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.
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.
NASA Technical Reports Server (NTRS)
Taasan, Shlomo; Zhang, Hong
1993-01-01
Waveform multigrid method is an efficient method for solving certain classes of time dependent PDEs. This paper studies the relationship between this method and the analogous multigrid method for steady-state problems. Using a Fourier-Laplace analysis, practical convergence rate estimates of the waveform multigrid iterations are obtained. Experimental results show that the analysis yields accurate performance prediction.
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.
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.
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.
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.
Directional Agglomeration Multigrid Techniques for High-Reynolds Number Viscous Flows
NASA Technical Reports Server (NTRS)
Mavriplis, Dimitri J.
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.
Multigrid methods in structural mechanics
NASA Technical Reports Server (NTRS)
Raju, I. S.; Bigelow, C. A.; Taasan, S.; Hussaini, M. Y.
1986-01-01
Although the application of multigrid methods to the equations of elasticity has been suggested, few such applications have been reported in the literature. In the present work, multigrid techniques are applied to the finite element analysis of a simply supported Bernoulli-Euler beam, and various aspects of the multigrid algorithm are studied and explained in detail. In this study, six grid levels were used to model half the beam. With linear prolongation and sequential ordering, the multigrid algorithm yielded results which were of machine accuracy with work equivalent to 200 standard Gauss-Seidel iterations on the fine grid. Also with linear prolongation and sequential ordering, the V(1,n) cycle with n greater than 2 yielded better convergence rates than the V(n,1) cycle. The restriction and prolongation operators were derived based on energy principles. Conserving energy during the inter-grid transfers required that the prolongation operator be the transpose of the restriction operator, and led to improved convergence rates. With energy-conserving prolongation and sequential ordering, the multigrid algorithm yielded results of machine accuracy with a work equivalent to 45 Gauss-Seidel iterations on the fine grid. The red-black ordering of relaxations yielded solutions of machine accuracy in a single V(1,1) cycle, which required work equivalent to about 4 iterations on the finest grid level.
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.
The multigrid preconditioned conjugate gradient method
NASA Technical Reports Server (NTRS)
Tatebe, Osamu
1993-01-01
A multigrid preconditioned conjugate gradient method (MGCG method), which uses the multigrid method as a preconditioner of the PCG method, is proposed. The multigrid method has inherent high parallelism and improves convergence of long wavelength components, which is important in iterative methods. By using this method as a preconditioner of the PCG method, an efficient method with high parallelism and fast convergence is obtained. First, it is considered a necessary condition of the multigrid preconditioner in order to satisfy requirements of a preconditioner of the PCG method. Next numerical experiments show a behavior of the MGCG method and that the MGCG method is superior to both the ICCG method and the multigrid method in point of fast convergence and high parallelism. This fast convergence is understood in terms of the eigenvalue analysis of the preconditioned matrix. From this observation of the multigrid preconditioner, it is realized that the MGCG method converges in very few iterations and the multigrid preconditioner is a desirable preconditioner of the conjugate gradient method.
Fuel agglomerates and method of agglomeration
Wen, Wu-Wey
1986-01-01
Solid fuel agglomerates are prepared of particulate coal or other carbonaceous material with a binder having a high humic acid or humate salt content. The humic acid is extracted from oxidized carbonaceous material with a mild aqueous alkali solution of, for instance, ammonia. The particulate material is blended with the extract which serves as the binder for the agglomerates. The water-resistant agglomerates are formed such as by pelletizing, followed by drying to remove moisture and solidify the humic acid binder throughout the agglomerate.
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.
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 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.
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.
A nonconforming multigrid method using conforming subspaces
NASA Technical Reports Server (NTRS)
Lee, Chang Ock
1993-01-01
For second-order elliptic boundary value problems, we develop a nonconforming multigrid method using the coarser-grid correction on the conforming finite element subspaces. The convergence proof with an arbitrary number of smoothing steps for nu-cycle is presented.
