover the pixelated image. A color for each one of the plurality of triangles is determined from the color pixels within each triangle. A filter is formed with a set of grouping rules related to features of the pixelated image and applied to the plurality of triangle edges to merge adjacent triangles consistent with the filter into polygons having a plurality of vertices. The pixelated image may be then reformed into an array of the polygons, that can be represented collectively and efficiently by standard vector image.
Development of a full scale selective oil agglomeration plant
Donnelly, J.C.; Cooney, B.; Hoare, I.; Waugh, B.; Robinson, R.
1998-12-31
A research and development program managed by Australian Mining Investments Limited (AMI) on behalf of an investment syndicate was conducted with the objective of improving the efficiency and economy of the Selective Oil Agglomeration Process (SOAP), and developing viable commercial sized operating plants. Fewer than half the coal preparation plants in Australia beneficiate fine coal by froth flotation, the only viable alternative to SOAP for the recovery of low ash, fine and ultra fine coal. Those plants without flotation generally dispose of the ultra fine material, approximately {minus}100{micro}m in size, as tailings to waste. In the majority of cases this ultra fine waste contains more than 50% relatively low ash coal of saleable quality. It is believed that this coal constitutes a loss of 8--10 million tonnes per annum and that the coal mining industry would welcome a recovery process which has low capital and operating costs and will function automatically with minimal operator attention. The authors carried out a comprehensive literature study of selective oil agglomeration in order to gain a full understanding of the process and to plan the research program. Extensive studies were then undertaken on oil dispersion in the water phase, formation of oil water emulsions with surfactants and the optimization of surfactant selection. Oil and emulsion properties were investigated including stability, viscosity, temperature, concentration of components, time of formation, and cost. This work was followed by characterization studies on coals from the Gunnedah Basin and agglomeration test work on these coals. These agglomeration studies were performed firstly at bench level and then by using a small, 200 kg/hr continuous process development unit. The results were sufficiently encouraging to justify the design and construction of a fully instrumented, PLC controlled, 2 tph pilot plant at Gunnedah Colliery Coal Preparation Plant. Extensive trials were carried out on
Combustion of metal agglomerates in a solid rocket core flow
NASA Astrophysics Data System (ADS)
Maggi, Filippo; Dossi, Stefano; DeLuca, Luigi T.
2013-12-01
The need for access to space may require the use of solid propellants. High thrust and density are appealing features for different applications, spanning from boosting phase to other service applications (separation, de-orbiting, orbit insertion). Aluminum is widely used as a fuel in composite solid rocket motors because metal oxidation increases enthalpy release in combustion chamber and grants higher specific impulse. Combustion process of metal particles is complex and involves aggregation, agglomeration and evolution of reacting particulate inside the core flow of the rocket. It is always stated that residence time should be enough in order to grant complete metal oxidation but agglomerate initial size, rocket grain geometry, burning rate, and other factors have to be reconsidered. New space missions may not require large rocket systems and metal combustion efficiency becomes potentially a key issue to understand whether solid propulsion embodies a viable solution or liquid/hybrid systems are better. A simple model for metal combustion is set up in this paper. Metal particles are represented as single drops trailed by the core flow and reacted according to Beckstead's model. The fluid dynamics is inviscid, incompressible, 1D. The paper presents parametric computations on ideal single-size particles as well as on experimental agglomerate populations as a function of operating rocket conditions and geometries.
NASA Astrophysics Data System (ADS)
Lu, Peizhen
X-ray computed tomography (CT) can characterize internal density gradients. An in-situ laser dilatometry has been constructed to track dimensional change at different positions of a sample during binder removal and sintering. This combination of tools not only allows us to better understand how microscopic change affects macroscopic dimensions, but also provides guidance for a variety of ceramic processes. Non-uniform agglomerate packing and deformation provide density gradients which drive binder migration during binder removal. Simultaneously, density undergoes a slight decrease accompanied by a 1.0% loss in dimensional tolerance. This and CT difference images suggest that capillary forces generated during binder melting can change the density distribution. During sintering, nonuniformities present in the green state persist into the fired state and become exaggerated. Regions of different initial density can occupy different stages sintering. At ˜88% sintered density, CT clearly showed that open porosity follows the distribution of low density areas. Mercury porosimetry detected three distinct levels of porosity. Microstructural examination correlated the porosity level with the coordination of (i) two to three or (ii) multiple grains around pores. Microstructural packing controls both the observed macroscopic expansion at T ≤ 1000°C and the onset of shrinkage. Neck formation initiates during expansion and not exclusively during shrinkage. Inter- and intra-agglomerate expansion/shrinkage proceed simultaneously but the effective 'transmission' of particle-level behavior to the macroscopic level appears to be controlled by the initial agglomerate bonding and internal agglomerate densities. Discrete element modeling provides corroborating evidence regarding the importance of compact continuity. Following the expansion-shrinkage transition, the higher the zone density the faster the initial shrinkage. The 25% RH sample shrank more rapidly than the same zone in
Drzymala, J.; Wheelock, T.D.
1996-07-01
In a selective oil agglomeration process for cleaning coal, fine-size particles are suspended in water and treated with a water-immiscible hydrocarbon which can range from pentane to heavy fuel oil. Vigorous agitation is applied to disperse the oil and to produce frequent contacts between oil-coated particles. In Part 1 of this series of papers, it was shown that a definite amount of air had to be present in a laboratory mixing unit which produced a moderate shear rate in order to form compact, spherical agglomerates in an aqueous suspension of moderately hydrophobic coal using heptane or hexadecane as an agglomerate. In this paper, the effects of different amounts of air including dissolved air are discussed. The results indicate that a small amount of air will trigger the process of agglomeration, and even the air dissolved in water under equilibrium conditions at room temperature and pressure is sufficient to promote agglomeration provided it is released from solution.
Belmeziti, Ali; Coutard, Olivier; de Gouvello, Bernard
2014-01-01
This paper is based on a prospective scenario of development of rainwater harvesting (RWH) on a given large urban area (such as metropolitan area or region). In such a perspective, a new method is proposed to quantify the related potential of potable water savings (PPWS) indicator on this type of area by adapting the reference model usually used on the building level. The method is based on four setting-up principles: gathering (definition of buildings-types and municipalities-types), progressing (use of an intermediate level), increasing (choice of an upper estimation) and prioritizing (ranking the stakes of RWH). Its application to the Paris agglomeration shows that is possible to save up to 11% of the total current potable water through the use of RWH. It also shows that the residential sector offers the most important part because it holds two-thirds of the agglomeration PPWS.
Beam optics in a MeV-class multi-aperture multi-grid accelerator for the ITER neutral beam injector.
Kashiwagi, M; Taniguchi, M; Umeda, N; de Esch, H P L; Grisham, L R; Boilson, D; Hemsworth, R S; Tanaka, M; Tobari, H; Watanabe, K; Inoue, T
2012-02-01
In a multi-aperture multi-grid accelerator of the ITER neutral beam injector, the beamlets are deflected due to space charge repulsion between beamlets and beam groups, and also due to magnetic field. Moreover, the beamlet deflection is influenced by electric field distortion generated by grid support structure. Such complicated beamlet deflections and the compensations have been examined utilizing a three-dimensional beam analysis. The space charge repulsion and the influence by the grid support structure were studied in a 1∕4 model of the accelerator including 320 beamlets. Beamlet deflection due to the magnetic field was studied by a single beamlet model. As the results, compensation methods of the beamlet deflection were designed, so as to utilize a metal bar (so-called field shaping plate) of 1 mm thick beneath the electron suppression grid (ESG), and an aperture offset of 1 mm in the ESG.
Henson, V E
2003-02-06
The purpose of this research project was to investigate, design, and implement new algebraic multigrid (AMG) algorithms to enable the effective use of AMG in large-scale multiphysics simulation codes. These problems are extremely large; storage requirements and excessive run-time make direct solvers infeasible. The problems are highly ill-conditioned, so that existing iterative solvers either fail or converge very slowly. While existing AMG algorithms have been shown to be robust and stable for a large class of problems, there are certain problems of great interest to the Laboratory for which no effective algorithm existed prior to this research.
An investigation of cell centered and cell vertex multigrid schemes for the Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Radespiel, R.; Swanson, R. C.
1989-01-01
Two efficient and robust finite-volume multigrid schemes for solving the Navier-Stokes equations are investigated. These schemes employ either a cell centered or a cell vertex discretization technique. An explicit Runge-Kutta algorithm is used to advance the solution in time. Acceleration techniques are applied to obtain faster steady-state convergence. Accuracy and convergence of the schemes are examined. Computational results for transonic airfoil flows are essentially the same, even for a coarse mesh. Both schemes exhibit good convergence rates for a broad range of artificial dissipation coefficients.