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)
Acoustic agglomeration methods and apparatus
NASA Technical Reports Server (NTRS)
Barmatz, M. B. (Inventor)
1984-01-01
Methods are described for using acoustic energy to agglomerate fine particles on the order of one micron diameter that are suspended in gas, to provide agglomerates large enough for efficient removal by other techniques. The gas with suspended particles, is passed through the length of a chamber while acoustic energy at a resonant chamber mode is applied to set up one or more acoustic standing wave patterns that vibrate the suspended particles to bring them together so they agglomerate. Several widely different frequencies can be applied to efficiently vibrate particles of widely differing sizes. The standing wave pattern can be applied along directions transversed to the flow of the gas. The particles can be made to move in circles by applying acoustic energy in perpendicular directions with the energy in both directions being of the same wavelength but 90 deg out of phase.
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.
The multigrid method for semi-implicit hydrodynamics codes
Brandt, A.; Dendy, J.E. Jr.; Ruppel, H.
1980-03-01
The multigrid method is applied to the pressure iteration in both Eulerian and Lagrangian codes, and computational examples of its efficiency are presented. In addition a general technique for speeding up the calculation of very low Mach number flows is presented. The latter feature is independent of the multigrid algorithm.
Multigrid method for semi-implicit hydrodynamics codes
Brandt, A.; Dendy, J.E. Jr.; Ruppel, H.
1980-03-01
The multigrid method is applied to the pressure iteration in both Eulerian and Lagrangian codes, and computational examples of its efficiency are presented. In addition a general technique for speeding up the calculation of very low Mach number flows is presented. The latter feature is independent of the multigrid algorithm.
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.
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.
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.
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.
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.
The mixed finite element multigrid method for stokes equations.
Muzhinji, K; Shateyi, S; Motsa, S S
2015-01-01
The stable finite element discretization of the Stokes problem produces a symmetric indefinite system of linear algebraic equations. A variety of iterative solvers have been proposed for such systems in an attempt to construct efficient, fast, and robust solution techniques. This paper investigates one of such iterative solvers, the geometric multigrid solver, to find the approximate solution of the indefinite systems. The main ingredient of the multigrid method is the choice of an appropriate smoothing strategy. This study considers the application of different smoothers and compares their effects in the overall performance of the multigrid solver. We study the multigrid method with the following smoothers: distributed Gauss Seidel, inexact Uzawa, preconditioned MINRES, and Braess-Sarazin type smoothers. A comparative study of the smoothers shows that the Braess-Sarazin smoothers enhance good performance of the multigrid method. We study the problem in a two-dimensional domain using stable Hood-Taylor Q2-Q1 pair of finite rectangular elements. We also give the main theoretical convergence results. We present the numerical results to demonstrate the efficiency and robustness of the multigrid method and confirm the theoretical results.
The Mixed Finite Element Multigrid Method for Stokes Equations
Muzhinji, K.; Shateyi, S.; Motsa, S. S.
2015-01-01
The stable finite element discretization of the Stokes problem produces a symmetric indefinite system of linear algebraic equations. A variety of iterative solvers have been proposed for such systems in an attempt to construct efficient, fast, and robust solution techniques. This paper investigates one of such iterative solvers, the geometric multigrid solver, to find the approximate solution of the indefinite systems. The main ingredient of the multigrid method is the choice of an appropriate smoothing strategy. This study considers the application of different smoothers and compares their effects in the overall performance of the multigrid solver. We study the multigrid method with the following smoothers: distributed Gauss Seidel, inexact Uzawa, preconditioned MINRES, and Braess-Sarazin type smoothers. A comparative study of the smoothers shows that the Braess-Sarazin smoothers enhance good performance of the multigrid method. We study the problem in a two-dimensional domain using stable Hood-Taylor Q2-Q1 pair of finite rectangular elements. We also give the main theoretical convergence results. We present the numerical results to demonstrate the efficiency and robustness of the multigrid method and confirm the theoretical results. PMID:25945361
Multigrid methods for parabolic distributed optimal control problems
NASA Astrophysics Data System (ADS)
Borzì, Alfio
2003-08-01
Multigrid schemes that solve parabolic distributed optimality systems discretized by finite differences are investigated. Accuracy properties of finite difference approximation are discussed and validated. Two multigrid methods are considered which are based on a robust relaxation technique and use two different coarsening strategies: semicoarsening and standard coarsening. The resulting multigrid algorithms show robustness with respect to changes of the value of [nu], the weight of the cost of the control, is sufficiently small. Fourier mode analysis is used to investigate the dependence of the linear twogrid convergence factor on [nu] and on the discretization parameters. Results of numerical experiments are reported that demonstrate sharpness of Fourier analysis estimates. A multigrid algorithm that solves optimal control problems with box constraints on the control is considered.
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.
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 relaxation 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.
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.
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.
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.
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
A multigrid nonoscillatory method for computing high speed flows
NASA Technical Reports Server (NTRS)
Li, C. P.; Shieh, T. H.
1993-01-01
A multigrid method using different smoothers has been developed to solve the Euler equations discretized by a nonoscillatory scheme up to fourth order accuracy. The best smoothing property is provided by a five-stage Runge-Kutta technique with optimized coefficients, yet the most efficient smoother is a backward Euler technique in factored and diagonalized form. The singlegrid solution for a hypersonic, viscous conic flow is in excellent agreement with the solution obtained by the third order MUSCL and Roe's method. Mach 8 inviscid flow computations for a complete entry probe have shown that the accuracy is at least as good as the symmetric TVD scheme of Yee and Harten. The implicit multigrid method is four times more efficient than the explicit multigrid technique and 3.5 times faster than the single-grid implicit technique. For a Mach 8.7 inviscid flow over a blunt delta wing at 30 deg incidence, the CPU reduction factor from the three-level multigrid computation is 2.2 on a grid of 37 x 41 x 73 nodes.
Multigrid Methods for the Computation of Propagators in Gauge Fields
NASA Astrophysics Data System (ADS)
Kalkreuter, Thomas
Multigrid methods were invented for the solution of discretized partial differential equations in order to overcome the slowness of traditional algorithms by updates on various length scales. In the present work generalizations of multigrid methods for propagators in gauge fields are investigated. Gauge fields are incorporated in algorithms in a covariant way. The kernel C of the restriction operator which averages from one grid to the next coarser grid is defined by projection on the ground-state of a local Hamiltonian. The idea behind this definition is that the appropriate notion of smoothness depends on the dynamics. The ground-state projection choice of C can be used in arbitrary dimension and for arbitrary gauge group. We discuss proper averaging operations for bosons and for staggered fermions. The kernels C can also be used in multigrid Monte Carlo simulations, and for the definition of block spins and blocked gauge fields in Monte Carlo renormalization group studies. Actual numerical computations are performed in four-dimensional SU(2) gauge fields. We prove that our proposals for block spins are “good”, using renormalization group arguments. A central result is that the multigrid method works in arbitrarily disordered gauge fields, in principle. It is proved that computations of propagators in gauge fields without critical slowing down are possible when one uses an ideal interpolation kernel. Unfortunately, the idealized algorithm is not practical, but it was important to answer questions of principle. Practical methods are able to outperform the conjugate gradient algorithm in case of bosons. The case of staggered fermions is harder. Multigrid methods give considerable speed-ups compared to conventional relaxation algorithms, but on lattices up to 184 conjugate gradient is superior.
Monolithic multigrid methods for two-dimensional resistive magnetohydrodynamics
Adler, James H.; Benson, Thomas R.; Cyr, Eric C.; ...
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.
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.
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.
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
Method for providing improved solid fuels from agglomerated subbituminous coal
Janiak, Jerzy S.; Turak, Ali A.; Pawlak, Wanda; Ignasiak, Boleslaw L.
1989-01-01
A method is provided for separating agglomerated subbituminous coal and the heavy bridging liquid used to form the agglomerates. The separation is performed by contacting the agglomerates with inert gas or steam at a temperature in the range of 250.degree. to 350.degree. C. at substantially atmospheric pressure.
High order multi-grid methods to solve the Poisson equation
NASA Technical Reports Server (NTRS)
Schaffer, S.
1981-01-01
High order multigrid methods based on finite difference discretization of the model problem are examined. The following methods are described: (1) a fixed high order FMG-FAS multigrid algorithm; (2) the high order methods; and (3) results are presented on four problems using each method with the same underlying fixed FMG-FAS algorithm.
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.
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.
Application of multi-grid methods for solving the Navier-Stokes equations
NASA Astrophysics Data System (ADS)
Demuren, A. O.