On the Performance of an Algebraic Multigrid Solver on Multicore Clusters
Baker, A; Schulz, M; Yang, U M
2009-11-24
Algebraic multigrid (AMG) solvers have proven to be extremely efficient on distributed-memory architectures. However, when executed on modern multicore cluster architectures, we face new challenges that can significantly harm AMG's performance. We discuss our experiences on such an architecture and present a set of techniques that help users to overcome the associated problems, including thread and process pinning and correct memory associations. We have implemented most of the techniques in a MultiCore SUPport library (MCSup), which helps to map OpenMP applications to multicore machines. We present results using both an MPI-only and a hybrid MPI/OpenMP model.
On the Performance of an Algebraic MultigridSolver on Multicore Clusters
Baker, A H; Schulz, M; Yang, U M
2010-04-29
Algebraic multigrid (AMG) solvers have proven to be extremely efficient on distributed-memory architectures. However, when executed on modern multicore cluster architectures, we face new challenges that can significantly harm AMG's performance. We discuss our experiences on such an architecture and present a set of techniques that help users to overcome the associated problems, including thread and process pinning and correct memory associations. We have implemented most of the techniques in a MultiCore SUPport library (MCSup), which helps to map OpenMP applications to multicore machines. We present results using both an MPI-only and a hybrid MPI/OpenMP model.
Field observations of artificial sand and oil agglomerates
Dalyander, Patricia (Soupy); Long, Joseph W.; Plant, Nathaniel G.; McLaughlin, Molly R.; Mickey, Rangley C.
2015-01-01
Oil that comes into the surf zone following spills, such as occurred during the 2010 Deepwater Horizon (DWH) blowout, can mix with local sediment to form heavier-than-water sand and oil agglomerates (SOAs), at times in the form of mats a few centimeters thick and tens of meters long. Smaller agglomerates that form in situ or pieces that break off of larger mats, sometimes referred to as surface residual balls (SRBs), range in size from sand-sized grains to patty-shaped pieces several centimeters (cm) in diameter. These mobile SOAs can cause beach oiling for extended periods following the spill, on the scale of years as in the case of DWH. Limited research, including a prior effort by the U.S. Geological Survey (USGS) investigating SOA mobility, alongshore transport, and seafloor interaction using numerical model output, focused on the physical dynamics of SOAs. To address this data gap, we constructed artificial sand and oil agglomerates (aSOAs) with sand and paraffin wax to mimic the size and density of genuine SOAs. These aSOAs were deployed in the nearshore off the coast of St. Petersburg, Florida, during a field experiment to investigate their movement and seafloor interaction. This report presents the methodology for constructing aSOAs and describes the field experiment. Data acquired during the field campaign, including videos and images of aSOA movement in the nearshore (1.5-meter and 0.5-meter water depth) and in the swash zone, are also presented in this report.
Intra-metropolitan migration in the Warsaw agglomeration.
Rykiel, Z
1984-01-01
"Two questions of intra-metropolitan migration are analyzed in the paper, intra-metropolitan hierarchy and intra-metropolitan spatial barriers. The former embraces four detailed questions: ranking of centers; spatial pattern of hierarchical subordination; degree of unequivocalness of the subordinations, or degree of dominance; and degree of hierarchicality of interrelationships. Two specialties of the Warsaw [Poland] agglomeration are discussed, the influence of the present crisis, and the administrative restrictions to migration to the city, or the spatial barriers. Social connotations of the latter are also presented."
Drug agglomeration and dissolution--what is the influence of powder mixing?
Kale, Kamakshi; Hapgood, Karen; Stewart, Peter
2009-05-01
This study determined the influence of mixing speed and time on the dissolution and deagglomeration of a micronised, poorly water-soluble drug, indomethacin, in lactose interactive mixtures. Mixing occurred in a Turbula mixer; dissolution studies were performed using the USP paddle method, and the extent of deagglomeration was determined using modelling strategies and laser diffraction particle sizing of the powder mixtures. During low energy mixing at low rates and short mixing times, dissolution profiles showed an unusual flat asymptote indicating incomplete extents of dissolution caused by agglomerates that did not readily disperse in the dissolution medium. The study showed that increasing both speed and time of mixing increased the extent of dissolution and deagglomeration of the indomethacin powder. Nonlinear least squares modelling of the dissolution data using a sigmoidal equation provided estimates of the extent and rate of dissolution. Mixing speed and time had a much greater influence on the extent of dissolution which was controlled by deagglomeration than on the initial dissolution rate which was related to dispersed indomethacin. While some deagglomeration did occur at higher mixing energies, the deagglomeration of the indomethacin was not complete with only about 58-80% of indomethacin particles overlapping with the primary indomethacin particle size distribution. The significant outcome of this study was that mixing conditions have a major influence on the mixing quality, especially in areas where agglomerate characteristics influence performance. PMID:19347972
Li, Weiyong; Woldu, Abraham; Kelly, Richard; McCool, Jim; Bruce, Rick; Rasmussen, Henrik; Cunningham, John; Winstead, Denita
2008-02-28
This research note describes a powder blending simulation study conducted using 20-mL scintillation vials and a bench-top rotating mixer on a scale of 2g for each sample. In order to investigate the impact of mean particle size and size distribution on blending behavior of an active pharmaceutical ingredient (API), the drug substance was separated into sieve fractions using the US standard sieves of 60, 80, 100, 200, and 325mesh. Each of the fractions was mixed with two excipients (hydroxypropyl methylcellulose and microcrystalline cellulose) for up to 20min. Then the blending samples were analyzed by a near infrared chemical imaging (NIR-CI) system. The NIR-CI system was able to measure API particles/domains (agglomerates) at 0.001mm(2) and above within a 11.2mmx9.0mm field of view. It was found that blends prepared with larger API particles (60-200 mesh) contain agglomerated API domains > or =0.1mm(2). The blends prepared with finer API particles (< or =325 mesh) show the characteristics of a randomized mixing. This simple and effective method can be used for evaluation of blending behavior for APIs in formulation development. PMID:17951017
NASA Astrophysics Data System (ADS)
Koldan, Jelena; Puzyrev, Vladimir; de la Puente, Josep; Houzeaux, Guillaume; Cela, José María
2014-06-01
We present an elaborate preconditioning scheme for Krylov subspace methods which has been developed to improve the performance and reduce the execution time of parallel node-based finite-element (FE) solvers for 3-D electromagnetic (EM) numerical modelling in exploration geophysics. This new preconditioner is based on algebraic multigrid (AMG) that uses different basic relaxation methods, such as Jacobi, symmetric successive over-relaxation (SSOR) and Gauss-Seidel, as smoothers and the wave front algorithm to create groups, which are used for a coarse-level generation. We have implemented and tested this new preconditioner within our parallel nodal FE solver for 3-D forward problems in EM induction geophysics. We have performed series of experiments for several models with different conductivity structures and characteristics to test the performance of our AMG preconditioning technique when combined with biconjugate gradient stabilized method. The results have shown that, the more challenging the problem is in terms of conductivity contrasts, ratio between the sizes of grid elements and/or frequency, the more benefit is obtained by using this preconditioner. Compared to other preconditioning schemes, such as diagonal, SSOR and truncated approximate inverse, the AMG preconditioner greatly improves the convergence of the iterative solver for all tested models. Also, when it comes to cases in which other preconditioners succeed to converge to a desired precision, AMG is able to considerably reduce the total execution time of the forward-problem code-up to an order of magnitude. Furthermore, the tests have confirmed that our AMG scheme ensures grid-independent rate of convergence, as well as improvement in convergence regardless of how big local mesh refinements are. In addition, AMG is designed to be a black-box preconditioner, which makes it easy to use and combine with different iterative methods. Finally, it has proved to be very practical and efficient in the
Numerical Methods for Forward and Inverse Problems in Discontinuous Media
Chartier, Timothy P.
2011-03-08
The research emphasis under this grant's funding is in the area of algebraic multigrid methods. The research has two main branches: 1) exploring interdisciplinary applications in which algebraic multigrid can make an impact and 2) extending the scope of algebraic multigrid methods with algorithmic improvements that are based in strong analysis.The work in interdisciplinary applications falls primarily in the field of biomedical imaging. Work under this grant demonstrated the effectiveness and robustness of multigrid for solving linear systems that result from highly heterogeneous finite element method models of the human head. The results in this work also give promise to medical advances possible with software that may be developed. Research to extend the scope of algebraic multigrid has been focused in several areas. In collaboration with researchers at the University of Colorado, Lawrence Livermore National Laboratory, and Los Alamos National Laboratory, the PI developed an adaptive multigrid with subcycling via complementary grids. This method has very cheap computing costs per iterate and is showing promise as a preconditioner for conjugate gradient. Recent work with Los Alamos National Laboratory concentrates on developing algorithms that take advantage of the recent advances in adaptive multigrid research. The results of the various efforts in this research could ultimately have direct use and impact to researchers for a wide variety of applications, including, astrophysics, neuroscience, contaminant transport in porous media, bi-domain heart modeling, modeling of tumor growth, and flow in heterogeneous porous media. This work has already led to basic advances in computational mathematics and numerical linear algebra and will continue to do so into the future.