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.
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.
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.
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.
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.
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.
A Multi-Grid Iterative Method for Photoacoustic Tomography.
Javaherian, Ashkan; Holman, Sean
2016-11-04
Inspired by the recent advances on minimizing nonsmooth or bound-constrained convex functions on models using varying degrees of fidelity, we propose a line search multigrid (MG) method for full-wave iterative image reconstruction in photoacoustic tomography (PAT) in heterogeneous media. To compute the search direction at each iteration, we decide between the gradient at the target level, or alternatively an approximate error correction at a coarser level, relying on some predefined criteria. To incorporate absorption and dispersion, we derive the analytical adjoint directly from the first-order acoustic wave system. The effectiveness of the proposed method is tested on a total-variation penalized Iterative Shrinkage Thresholding algorithm (ISTA) and its accelerated variant (FISTA), which have been used in many studies of image reconstruction in PAT. The results show the great potential of the proposed method in improving speed of iterative image reconstruction.
Annual Copper Mountain Conferences on Multigrid and Iterative Methods, Copper Mountain, Colorado
McCormick, Stephen F.
2016-03-25
This project supported the Copper Mountain Conference on Multigrid and Iterative Methods, held from 2007 to 2015, at Copper Mountain, Colorado. The subject of the Copper Mountain Conference Series alternated between Multigrid Methods in odd-numbered years and Iterative Methods in even-numbered years. Begun in 1983, the Series represents an important forum for the exchange of ideas in these two closely related fields. This report describes the Copper Mountain Conference on Multigrid and Iterative Methods, 2007-2015. Information on the conference series is available at http://grandmaster.colorado.edu/~copper/.
NASA Technical Reports Server (NTRS)
Golik, W. L.
1996-01-01
A robust solver for the elliptic grid generation equations is sought via a numerical study. The system of PDEs is discretized with finite differences, and multigrid methods are applied to the resulting nonlinear algebraic equations. Multigrid iterations are compared with respect to the robustness and efficiency. Different smoothers are tried to improve the convergence of iterations. The methods are applied to four 2D grid generation problems over a wide range of grid distortions. The results of the study help to select smoothing schemes and the overall multigrid procedures for elliptic grid generation.
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
A Conforming Multigrid Method for the Pure Traction Problem of Linear Elasticity: Mixed Formulation
NASA Technical Reports Server (NTRS)
Lee, Chang-Ock
1996-01-01
A multigrid method using conforming P-1 finite element is developed for the two-dimensional pure traction boundary value problem of linear elasticity. The convergence is uniform even as the material becomes nearly incompressible. A heuristic argument for acceleration of the multigrid method is discussed as well. Numerical results with and without this acceleration as well as performance estimates on a parallel computer are included.
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.
Numerical non-LTE 3D radiative transfer using a multigrid method
NASA Astrophysics Data System (ADS)
Bjørgen, Johan P.; Leenaarts, Jorrit
2017-03-01
Context. 3D non-LTE radiative transfer problems are computationally demanding, and this sets limits on the size of the problems that can be solved. So far, multilevel accelerated lambda iteration (MALI) has been the method of choice to perform high-resolution computations in multidimensional problems. The disadvantage of MALI is that its computing time scales as O(n2), with n the number of grid points. When the grid becomes finer, the computational cost increases quadratically. Aims: We aim to develop a 3D non-LTE radiative transfer code that is more efficient than MALI. Methods: We implement a non-linear multigrid, fast approximation storage scheme, into the existing Multi3D radiative transfer code. We verify our multigrid implementation by comparing with MALI computations. We show that multigrid can be employed in realistic problems with snapshots from 3D radiative magnetohydrodynamics (MHD) simulations as input atmospheres. Results: With multigrid, we obtain a factor 3.3-4.5 speed-up compared to MALI. With full-multigrid, the speed-up increases to a factor 6. The speed-up is expected to increase for input atmospheres with more grid points and finer grid spacing. Conclusions: Solving 3D non-LTE radiative transfer problems using non-linear multigrid methods can be applied to realistic atmospheres with a substantial increase in speed.
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.
Inverse airfoil design procedure using a multigrid Navier-Stokes method
NASA Technical Reports Server (NTRS)
Malone, J. B.; Swanson, R. C.