A hybrid multigrid technique for computing steady-state solutions to supersonic flows
NASA Technical Reports Server (NTRS)
Sanders, Richard
1992-01-01
Recently, Li and Sanders have introduced a class of finite difference schemes to approximate generally discontinuous solutions to hyperbolic systems of conservation laws. These equations have the form together with relevant boundary conditions. When modelling hypersonic spacecraft reentry, the differential equations above are frequently given by the compressible Euler equations coupled with a nonequilibrium chemistry model. For these applications, steady state solutions are often sought. Many tens (to hundreds) of super computer hours can be devoted to a single three space dimensional simulation. The primary difficulty is the inability to rapidly and reliably capture the steady state. In these notes, we demonstrate that a particular variant from the schemes presented can be combined with a particular multigrid approach to capture steady state solutions to the compressible Euler equations in one space dimension. We show that the rate of convergence to steady state coming from this multigrid implementation is vastly superior to the traditional approach of artificial time relaxation. Moreover, we demonstrate virtual grid independence. That is, the rate of convergence does not depend on the degree of spatial grid refinement.
10B multi-grid proportional gas counters for large area thermal neutron detectors
NASA Astrophysics Data System (ADS)
Andersen, K.; Bigault, T.; Birch, J.; Buffet, J. C.; Correa, J.; Hall-Wilton, R.; Hultman, L.; Höglund, C.; Guérard, B.; Jensen, J.; Khaplanov, A.; Kirstein, O.; Piscitelli, F.; Van Esch, P.; Vettier, C.
2013-08-01
3He was a popular material in neutrons detectors until its availability dropped drastically in 2008. The development of techniques based on alternative convertors is now of high priority for neutron research institutes. Thin films of 10B or 10B4C have been used in gas proportional counters to detect neutrons, but until now, only for small or medium sensitive area. We present here the multi-grid design, introduced at the ILL and developed in collaboration with ESS for LAN (large area neutron) detectors. Typically thirty 10B4C films of 1 μm thickness are used to convert neutrons into ionizing particles which are subsequently detected in a proportional gas counter. The principle and the fabrication of the multi-grid are described and some preliminary results obtained with a prototype of 200 cm×8 cm are reported; a detection efficiency of 48% has been measured at 2.5 Å with a monochromatic neutron beam line, showing the good potential of this new technique.
Mechanism of nanoparticle agglomeration during the combustion synthesis
NASA Astrophysics Data System (ADS)
Altman, Igor S.; Agranovski, Igor E.; Choi, Mansoo
2005-08-01
The mechanism of agglomeration of nanoparticles generated during combustion synthesis is discussed. This is based on the analysis of the transmission electron microscope images of probes collected at different heights. Although direct temperature measurements were not available, the qualitative temperature dependence of the particle formation streamlines is taken into account. It is demonstrated that agglomeration of the MgO nanoparticles, which are formed during a Mg particle combustion, occurs as the result of bonding the mature nanoparticles by the supercritical clusters existing in the system. Accumulation of these supercritical clusters in the flame has been revealed and their nature has been explained in our recent paper [I.S. Altman, I.E. Agranovski, and M. Choi, Phys. Rev E 70, 062603 (2004)]. Also, some inspection of the previously published experimental data on the nanoparticle generation shows that the similar supercritical clusters may exist in another flame reactor generating titania nanopaprticles. If this is the case, the cluster-based process of nanoparticle bonding we suggest can be considered to be general.
Agglomeration of Luminescent Porous Silicon Nanoparticles in Colloidal Solutions.
Herynková, Kateřina; Šlechta, Miroslav; Šimáková, Petra; Fučíková, Anna; Cibulka, Ondřej
2016-12-01
We have prepared colloidal solutions of clusters composed from porous silicon nanoparticles in methanol, water and phosphate-buffered saline (PBS). Even if the size of the nanoclusters is between 60 and 500 nm, due to their highly porous "cauliflower"-like structure, the porous silicon nanoparticles are composed of interconnected nanocrystals having around 2.5 nm in size and showing strong visible luminescence in the orange-red spectral region (centred at 600-700 nm). Hydrophilic behaviour and good solubility of the nanoclusters in water and water-based solutions were obtained by adding hydrogen peroxide into the etching solution during preparation and 16 min long after-bath in hydrogen peroxide. By simple filtration of the solutions with syringe filters, we have extracted smaller nanoclusters with sizes of approx. 60-70 nm; however, these nanoclusters in water and PBS solution (pH neutral) are prone to agglomeration, as was confirmed by zeta potential measurements. When the samples were left at ambient conditions for several weeks, the typical nanocluster size increased to approx. 330-400 nm and then remained stable. However, both freshly filtered and aged samples (with agglomerated porous silicon nanoparticles) of porous silicon in water and PBS solutions can be further used for biological studies or as luminescent markers in living cells. PMID:27541815
Synthesis and agglomeration of gold nanoparticles in reverse micelles
NASA Astrophysics Data System (ADS)
Herrera, Adriana P.; Resto, Oscar; Briano, Julio G.; Rinaldi, Carlos
2005-07-01
Reverse micelles prepared in the system water, sodium bis-(2-ethylhexyl) sulfoccinate (AOT), and isooctane were investigated as a templating system for the production of gold nanoparticles from Au(III) and the reducing agent sulfite. A core-shell Mie model was used to describe the optical properties of gold nanoparticles in the reverse micelles. Dynamic light scattering of gold colloids in aqueous media and in reverse micelle solution indicated agglomeration of micelles containing particles. This was verified theoretically with an analysis of the total interaction energy between pairs of particles as a function of particle size. The analysis indicated that particles larger than about 8 nm in diameter should reversibly flocculate. Transmission electron microscopy measurements of gold nanoparticles produced in our reverse micelles showed diameters of 8-10 nm. Evidence of cluster formation was also observed. Time-correlated UV-vis absorption measurements showed a red shift for the peak wavelength. This was interpreted as the result of multiple scattering and plasmon interaction between particles due to agglomeration of micelles with particles larger than 8 nm.
Agglomeration of Luminescent Porous Silicon Nanoparticles in Colloidal Solutions.
Herynková, Kateřina; Šlechta, Miroslav; Šimáková, Petra; Fučíková, Anna; Cibulka, Ondřej
2016-12-01
We have prepared colloidal solutions of clusters composed from porous silicon nanoparticles in methanol, water and phosphate-buffered saline (PBS). Even if the size of the nanoclusters is between 60 and 500 nm, due to their highly porous "cauliflower"-like structure, the porous silicon nanoparticles are composed of interconnected nanocrystals having around 2.5 nm in size and showing strong visible luminescence in the orange-red spectral region (centred at 600-700 nm). Hydrophilic behaviour and good solubility of the nanoclusters in water and water-based solutions were obtained by adding hydrogen peroxide into the etching solution during preparation and 16 min long after-bath in hydrogen peroxide. By simple filtration of the solutions with syringe filters, we have extracted smaller nanoclusters with sizes of approx. 60-70 nm; however, these nanoclusters in water and PBS solution (pH neutral) are prone to agglomeration, as was confirmed by zeta potential measurements. When the samples were left at ambient conditions for several weeks, the typical nanocluster size increased to approx. 330-400 nm and then remained stable. However, both freshly filtered and aged samples (with agglomerated porous silicon nanoparticles) of porous silicon in water and PBS solutions can be further used for biological studies or as luminescent markers in living cells.
DETERMINATION OF STOKES SHAPE FACTOR FOR SINGLE PARTICLES AND AGGLOMERATES
Matyas, Josef; Schaible, Micah J.; Vienna, John D.
2011-09-01
The large octahedral crystals of spinel can precipitate from glass during the high-level waste vitrification process and potentially block the glass discharge riser of electrically heated ceramic melters. To help predict the settling behavior of spinel in the riser, the settling of single particles and agglomerates was studied in stagnant and transparent viscosity oils at room temperature with developed optical particle-dynamics-analyzer. Determined dimensions and terminal settling velocities of particles were used for calculation of their Stokes shape factors. Calculated shape factor for the glass beads was almost identical with the theoretical shape factor of 2/9 for a perfect sphere. The shape factor for single spinel crystal was about 7.6 % higher compare to the theoretically predicted value for octahedron. Stokes shape factor of irregularly shaped multi-particle agglomerates was lower than that of the glass beads and individual spinel crystals because of the higher surface drag caused by the larger surface area to volume ratio.
Agglomeration of Luminescent Porous Silicon Nanoparticles in Colloidal Solutions
NASA Astrophysics Data System (ADS)
Herynková, Kateřina; Šlechta, Miroslav; Šimáková, Petra; Fučíková, Anna; Cibulka, Ondřej
2016-08-01
We have prepared colloidal solutions of clusters composed from porous silicon nanoparticles in methanol, water and phosphate-buffered saline (PBS). Even if the size of the nanoclusters is between 60 and 500 nm, due to their highly porous "cauliflower"-like structure, the porous silicon nanoparticles are composed of interconnected nanocrystals having around 2.5 nm in size and showing strong visible luminescence in the orange-red spectral region (centred at 600-700 nm). Hydrophilic behaviour and good solubility of the nanoclusters in water and water-based solutions were obtained by adding hydrogen peroxide into the etching solution during preparation and 16 min long after-bath in hydrogen peroxide. By simple filtration of the solutions with syringe filters, we have extracted smaller nanoclusters with sizes of approx. 60-70 nm; however, these nanoclusters in water and PBS solution (pH neutral) are prone to agglomeration, as was confirmed by zeta potential measurements. When the samples were left at ambient conditions for several weeks, the typical nanocluster size increased to approx. 330-400 nm and then remained stable. However, both freshly filtered and aged samples (with agglomerated porous silicon nanoparticles) of porous silicon in water and PBS solutions can be further used for biological studies or as luminescent markers in living cells.
Single domain PEMFC model based on agglomerate catalyst geometry
NASA Astrophysics Data System (ADS)
Siegel, N. P.; Ellis, M. W.; Nelson, D. J.; von Spakovsky, M. R.
A steady two-dimensional computational model for a proton exchange membrane (PEM) fuel cell is presented. The model accounts for species transport, electrochemical kinetics, energy transport, current distribution, and water uptake and release in the catalyst layer. The governing differential equations are solved over a single computational domain, which consists of a gas channel, gas diffusion layer, and catalyst layer for both the anode and cathode sides of the cell as well as the solid polymer membrane. The model for the catalyst regions is based on an agglomerate geometry, which requires water species to exist in both dissolved and gaseous forms simultaneously. Data related to catalyst morphology, which was required by the model, was obtained via a microscopic analysis of a commercially available membrane electrode assembly (MEA). The coupled set of differential equations is solved with the commercial computational fluid dynamics (CFD) solver, CFDesign™, and is readily adaptable with respect to geometry and material property definitions. The results show that fuel cell performance is highly dependent on catalyst structure, specifically the relative volume fractions of gas pores and polymer membrane contained within the active region as well as the geometry of the individual agglomerates.
Planetary Rings: Statistical Description of Fragmentation of Ring-agglomerates
NASA Astrophysics Data System (ADS)
Spahn, Frank; Vieira Neto, E.; Guimaraes, A. H. F.; Brilliantov, N. V.; Gorban, A. N.
2009-09-01
We study the fragmentation dynamics of a two-dimensional agglomerate, hold together by adhesive bonds, caused by an impacting projectile of given mass and impact speed/energy. The agglomerate is made of identical adhering spheres (constituents) forming a regular cubic lattice. A rather simple "random walk model" of a crack propagation has been studied numerically and analytically, where subsequent breaking of adhesive bonds (defining the crack path) is organized randomly and the breakage continues until the impact energy of the projectile is exhausted. A large number of repeated numerical breakage experiments have yielded a surprising agreement with egg-shell crushing experiments (Hermann et al., Physica A 371 (2006), 59) - i.e. the size distribution of the fragments obeys a power law, p(s) sa with a = -3/2. This distribution can theoretically described by a one-dimensional random walk model to mimick the propagation of the crack. With this prerequisite the fragment sizes can be mapped to the mean time of two distant cracks to meet (mean free passage time) in this way justifying the above distribution. These studies will serve as an input for a kinetic description (Spahn et al. 2004, Europhys. Lett. 67 (2004), 545) of a balance between coagulation and fragmentation to describe the "meso-scopic" dynamics of dense planetary rings.
Chemical and physicochemial properties of submicron aerosol agglomerates
Scripsick, R.C.; Ehrman, S.; Friedlander, S.K.
1998-12-31
This is the final report of a three-year, Laboratory Directed Research and Development (LDRD) project at Los Alamos National Laboratory. The formation of nanometer-sized aerosol particles in a premixed methane flame from both solid-phase aerosol precursors and gas-phase precursors was investigated. Techniques were developed to determine the distribution of the individual chemical species as a function of agglomerate size by using inductively coupled plasma atomic emission spectroscopy (ICP-AES). To determine the distribution of chemical species both from particle to particle and within the particles on a nanometer scale, we used the analytical electron microscopy techniques of energy dispersive x-ray spectrometry (EDS) and electron energy loss spectrometry (EELS) coupled with transmission electron microscopy (TEM). The observed distribution of individual chemical species as a function of agglomerate size was linked to the material properties of the solid-phase precursors. For aerosol formed from gas-phase precursors by gas-to-particle conversion, the distribution of species on a manometer scale was found to correspond to the equilibrium phase distribution expected from equilibrium for the system at the flame temperatures.
Agglomeration of soot particles in diffusion flames under microgravity
Ito, H.; Fujita, O.; Ito, K.
1994-11-01
Experiments have been conducted to investigate the behavior of soot particles in diffusion flames under microgravity conditions using a 490-m drop shaft (10-s microgravity duration) in Hokkaido, Japan. Flames from the combustion of paper sheets and butane jet diffusion flames are observed under microgravity. The oxygen concentration of the surroundings, the butane flow rate,and the burner diameter are varied as experimental parameters. The generated soot particles are sampled under microgravity and observed using scanning electron and transmission electron microscopes. The flames with a residual convection or forced convection are also observed to examine the influence of flow field on soot particle generation under microgravity. From these results, it is found that a number of large luminous spots appear in diffusion flames under microgravity. From the observation of TEM images, the luminous spots are the result of agglomerated soot particles and the growth of their diameters to a discernible level. The diameter of the agglomerated particles measure about 0.1 mm, 200 to 500 times as large as those generated under normal gravity. It is suggested that these large soot particles are generated in the limited areas where the conditions for the formation of these particles, such as gas velocity (residence time) and oxygen concentration, are satisfied.
A multi-grid code for 3-D transonic potential flow about axisymmetric inlets at angle of attack
NASA Technical Reports Server (NTRS)
Mccarthy, D. R.; Reyhner, T. A.
1980-01-01
In the present work, an existing transonic potential code is adapted to utilize the Multiple Level Adaptive technique proposed by A. Brandt. It is shown that order of magnitude improvements in speed and greatly improved accuracy over the unmodified code are achieved. Consideration is given to the difficulties of multi-grid programming, and possible future applications are surveyed.
Smoothed aggregation adaptive spectral element-based algebraic multigrid
2015-01-20
SAAMGE provides parallel methods for building multilevel hierarchies and solvers that can be used for elliptic equations with highly heterogeneous coefficients. Additionally, hierarchy adaptation is implemented allowing solving multiple problems with close coefficients without rebuilding the hierarchy.
Numerical derivation of forces on particles and agglomerates in a resonant acoustic field
NASA Astrophysics Data System (ADS)
Knoop, Claas; Fritsching, Udo
2013-10-01
Particles and agglomerates are investigated in gaseous acoustic flow fields. Acoustic fields exert forces on solid objects, which can influence the shape of the exposed bodies, even to the point of breakage of the structures. Motivated by experimentally observed breakage of agglomerates in an acoustic levitator (f = 20 kHz), a numerical study is presented that derives the acoustic forces on a complex model agglomerate from the pressure and velocity fields of a resonant standing ultrasound wave, calculated by computational fluid dynamics (CFD). It is distinguished between the drag and lift/lateral forces on the overall agglomerate and on the different primary particles of the model.
Multigrid waveform relaxation on spatial finite element meshes
Janssen, J.; Vandewalle, S.
1994-12-31
The authors shall discuss the numerical solution of a parabolic partial differential equation {partial_derivative}u/{partial_derivative}t(x,t) = Lu(x,t) + f(x,t), x{element_of}{Omega}, t>0, (1) supplied with a boundary condition and given initial values. The spatial finite element discretization of (1) on a discrete grid {Omega}{sub h} leads to an initial value problem of the form B{dot u} + Au = f, u(0) = u{sub o}, t > 0, (2) with B a non-singular matrix. The waveform relaxation method is a method for solving ordinary differential equations. It differs from most standard iterative techniques in that it is a continuous-time method, iterating with functions in time, and thereby well-suited for parallel computation.
Wheelock, T.D.
1996-09-01
The series of agglomeration tests designed to study the agglomeration characteristics of Pittsburgh No. 8 coal with i-octane was continued using a larger agitated tank. This series is designed to determine the effects of various parameters on the size and structure of the agglomerates formed, the rate of agglomeration, coal recovery, and ash rejection. The results reported here show that once spherical agglomerates are formed they continue to grow at almost a constant rate which is proportional to the concentration of i-octane. The constant growth rate is interrupted when spherical agglomerates combine to form large clusters. This only seems to occur with a large concentration of i-octane (e.g., 30 v/w%) and limited agitator power. The present results also show that coal recovery and ash rejection are highly dependent on agglomerate size when the mean agglomerate diameter is less than the size of the openings in the screen used for recovering the agglomerates.