1991-01-01
The Modified Garabedian McFadden (MGM) design procedure was incorporated into an existing 2-D multigrid Navier-Stokes airfoil analysis method. The resulting design method is an iterative procedure based on a residual correction algorithm and permits the automated design of airfoil sections with prescribed surface pressure distributions. The new design method, Multigrid Modified Garabedian McFadden (MG-MGM), is demonstrated for several different transonic pressure distributions obtained from both symmetric and cambered airfoil shapes. The airfoil profiles generated with the MG-MGM code are compared to the original configurations to assess the capabilities of the inverse design method.
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.
Advanced discretizations and multigrid methods for liquid crystal configurations
NASA Astrophysics Data System (ADS)
Emerson, David B.
addition, we present two novel, optimally scaling, multigrid approaches for these systems based on Vanka- and Braess-Sarazin-type relaxation. Both approaches outperform direct methods and represent highly efficient and scalable iterative solvers. Finally, a three-dimensional problem considering the effects of geometrically patterned surfaces is presented, which gives rise to a nonlinear anisotropic reaction-diffusion equation. Well-posedness is shown for the intermediate linearization systems of the proposed Newton linearization. The configurations under consideration are part of ongoing physics research seeking new bistable configurations induced by geometric nano-patterning.
Numerical solution of the Navier-Stokes equations by a multigrid method
NASA Astrophysics Data System (ADS)
Cambier, L.; Couaillier, V.; Veuillot, J. P.
This article describes the use of a multigrid method to compute compressible two-dimensional turbulent flows by solving the averaged Navier-Stokes equations, complemented by a turbulence model. The numerical method is described in detail. It is based on an explicit, centered scheme of the Lax-Wendroff type, the convergence of which is accelerated by a multigrid phase similar to the one proposed by Ni. The effect of the parameters introduced in the multigrid acceleration phase is studied in numerical simulations to increase their effectiveness. The applications covered relate to high-Reynolds flows around a wing profile and in a two-dimensional cascade. Comparisons with experimental data are given for these two types of application.
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.
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.
A multigrid method for steady Euler equations on unstructured adaptive grids
NASA Technical Reports Server (NTRS)
Riemslagh, Kris; Dick, Erik
1993-01-01
A flux-difference splitting type algorithm is formulated for the steady Euler equations on unstructured grids. The polynomial flux-difference splitting technique is used. A vertex-centered finite volume method is employed on a triangular mesh. The multigrid method is in defect-correction form. A relaxation procedure with a first order accurate inner iteration and a second-order correction performed only on the finest grid, is used. A multi-stage Jacobi relaxation method is employed as a smoother. Since the grid is unstructured a Jacobi type is chosen. The multi-staging is necessary to provide sufficient smoothing properties. The domain is discretized using a Delaunay triangular mesh generator. Three grids with more or less uniform distribution of nodes but with different resolution are generated by successive refinement of the coarsest grid. Nodes of coarser grids appear in the finer grids. The multigrid method is started on these grids. As soon as the residual drops below a threshold value, an adaptive refinement is started. The solution on the adaptively refined grid is accelerated by a multigrid procedure. The coarser multigrid grids are generated by successive coarsening through point removement. The adaption cycle is repeated a few times. Results are given for the transonic flow over a NACA-0012 airfoil.
An Assessment of Linear Versus Non-linear Multigrid Methods for Unstructured Mesh Solvers
2001-05-01
problems is investigated. The first case consists of a transient radiation-diffusion problem for which an exact linearization is available, while the...to the Jacobian of a second-order accurate discretization. When an exact linearization is employed, the linear and non-linear multigrid methods
On spectral multigrid methods for the time-dependent Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Zang, T. A.; Hussaini, M. Y.
1985-01-01
A splitting scheme is proposed for the numerical solution of the time-dependent, incompressible Navier-Stokes equations by spectral methods. A staggered grid is used for the pressure, improved intermediate boundary conditions are employed in the split step for the velocity, and spectral multigrid techniques are used for the solution of the implicit equations.
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.
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.
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.