Hou, Kang; Zhou, Jieting; Li, Xuxiang; Ge, Shengbin
2016-01-01
Analysis of human living environmental quality of Shenyang-Dalian urban agglomerations has important theoretical and practical significance in rapid development region. A lot of investigations have been carried for Shenyang-Dalian urban agglomerations, including 38 counties. Based on the carrying capacity of resources, natural and socioeconomic environmental factors and regional changes of human living environmental evaluation are analyzed with the application of geographic information systems (GIS) software. By using principal component analysis (PCA) model and natural breaks classification (NBC) method, the evaluation results are divided into five categories. The results show that the human living environmental evaluation (HLEE) indexes of Dalian, Shenyang, and Liaoyang are higher than other counties. Among these counties, the human living environmental evaluation (HLEE) indexes of coastal counties are significantly higher than inland counties. The range of the human living environmental evaluation index in most of the study area is at III, IV, and V levels, accounting for 80.01%. Based on these results, it could illustrate the human living environment is in relatively suitable condition in Shenyang-Dalian urban agglomeration. PMID:27200212
Hou, Kang; Zhou, Jieting; Li, Xuxiang; Ge, Shengbin
2016-01-01
Analysis of human living environmental quality of Shenyang-Dalian urban agglomerations has important theoretical and practical significance in rapid development region. A lot of investigations have been carried for Shenyang-Dalian urban agglomerations, including 38 counties. Based on the carrying capacity of resources, natural and socioeconomic environmental factors and regional changes of human living environmental evaluation are analyzed with the application of geographic information systems (GIS) software. By using principal component analysis (PCA) model and natural breaks classification (NBC) method, the evaluation results are divided into five categories. The results show that the human living environmental evaluation (HLEE) indexes of Dalian, Shenyang, and Liaoyang are higher than other counties. Among these counties, the human living environmental evaluation (HLEE) indexes of coastal counties are significantly higher than inland counties. The range of the human living environmental evaluation index in most of the study area is at III, IV, and V levels, accounting for 80.01%. Based on these results, it could illustrate the human living environment is in relatively suitable condition in Shenyang-Dalian urban agglomeration. PMID:27200212
Time-accurate Navier-Stokes calculations with multigrid acceleration
NASA Technical Reports Server (NTRS)
Melson, N. D.; Sanetrik, Mark D.; Atkins, Harold L.
1993-01-01
An efficient method for calculating unsteady flows is presented, with emphasis on a modified version of the thin-layer Navier-Stokes equations. Fourier stability analysis is used to illustrate the effect of treating the source term implicitly instead of explicity, as well as to illustrate other algorithmic choices. A 2D circular cylinder (with a Reynolds number of 1200 and a Mach number of 0.3) is calculated. The present scheme requires only about 10 percent of the computer time required by global minimum time stepping.
Intensive drying and the related microstructure features in agglomerate spheres
NASA Astrophysics Data System (ADS)
Kudlyk, Rostyslav
Most metal ore concentrates are fine particulates with a wide particle-size distribution. Industrially they are pelletized by tumbling in balling discs or drums into spheres, an operation which requires the addition of typically up to 10% by weight of water. Further processing of these agglomerates involves first drying and then induration by heating up to 1250°C. The main objective of this thesis was the study of the interrelationship between the microstructure of the agglomerates with, on the one hand, the mechanical and physical properties of the pellets and their behaviour during intensive drying, on the other. The previously developed model of the drying process identified the loss of capillarity, resulting from the vapour lock, to be a critical component of the mechanism of intense as opposed to 'classical' drying. It was shown that the absence of the constant-rate drying period is a natural consequence of this effect. Several significant shortcomings of the previous model have been identified. This model treats the period of transition between surface- and shrinking-core drying as an instantaneous event. The new extended model, which overcomes the original model limitations, was developed in this project. In its formalism, the new model includes the pore-size distribution and thus simulates a gradual surface/shrinking-core transition. It was shown that the nature of the transition between the surface- and shrinking-core drying regimes during intensive drying is fundamentally different from that of classical drying, i.e. carried out at mild temperatures. In the latter case, liquid is being delivered to the surface through the network of interconnected small pores reaching the surface. The transition occurs when the larger pores, also reaching the surface, are being drained. On the other hand, under intense-drying conditions, the rate-limiting factor is the vapour lock. The latter phenomenon will occur in the smaller pores first, as they have smaller liquid
Constructing Political Region Agglomerations for Effective Science Communcation
NASA Astrophysics Data System (ADS)
Rising, J. A.
2015-12-01
Often political regions form a better scale for modeling than regulargrids, since they are used for collecting socioeconomic data and aremore relevant to stakeholders and policy-makers. However, differentpolitical regions can enclose very different areas, populations,ranges of climatic variability, and for many countries there are anundesireable number of regions available at any administrative level.We provide a solution to this problem, by providing a general systemfor agglomerating regions to a larger scale, to approximately optimizearbitrary objectives. These regions provide an intermediate scale formodeling and greater comparability than unagglomerated regions. Wefirst apply the approach to the US, producing region agglomerationsthat normalize region size, population, income, and climaticvariability. We then apply the technique globally, generating acononical collection of regions for studying the impacts of climatechange.
Remediation of Sucarnoochee soil by agglomeration with fine coal
Narayanan, P.S.; Arnold, D.W.; Rahnama, M.B. )
1994-01-01
Fine-sized Blue Creek coal was used to remove high molecular weight hydrocarbons from Sucarnoochee soil, a fine-sized high-organic soil. Fine coal in slurry form was blended with Sucarnoochee soil contaminated with 15.0% by wt of crude oil, and agglomerates were removed in a standard flotation cell. Crude oil in the remediated soil was reduced from the original 15.0% to less than a tenth of a wt% by a two-step process. Oil removal of approx. 99.3% was obtained. An added benefit was that the low-grade coal used in the process was simultaneously upgraded. The final level of cleaning was not affected by initial oil concentration. The process compared favorably with a hot water wash technique used to recovery oils from contaminated soil.
Upgrading of coal liquefaction feedstock by selective agglomeration
Lai, R.; Sinha, K.; Richardson, A.; Killmeyer, R.; Utz, B.; Hickey, R.; Cillo, D.
1994-03-01
The technical feasibility study of using selective agglomeration (with coal-derived oil) to upgrade Illinois No. 6 coal for a liquefaction feedstock was completed. Effects of coal particle size, slurry pH, oil-to-coal ratio, and operating temperature on mineral matter reduction, clean coal weight recovery, and clean coal moisture content were studied. The addition of coal-derived naphtha or kerosene as conditioners to increase hydrophobicity and recovery of coal was also investigated. Results showed that approximately 70% of the mineral matter could be removed from this coal at a clean coal weight recovery of over 85% by grinding the coal to a mean volume diameter of about 10 microns and properly selecting of the operation variables.
Molecular mechanisms responsible for hydrate anti-agglomerant performance.
Phan, Anh; Bui, Tai; Acosta, Erick; Krishnamurthy, Pushkala; Striolo, Alberto
2016-09-28
Steered and equilibrium molecular dynamics simulations were employed to study the coalescence of a sI hydrate particle and a water droplet within a hydrocarbon mixture. The size of both the hydrate particle and the water droplet is comparable to that of the aqueous core in reverse micelles. The simulations were repeated in the presence of various quaternary ammonium chloride surfactants. We investigated the effects due to different groups on the quaternary head group (e.g. methyl vs. butyl groups), as well as different hydrophobic tail lengths (e.g. n-hexadecyl vs. n-dodecyl tails) on the surfactants' ability to prevent coalescence. Visual inspection of sequences of simulation snapshots indicates that when the water droplet is not covered by surfactants it is more likely to approach the hydrate particle, penetrate the protective surfactant film, reach the hydrate surface, and coalesce with the hydrate than when surfactants are present on both surfaces. Force-distance profiles obtained from steered molecular dynamics simulations and free energy profiles obtained from umbrella sampling suggest that surfactants with butyl tripods on the quaternary head group and hydrophobic tails with size similar to the solvent molecules can act as effective anti-agglomerants. These results qualitatively agree with macroscopic experimental observations. The simulation results provide additional insights, which could be useful in flow assurance applications: the butyl tripod provides adhesion between surfactants and hydrates; when the length of the surfactant tail is compatible with that of the hydrocarbon in the liquid phase a protective film can form on the hydrate; however, once a molecularly thin chain of water molecules forms through the anti-agglomerant film, connecting the water droplet and the hydrate, water flows to the hydrate and coalescence is inevitable. PMID:27436688
A MODEL FOR FINE PARTICLE AGGLOMERATION IN CIRCULATING FLUIDIZED BED ABSORBERS
A model for fine particle agglomeration in circulating fluidized bed absorbers (CFBAS) has been developed. It can model the influence of different factors on agglomeration, such as the geometry of CFBAs, superficial gas velocity, initial particle size distribution, and type of ag...