A multiblock multigrid method for the solution of the three-dimensional Euler equations
NASA Technical Reports Server (NTRS)
Cannizzaro, Frank E.; Elmiligui, Alaa; Melson, N. Duane; Von Lavante, E.
1990-01-01
A general multiblock, multigrid method for the solution of the Euler equations has been developed. Two types of numerical methods were investigated, van Leer's flux-vector-splitting and Roe's flux-difference-splitting, with MUSCL type differencing used in both methods. An explicit two-step method and a multi-stage Runge-Kutta method have been tested. Results are presented for test cases of a channel flow, nozzle exhaust flow, and a transonic wing.
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.
Parallel Multigrid Equation Solver
Adams, Mark
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.
Application of multi-grid method on the simulation of incremental forging processes
NASA Astrophysics Data System (ADS)
Ramadan, Mohamad; Khaled, Mahmoud; Fourment, Lionel
2016-10-01
Numerical simulation becomes essential in manufacturing large part by incremental forging processes. It is a splendid tool allowing to show physical phenomena however behind the scenes, an expensive bill should be paid, that is the computational time. That is why many techniques are developed to decrease the computational time of numerical simulation. Multi-Grid method is a numerical procedure that permits to reduce computational time of numerical calculation by performing the resolution of the system of equations on several mesh of decreasing size which allows to smooth faster the low frequency of the solution as well as its high frequency. In this paper a Multi-Grid method is applied to cogging process in the software Forge 3. The study is carried out using increasing number of degrees of freedom. The results shows that calculation time is divide by two for a mesh of 39,000 nodes. The method is promising especially if coupled with Multi-Mesh method.
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.
General relaxation schemes in multigrid algorithms for higher order singularity methods
NASA Technical Reports Server (NTRS)
Oskam, B.; Fray, J. M. J.
1981-01-01
Relaxation schemes based on approximate and incomplete factorization technique (AF) are described. The AF schemes allow construction of a fast multigrid method for solving integral equations of the second and first kind. The smoothing factors for integral equations of the first kind, and comparison with similar results from the second kind of equations are a novel item. Application of the MD algorithm shows convergence to the level of truncation error of a second order accurate panel method.
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.
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.
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.
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
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.
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.
The Multigrid-Mask Numerical Method for Solution of Incompressible Navier-Stokes Equations
NASA Technical Reports Server (NTRS)
Ku, Hwar-Ching; Popel, Aleksander S.
1996-01-01
A multigrid-mask method for solution of incompressible Navier-Stokes equations in primitive variable form has been developed. The main objective is to apply this method in conjunction with the pseudospectral element method solving flow past multiple objects. There are two key steps involved in calculating flow past multiple objects. The first step utilizes only Cartesian grid points. This homogeneous or mask method step permits flow into the interior rectangular elements contained in objects, but with the restriction that the velocity for those Cartesian elements within and on the surface of an object should be small or zero. This step easily produces an approximate flow field on Cartesian grid points covering the entire flow field. The second or heterogeneous step corrects the approximate flow field to account for the actual shape of the objects by solving the flow field based on the local coordinates surrounding each object and adapted to it. The noise occurring in data communication between the global (low frequency) coordinates and the local (high frequency) coordinates is eliminated by the multigrid method when the Schwarz Alternating Procedure (SAP) is implemented. Two dimensional flow past circular and elliptic cylinders will be presented to demonstrate the versatility of the proposed method. An interesting phenomenon is found that when the second elliptic cylinder is placed in the wake of the first elliptic cylinder a traction force results in a negative drag coefficient.
Is the Multigrid Method Fault Tolerant? The Two-Grid Case
Ainsworth, Mark; Glusa, Christian
2016-06-30
The predicted reduced resiliency of next-generation high performance computers means that it will become necessary to take into account the effects of randomly occurring faults on numerical methods. Further, in the event of a hard fault occurring, a decision has to be made as to what remedial action should be taken in order to resume the execution of the algorithm. The action that is chosen can have a dramatic effect on the performance and characteristics of the scheme. Ideally, the resulting algorithm should be subjected to the same kind of mathematical analysis that was applied to the original, deterministic variant. The purpose of this work is to provide an analysis of the behaviour of the multigrid algorithm in the presence of faults. Multigrid is arguably the method of choice for the solution of large-scale linear algebra problems arising from discretization of partial differential equations and it is of considerable importance to anticipate its behaviour on an exascale machine. The analysis of resilience of algorithms is in its infancy and the current work is perhaps the first to provide a mathematical model for faults and analyse the behaviour of a state-of-the-art algorithm under the model. It is shown that the Two Grid Method fails to be resilient to faults. Attention is then turned to identifying the minimal necessary remedial action required to restore the rate of convergence to that enjoyed by the ideal fault-free method.