Generation of nanoparticle agglomerates and their dispersion in lung serum simulant or water
NASA Astrophysics Data System (ADS)
Wong, B. A.; Nash, D. G.; Moss, O. R.
2009-02-01
Nanoparticles released into the atmosphere, due to their high diffusivity, will likely begin to agglomerate. The state of agglomeration upon inhalation and the potential to disperse back into nanoparticles may affect the toxicity of the inhaled material. In order to investigate particle dispersion, a system was set up to generate aggregates from agglomerates. Primary particles, composed of zinc, were generated using zinc rods in a spark generator (Palas GFG-1000, Karlsrhue, Germany). These particles formed agglomerates which were passed through a room temperature aging chamber or through a tube furnace (Carbolite HST, Derbyshire, UK). Agglomerate size was measured with a scanning mobility particle sizer (SMPS model 3936, TSI Inc., Shoreview, MN). When furnace temperature was set near the zinc coalescence temperature, instead of decreasing in size, agglomerate size increased up to 30%; a percentage increase duplicated with the room temperature aging chamber. Starting with an aerosol of primary zinc particles, equal concentrations of agglomerate and aggregrate aerosol were produced. The extent of breakup and dispersion of agglomerates and aggregates to individual nanoparticles in lung serum simulant will be assessed using transmission electron microscopy.
Agglomeration characteristics of river sand and wheat stalk ash mixture at high temperatures
NASA Astrophysics Data System (ADS)
Shang, Linlin; Li, Shiyuan; Lu, Qinggang
2013-02-01
The agglomeration characteristics of river sand and wheat stalk ash mixture at various temperatures are investigated using a muffle furnace. The surface structural changes, as well as the elemental makeup of the surface and cross-section of the agglomerates, are analyzed by polarized light microscopy, scanning electron microscopy (SEM), and energy dispersive X-ray (EDX). Multi-phase equilibrium calculation is performed with FactSage in identifying the melting behavior of the river sand-wheat stalk ash mixture at high temperatures. No indication of agglomeration is detected below 850°C. At a temperature of 900-1000°C, however, obvious agglomeration is observed and the agglomerates solidify further as temperature increases. The presence of potassium and calcium enrichment causes the formation of a sticky sand surface that induces agglomeration. The main component of the agglomerate surface is K2O-CaO-SiO2, which melts at low temperatures. The formation of molten silicates causes particle cohesion. The main ingredient of the binding phase in the cross-section is K2O-SiO2-Na2O-Al2O3-CaO; the agglomeration is not the result of the melting behavior of wheat stalk ash itself but the comprehensive results of chemical reaction and the melting behavior at high temperatures. The multi-phase equilibrium calculations agree well with the experimental results.
NASA Astrophysics Data System (ADS)
Tong, M.; Jagarlapudi, S. C.; Patel, J. B.; Stone, I. C.; Fan, Z.; Browne, D. J.
2015-06-01
Physically conditioning molten scrap aluminium alloys using high shear processing (HSP) was recently found to be a promising technology for purification of contaminated alloys. HSP refines the solid oxide agglomerates in molten alloys, so that they can act as sites for the nucleation of Fe-rich intermetallic phases which can subsequently be removed by the downstream de-drossing process. In this paper, a computational modelling for predicting the evolution of size of oxide clusters during HSP is presented. We used CFD to predict the macroscopic flow features of the melt, and the resultant field predictions of temperature and melt shear rate were transferred to a population balance model (PBM) as its key inputs. The PBM is a macroscopic model that formulates the microscopic agglomeration and breakage of a population of a dispersed phase. Although it has been widely used to study conventional deoxidation of liquid metal, this is the first time that PBM has been used to simulate the melt conditioning process within a rotor/stator HSP device. We employed a method which discretizes the continuous profile of size of the dispersed phase into a collection of discrete bins of size, to solve the governing population balance equation for the size of agglomerates. A finite volume method was used to solve the continuity equation, the energy equation and the momentum equation. The overall computation was implemented mainly using the FLUENT module of ANSYS. The simulations showed that there is a relatively high melt shear rate between the stator and sweeping tips of the rotor blades. This high shear rate leads directly to significant fragmentation of the initially large oxide aggregates. Because the process of agglomeration is significantly slower than the breakage processes at the beginning of HSP, the mean size of oxide clusters decreases very rapidly. As the process of agglomeration gradually balances the process of breakage, the mean size of oxide clusters converges to a
Relaxation Revisited: A Fresh Look at Multigrid for Steady Flows
NASA Technical Reports Server (NTRS)
Roberts, Thomas W.; Swanson, R. C.; Sidilkover, David
1997-01-01
The year 1971 saw the publication of one of the landmark papers in computational aerodynamics, that of Murman and Cole. As with many seminal works, its significance lies not so much in the specific problem that it addressed| small disturbance, plane transonic flow - but in the identification of a general approach to the solution of a technically important and theoretically difficult problem. The key features of Murman and Cole's work were the use of type- dependent differencing to correctly account for the proper domain of dependence of a mixed elliptic/hyperbolic equation, and the introduction of line relaxation to solve the steady flow equation. All subsequent work in transonic potential flows was based on these concepts. Jameson extended Murman and Cole's ideas to the full potential equation with two important contributions. First, he introduced the rotated difference stencil, which generalized the Murman and Cole type-dependent difference operator to general coordinates. Second, he used the interpretation, introduced by Garabedian, of relaxation as an iteration in artificial time to construct stable relaxation schemes, generalizing the original line relaxation method of Reference. The decade of the 1970s saw an explosion of activity in the solution of transonic potential flows, which has been summarized in the review article of Caughey.
Assessing mobility and redistribution patterns of sand and oil agglomerates in the surf zone
Dalyander, P. Soupy; Long, Joesph W.; Plant, Nathaniel G.; Thompson, David M.
2014-01-01
Heavier-than-water sand and oil agglomerates that formed in the surf zone following the Deepwater Horizon oil spill continued to cause beach re-oiling 3 years after initial stranding. To understand this phenomena and inform operational response now and for future spills, a numerical method to assess the mobility and alongshore movement of these “surface residual balls” (SRBs) was developed and applied to the Alabama and western Florida coasts. Alongshore flow and SRB mobility and potential flux were used to identify likely patterns of transport and deposition. Results indicate that under typical calm conditions, cm-size SRBs are unlikely to move alongshore, whereas mobility and transport is likely during storms. The greater mobility of sand compared to SRBs makes burial and exhumation of SRBs likely, and inlets were identified as probable SRB traps. Analysis of field data supports these model results.
Influence of primary-particle density in the morphology of agglomerates.
Camejo, M D; Espeso, D R; Bonilla, L L
2014-07-01
Agglomeration processes occur in many different realms of science, such as colloid and aerosol formation or formation of bacterial colonies. We study the influence of primary-particle density in agglomerate structures using diffusion-controlled Monte Carlo simulations with realistic space scales through different regimes (diffusion-limited aggregation and diffusion-limited colloid aggregation). The equivalence of Monte Carlo time steps to real time scales is given by Hirsch's hydrodynamical theory of Brownian motion. Agglomerate behavior at different time stages of the simulations suggests that three indices (the fractal exponent, the coordination number, and the eccentricity index) characterize agglomerate geometry. Using these indices, we have found that the initial density of primary particles greatly influences the final structure of the agglomerate, as observed in recent experimental works. PMID:25122302
Influence of primary-particle density in the morphology of agglomerates
NASA Astrophysics Data System (ADS)
Camejo, M. D.; Espeso, D. R.; Bonilla, L. L.
2014-07-01
Agglomeration processes occur in many different realms of science, such as colloid and aerosol formation or formation of bacterial colonies. We study the influence of primary-particle density in agglomerate structures using diffusion-controlled Monte Carlo simulations with realistic space scales through different regimes (diffusion-limited aggregation and diffusion-limited colloid aggregation). The equivalence of Monte Carlo time steps to real time scales is given by Hirsch's hydrodynamical theory of Brownian motion. Agglomerate behavior at different time stages of the simulations suggests that three indices (the fractal exponent, the coordination number, and the eccentricity index) characterize agglomerate geometry. Using these indices, we have found that the initial density of primary particles greatly influences the final structure of the agglomerate, as observed in recent experimental works.
Acoustic agglomeration of power-plant fly ash. A comprehensive semi-annual progress report
Reethof, G.
1980-02-01
Results obtained during the reporting period are presented. The agglomeration of submicron fly ash particles has been studied as a function of sound pressure level, sound frequency, loading, and exposure time. A second generation model of the agglomeration process is being developed. A high-frequency, high-intensity variable speed siren delivering at least 600 W at frequencies up to 4000 Hz has been developed and tested. Details on the design and operation are presented. The agglomeration chamber has been completely cleaned and the aerosol generating system has been rebuilt. A mathematical model of the acoustics of agglomeration is being developed. Preliminary results of computerized electron microscopic scanning of fly ash particles during agglomeration are presented. (DMC)
The Development of a Factorizable Multigrid Algorithm for Subsonic and Transonic Flow
NASA Technical Reports Server (NTRS)
Roberts, Thomas W.