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 on massively parallel architectures
Falgout, R D; Jones, J E
1999-09-17
The scalable implementation of multigrid methods for machines with several thousands of processors is investigated. Parallel performance models are presented for three different structured-grid multigrid algorithms, and a description is given of how these models can be used to guide implementation. Potential pitfalls are illustrated when moving from moderate-sized parallelism to large-scale parallelism, and results are given from existing multigrid codes to support the discussion. Finally, the use of mixed programming models is investigated for multigrid codes on clusters of SMPs.
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.
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.
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.
Viscous analysis of three-dimensional rotor flows using a multigrid method
NASA Technical Reports Server (NTRS)
Arnone, A.
1993-01-01
A three-dimensional code for rotating blade-row flow analysis was developed. The space discretization uses a cell-centered scheme with eigenvalues scaling for the artificial dissipation. The computational efficiency of a four-stage Runge-Kutta scheme is enhanced by using variable coefficients, implicit residual smoothing, and a full-multigrid method. An application is presented for the NASA rotor 67 transonic fan. Due to the blade stagger and twist, a zonal, non-periodic H-type grid is used to minimize the mesh skewness. The calculation is validated by comparing it with experiments in the range from the maximum flow rate to a near-stall condition. A detailed study of the flow structure near peak efficiency and near stall is presented by means of pressure distribution and particle traces inside boundary layers.
A cell-vertex multigrid method for the Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Radespiel, R.
1989-01-01
A cell-vertex scheme for the Navier-Stokes equations, which is based on central difference approximations and Runge-Kutta time stepping, is described. Using local time stepping, implicit residual smoothing, a multigrid method, and carefully controlled artificial dissipative terms, very good convergence rates are obtained for a wide range of two- and three-dimensional flows over airfoils and wings. The accuracy of the code is examined by grid refinement studies and comparison with experimental data. For an accurate prediction of turbulent flows with strong separations, a modified version of the nonequilibrium turbulence model of Johnson and King is introduced, which is well suited for an implementation into three-dimensional Navier-Stokes codes. It is shown that the solutions for three-dimensional flows with strong separations can be dramatically improved, when a nonequilibrium model of turbulence is used.
NASA Astrophysics Data System (ADS)
Matveev, A. D.
2016-11-01
To calculate the three-dimensional elastic body of heterogeneous structure under static loading, a method of multigrid finite element is provided, when implemented on the basis of algorithms of finite element method (FEM), using homogeneous and composite threedimensional multigrid finite elements (MFE). Peculiarities and differences of MFE from the currently available finite elements (FE) are to develop composite MFE (without increasing their dimensions), arbitrarily small basic partition of composite solids consisting of single-grid homogeneous FE of the first order can be used, i.e. in fact, to use micro approach in finite element form. These small partitions allow one to take into account in MFE, i.e. in the basic discrete models of composite solids, complex heterogeneous and microscopically inhomogeneous structure, shape, the complex nature of the loading and fixation and describe arbitrarily closely the stress and stain state by the equations of three-dimensional elastic theory without any additional simplifying hypotheses. When building the m grid FE, m of nested grids is used. The fine grid is generated by a basic partition of MFE, the other m —1 large grids are applied to reduce MFE dimensionality, when m is increased, MFE dimensionality becomes smaller. The procedures of developing MFE of rectangular parallelepiped, irregular shape, plate and beam types are given. MFE generate the small dimensional discrete models and numerical solutions with a high accuracy. An example of calculating the laminated plate, using three-dimensional 3-grid FE and the reference discrete model is given, with that having 2.2 milliards of FEM nodal unknowns.
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)
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.