2001-01-01
The factorizable discretization of Sidilkover for the compressible Euler equations previously demonstrated for channel flows has been extended to external flows.The dissipation of the original scheme has been modified to maintain stability for moderately stretched grids. The discrete equations are solved by symmetric collective Gauss-Seidel relaxation and FAS multigrid. Unlike the earlier work ordering the grid vertices in the flow direction has been found to be unnecessary. Solutions for essential incompressible flow (Mach 0.01) and supercritical flows have obtained for a Karman-Trefftz airfoil with it conformally mapped grid,as well as a NACA 0012 on an algebraically generated grid. The current work demonstrates nearly 0(n) convergence for subsonic and slightly transonic flows.
A three dimensional multigrid Reynolds-averaged Navier-Stokes solver for unstructured meshes
NASA Technical Reports Server (NTRS)
Mavriplis, D. J.
1994-01-01
A three-dimensional unstructured mesh Reynolds averaged Navier-Stokes solver is described. Turbulence is simulated using a single field-equation model. Computational overheads are minimized through the use of a single edge-based data-structure, and efficient multigrid solution technique, and the use of multi-tasking on shared memory multi-processors. The accuracy and efficiency of the code are evaluated by computing two-dimensional flows in three dimensions and comparing with results from a previously validated two-dimensional code which employs the same solution algorithm. The feasibility of computing three-dimensional flows on grids of several million points in less than two hours of wall clock time is demonstrated.
NASA Technical Reports Server (NTRS)
Wang, Gang
2003-01-01
A multi grid solution procedure for the numerical simulation of turbulent flows in complex geometries has been developed. A Full Multigrid-Full Approximation Scheme (FMG-FAS) is incorporated into the continuity and momentum equations, while the scalars are decoupled from the multi grid V-cycle. A standard kappa-Epsilon turbulence model with wall functions has been used to close the governing equations. The numerical solution is accomplished by solving for the Cartesian velocity components either with a traditional grid staggering arrangement or with a multiple velocity grid staggering arrangement. The two solution methodologies are evaluated for relative computational efficiency. The solution procedure with traditional staggering arrangement is subsequently applied to calculate the flow and temperature fields around a model Short Take-off and Vertical Landing (STOVL) aircraft hovering in ground proximity.
Analysis of V-cycle multigrid algorithms for forms defined by numerical quadrature
Bramble, J.H. . Dept. of Mathematics); Goldstein, C.I.; Pasciak, J.E. . Applied Mathematics Dept.)
1994-05-01
The authors describe and analyze certain V-cycle multigrid algorithms with forms defined by numerical quadrature applied to the approximation of symmetric second-order elliptic boundary value problems. This approach can be used for the efficient solution of finite element systems resulting from numerical quadrature as well as systems arising from finite difference discretizations. The results are based on a regularity free theory and hence apply to meshes with local grid refinement as well as the quasi-uniform case. It is shown that uniform (independent of the number of levels) convergence rates often hold for appropriately defined V-cycle algorithms with as few as one smoothing per grid. These results hold even on applications without full elliptic regularity, e.g., a domain in R[sup 2] with a crack.
Multigrid solution of compressible turbulent flow on unstructured meshes using a two-equation model
NASA Technical Reports Server (NTRS)
Mavriplis, D. J.; Martinelli, L.
1991-01-01
The system of equations consisting of the full Navier-Stokes equations and two turbulence equations was solved for in the steady state using a multigrid strategy on unstructured meshes. The flow equations and turbulence equations are solved in a loosely coupled manner. The flow equations are advanced in time using a multistage Runge-Kutta time stepping scheme with a stability bound local time step, while the turbulence equations are advanced in a point-implicit scheme with a time step which guarantees stability and positively. Low Reynolds number modifications to the original two equation model are incorporated in a manner which results in well behaved equations for arbitrarily small wall distances. A variety of aerodynamic flows are solved for, initializing all quantities with uniform freestream values, and resulting in rapid and uniform convergence rates for the flow and turbulence equations.
Mizuno, T; Taniguchi, M; Kashiwagi, M; Umeda, N; Tobari, H; Watanabe, K; Dairaku, M; Sakamoto, K; Inoue, T
2010-02-01
Heat load on acceleration grids by secondary particles such as electrons, neutrals, and positive ions, is a key issue for long pulse acceleration of negative ion beams. Complicated behaviors of the secondary particles in multiaperture, multigrid (MAMuG) accelerator have been analyzed using electrostatic accelerator Monte Carlo code. The analytical result is compared to experimental one obtained in a long pulse operation of a MeV accelerator, of which second acceleration grid (A2G) was removed for simplification of structure. The analytical results show that relatively high heat load on the third acceleration grid (A3G) since stripped electrons were deposited mainly on A3G. This heat load on the A3G can be suppressed by installing the A2G. Thus, capability of MAMuG accelerator is demonstrated for suppression of heat load due to secondary particles by the intermediate grids.
Spectrum of the Dirac operator and multigrid algorithm with dynamical staggered fermions
Kalkreuter, T. Fachbereich Physik , Humboldt-Universitaet, Invalidenstrasse 110, D-10099 Berlin )
1995-02-01
Complete spectra of the staggered Dirac operator [ital ];sD are determined in quenched four-dimensional SU(2) gauge fields, and also in the presence of dynamical fermions. Periodic as well as antiperiodic boundary conditions are used. An attempt is made to relate the performance of multigrid (MG) and conjugate gradient (CG) algorithms for propagators with the distribution of the eigenvalues of [ital ];sD. The convergence of the CG algorithm is determined only by the condition number [kappa] and by the lattice size. Since [kappa]'s do not vary significantly when quarks become dynamic, CG convergence in unquenched fields can be predicted from quenched simulations. On the other hand, MG convergence is not affected by [kappa] but depends on the spectrum in a more subtle way.
Lee, B C; Schulz, M; de Supinski, B R
2006-09-28
Increasing system and algorithmic complexity, combined with a growing number of tunable application parameters, pose significant challenges for analytical performance modeling. This report outlines a series of robust techniques that enable efficient parameter space exploration based on empirical statistical modeling. In particular, this report applies statistical techniques such as clustering, association, correlation analyses to understand the parameter space better. Results from these statistical techniques guide the construction of piecewise polynomial regression models. Residual and significance tests ensure the resulting model is unbiased and efficient. We demonstrate these techniques in R, a statistical computing environment, for predicting the performance of semicoarsening multigrid. 50 and 75 percent of predictions achieve error rates of 5.5 and 10.0 percent or less, respectively.
Coarsening Strategies for Unstructured Multigrid Techniques with Application to Anisotropic Problems
NASA Technical Reports Server (NTRS)
Morano, E.; Mavriplis, D. J.; Venkatakrishnan, V.
1996-01-01
Over the years, multigrid has been demonstrated as an efficient technique for solving inviscid flow problems. However, for viscous flows, convergence rates often degrade. This is generally due to the required use of stretched meshes (i.e. the aspect-ratio AR = (delta)y/(delta)x much less than 1) in order to capture the boundary layer near the body. Usual techniques for generating a sequence of grids that produce proper convergence rates on isotropic meshes are not adequate for stretched meshes. This work focuses on the solution of Laplace's equation, discretized through a Galerkin finite-element formulation on unstructured stretched triangular meshes. A coarsening strategy is proposed and results are discussed.
Coarsening strategies for unstructured multigrid techniques with application to anisotropic problems
NASA Technical Reports Server (NTRS)
Morano, E.; Mavriplis, D. J.; Venkatakrishnan, V.
1995-01-01
Over the years, multigrid has been demonstrated as an efficient technique for solving inviscid flow problems. However, for viscous flows, convergence rates often degrade. This is generally due to the required use of stretched meshes (i.e., the aspect-ratio AR = delta y/delta x is much less than 1) in order to capture the boundary layer near the body. Usual techniques for generating a sequence of grids that produce proper convergence rates on isotopic meshes are not adequate for stretched meshes. This work focuses on the solution of Laplace's equation, discretized through a Galerkin finite-element formulation on unstructured stretched triangular meshes. A coarsening strategy is proposed and results are discussed.
Born, Philip; Kraus, Tobias
2013-06-01
The stability of nanoparticle suspensions and the details of their agglomeration depend on the interactions between particles. We study this relationship in gold nanoparticles stabilized with different alkyl thiols in heptane. Temperature-dependent interactions were inferred from small-angle x-ray scattering, agglomeration kinetics from dynamic light scattering, and agglomerate morphologies from transmission electron microscopy. We find that the particles precipitate at temperatures below the melting temperatures of the dry ligands. Agglomerates grow with rates that depend on the temperature: Around precipitation temperature, globular agglomerates form slowly, while at lower temperatures, fibrilar agglomerates form rapidly. All agglomerates contain random dense packings rather than crystalline superlattices. We conclude that ligand-ligand and ligand-solvent interactions of the individual particles dominate suspension stability and agglomeration kinetics. The microscopic packing is dominated by interactions between the ligands of different nanoparticles.
Some recent developments in spectral methods
NASA Technical Reports Server (NTRS)
Hussaini, M. Y.
1986-01-01
This paper is solely devoted to spectral iterative methods including spectral multigrid methods. These techniques are explained with reference to simple model problems. Some Navier-Stokes algorithms based on these techniques are mentioned. Results on transition simulation using these algorithms are presented.
Chandler, S.; Hogg, R.
1996-04-01
Goals are to demonstrate the technical and economic feasibility of a micro-agglomerate flotation process (combination of oil-agglomeration and froth flotation) and to establish the essential criteria for reagent selection and system design and operation. The research program was organized into the following tasks: interfacial studies, emulsification, agglomerate growth and structure, and agglomerate flotation. Work on the first two tasks has been completed.
Nanoparticle agglomeration in an evaporating levitated droplet for different acoustic amplitudes
NASA Astrophysics Data System (ADS)
Tijerino, Erick; Basu, Saptarshi; Kumar, Ranganathan
2013-01-01
Radiatively heated levitated functional droplets with nanosilica suspensions exhibit three distinct stages namely pure evaporation, agglomeration, and finally structure formation. The temporal history of the droplet surface temperature shows two inflection points. One inflection point corresponds to a local maximum and demarcates the end of transient heating of the droplet and domination of vaporization. The second inflection point is a local minimum and indicates slowing down of the evaporation rate due to surface accumulation of nanoparticles. Morphology and final precipitation structures of levitated droplets are due to competing mechanisms of particle agglomeration, evaporation, and shape deformation. In this work, we provide a detailed analysis for each process and propose two important timescales for evaporation and agglomeration that determine the final diameter of the structure formed. It is seen that both agglomeration and evaporation timescales are similar functions of acoustic amplitude (sound pressure level), droplet size, viscosity, and density. However, we show that while the agglomeration timescale decreases with initial particle concentration, the evaporation timescale shows the opposite trend. The final normalized diameter can be shown to be dependent solely on the ratio of agglomeration to evaporation timescales for all concentrations and acoustic amplitudes. The structures also exhibit various aspect ratios (bowls, rings, spheroids) which depend on the ratio of the deformation timescale (tdef) and the agglomeration timescale (tg). For tdef
Srinath Vadlamani; Scott Kruger; Travis Austin
2008-06-19
Extended magnetohydrodynamic (MHD) codes are used to model the large, slow-growing instabilities that are projected to limit the performance of International Thermonuclear Experimental Reactor (ITER). The multiscale nature of the extended MHD equations requires an implicit approach. The current linear solvers needed for the implicit algorithm scale poorly because the resultant matrices are so ill-conditioned. A new solver is needed, especially one that scales to the petascale. The most successful scalable parallel processor solvers to date are multigrid solvers. Applying multigrid techniques to a set of equations whose fundamental modes are dispersive waves is a promising solution to CEMM problems. For the Phase 1, we implemented multigrid preconditioners from the HYPRE project of the Center for Applied Scientific Computing at LLNL via PETSc of the DOE SciDAC TOPS for the real matrix systems of the extended MHD code NIMROD which is a one of the primary modeling codes of the OFES-funded Center for Extended Magnetohydrodynamic Modeling (CEMM) SciDAC. We implemented the multigrid solvers on the fusion test problem that allows for real matrix systems with success, and in the process learned about the details of NIMROD data structures and the difficulties of inverting NIMROD operators. The further success of this project will allow for efficient usage of future petascale computers at the National Leadership Facilities: Oak Ridge National Laboratory, Argonne National Laboratory, and National Energy Research Scientific Computing Center. The project will be a collaborative effort between computational plasma physicists and applied mathematicians at Tech-X Corporation, applied mathematicians Front Range Scientific Computations, Inc. (who are collaborators on the HYPRE project), and other computational plasma physicists involved with the CEMM project.
Ashby, S.F.; Falgout, R.D.; Smith, S.G.; Fogwell, T.W.
1994-09-01
This paper discusses the numerical simulation of groundwater flow through heterogeneous porous media. The focus is on the performance of a parallel multigrid preconditioner for accelerating convergence of conjugate gradients, which is used to compute the hydraulic pressure head. The numerical investigation considers the effects of enlarging the domain, increasing the grid resolution, and varying the geostatistical parameters used to define the subsurface realization. The results were obtained using the PARFLOW groundwater flow simulator on the Cray T3D massively parallel computer.
White, M.J.; Iskander, M.F.; Kimrey, H.D.
1996-12-31
The Finite-Difference Time-Domain (FDTD) code available at the University of Utah has been used to simulate sintering of ceramics in single and multimode cavities, and many useful results have been reported in literature. More detailed and accurate results, specifically around and including the ceramic sample, are often desired to help evaluate the adequacy of the heating procedure. In electrically large multimode cavities, however, computer memory requirements limit the number of the mathematical cells, and the desired resolution is impractical to achieve due to limited computer resources. Therefore, an FDTD algorithm which incorporates multiple-grid regions with variable-grid sizes is required to adequately perform the desired simulations. In this paper the authors describe the development of a three-dimensional multi-grid FDTD code to help focus a large number of cells around the desired region. Test geometries were solved using a uniform-grid and the developed multi-grid code to help validate the results from the developed code. Results from these comparisons, as well as the results of comparisons between the developed FDTD code and other available variable-grid codes are presented. In addition, results from the simulation of realistic microwave sintering experiments showed improved resolution in critical sites inside the three-dimensional sintering cavity. With the validation of the FDTD code, simulations were performed for electrically large, multimode, microwave sintering cavities to fully demonstrate the advantages of the developed multi-grid FDTD code.
Reducing adhesion and agglomeration within a cloud of combustible particles
NASA Technical Reports Server (NTRS)
Ross, Howard D.
1988-01-01
The study of combustible particle clouds inside flame tubes is of fundamental scientific interest as well as a practical concern. Only the suspended concentration is important to the combustion process, so that assurances must be provided that a minimum of particles adheres to the tube wall. This paper demonstrates experimentally the ability to minimize adhesion and agglomeration of acoustically-mixed lycopodium particles within a 5-cm diameter lexan flame tube. The area density of particles (ADP) adhering to the wall of bare lexan tubes was measured at greater than 100 particles/sq mm. The nature of adhesion was found to be clearly electrostatic, with the ADP level aggravated by increased mixing time, vigor, and the concentration of particles. Increases in the conductivity of the air and the tube wall did not affect ADP levels substantially. However, the observed adhesion was reduced to less than 10 p/sq mm when the air was ionized by use of an alpha emitter mounted on the inner walls of the flame tube.
Nearshore dynamics of artificial sand and oil agglomerates
Dalyander, P. Soupy; Plant, Nathaniel G.; Long, Joseph W.; McLaughlin, Molly R.
2015-01-01
Weathered oil can mix with sediment to form heavier-than-water sand and oil agglomerates (SOAs) that can cause beach re-oiling for years after a spill. Few studies have focused on the physical dynamics of SOAs. In this study, artificial SOAs (aSOAs) were created and deployed in the nearshore, and shear stress-based mobility formulations were assessed to predict SOA response. Prediction sensitivity to uncertainty in hydrodynamic conditions and shear stress parameterizations were explored. Critical stress estimates accounting for large particle exposure in a mixed bed gave the best predictions of mobility under shoaling and breaking waves. In the surf zone, the 10-cm aSOA was immobile and began to bury in the seafloor while smaller size classes dispersed alongshore. aSOAs up to 5 cm in diameter were frequently mobilized in the swash zone. The uncertainty in predicting aSOA dynamics reflects a broader uncertainty in applying mobility and transport formulations to cm-sized particles.
Assessment of Traffic Noise on Highway Passing from Urban Agglomeration
NASA Astrophysics Data System (ADS)
Vijay, Ritesh; Kori, Chandan; Kumar, Manoj; Chakrabarti, T.; Gupta, Rajesh
2014-09-01
Assessment of traffic noise pollution in developing countries is complex due to heterogeneity in traffic conditions like traffic volume, road width, honking, etc. To analyze the impact of such variables, a research study was carried out on a national highway passing from an urban agglomeration. Traffic volume and noise levels (L10, Lmin, Lmax, Leq and L90) were measured during morning and evening peak hours. Contribution of noise by individual vehicle was estimated using passenger car noise unit. Extent of noise pollution and impact of noisy vehicles were estimated using noise pollution level and traffic noise index, respectively. Noise levels were observed to be above the prescribed Indian and International standards. As per audio spectrum analysis of traffic noise, honking contributed an additional 3-4 dB(A) noise. Based on data analysis, a positive relationship was observed between noise levels and honking while negative correlation was observed between noise levels and road width. The study suggests that proper monitoring and analysis of traffic data is required for better planning of noise abatement measures.