2007-06-01
simple iterative method such as Jacobi or Gauss - Seidel . The method used to coarsening the grid defines if the multigrid method is geometric or algebraic...chosen here is Gauss - Seidel (GS) [25]. We achieved the best rates of convergence for AMG using an implementation that on the finest grid corresponds to...a Symmetric- Red - Black GS, while on the other grids we alternate the order of relaxation as we did on the finest grid, but based only on the order
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.
An application of multigrid methods for a discrete elastic model for epitaxial systems
Caflisch, R.E. . E-mail: caflisch@math.ucla.edu; Lee, Y.-J. . E-mail: yjlee@math.ucla.edu; Shu, S. . E-mail: shushi@xtu.edu.cn; Xiao, Y.-X. . E-mail: xyx610xyx@yahoo.com.cn; Xu, J. . E-mail: xu@math.psu.edu
2006-12-10
We apply an efficient and fast algorithm to simulate the atomistic strain model for epitaxial systems, recently introduced by Schindler et al. [Phys. Rev. B 67, 075316 (2003)]. The discrete effects in this lattice statics model are crucial for proper simulation of the influence of strain for thin film epitaxial growth, but the size of the atomistic systems of interest is in general quite large and hence the solution of the discrete elastic equations is a considerable numerical challenge. In this paper, we construct an algebraic multigrid method suitable for efficient solution of the large scale discrete strain model. Using this method, simulations are performed for several representative physical problems, including an infinite periodic step train, a layered nanocrystal, and a system of quantum dots. The results demonstrate the effectiveness and robustness of the method and show that the method attains optimal convergence properties, regardless of the problem size, the geometry and the physical parameters. The effects of substrate depth and of invariance due to traction-free boundary conditions are assessed. For a system of quantum dots, the simulated strain energy density supports the observations that trench formation near the dots provides strain relief.
Peláez, Daniel; Meyer, Hans-Dieter
2013-01-07
In this article, a new method, multigrid POTFIT (MGPF), is presented. MGPF is a grid-based algorithm which transforms a general potential energy surface into product form, that is, a sum of products of one-dimensional functions. This form is necessary to profit from the computationally advantageous multiconfiguration time-dependent Hartree method for quantum dynamics. MGPF circumvents the dimensionality related issues present in POTFIT [A. Jäckle and H.-D. Meyer, J. Chem. Phys. 104, 7974 (1996)], allowing quantum dynamical studies of systems up to about 12 dimensions. MGPF requires the definition of a fine grid and a coarse grid, the latter being a subset of the former. The MGPF approximation relies on a series of underlying POTFIT calculations on grids which are smaller than the fine one and larger than or equal to the coarse one. This aspect makes MGPF a bit less accurate than POTFIT but orders of magnitude faster and orders of magnitude less memory demanding than POTFIT. Moreover, like POTFIT, MGPF is variational and provides an efficient error control.
Summary Report: Multigrid for Systems of Elliptic PDEs
Lee, Barry
2016-11-17
We are interested in determining if multigrid can be effectively applied to the system. The conclusion that I seem to be drawn to is that it is impossible to develop a blackbox multigrid solver for these general systems. Analysis of the system of PDEs must be conducted first to determine pre-processing procedures on the continuous problem before applying a multigrid method. Determining this pre-processing is currently not incorporated in black-box multigrid strategies. Nevertheless, we characterize some system features that will make the system more amenable to multigrid approaches, techniques that may lead to more amenable systems, and multigrid procedures that are generally more appropriate for these systems.
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.
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.
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.
Agglomeration of Celecoxib by Quasi Emulsion Solvent Diffusion Method: Effect of Stabilizer
Maghsoodi, Maryam; Nokhodchi, Ali
2016-01-01
Purpose: The quasi-emulsion solvent diffusion (QESD) has evolved into an effective technique to manufacture agglomerates of API crystals. Although, the proposed technique showed benefits, such as cost effectiveness, that is considerably sensitive to the choice of a stabilizer, which agonizes from a absence of systemic understanding in this field. In the present study, the combination of different solvents and stabilizers were compared to investigate any connections between the solvents and stabilizers. Methods: Agglomerates of celecoxib were prepared by QESD method using four different stabilizers (Tween 80, HPMC, PVP and SLS) and three different solvents (methyl acetate, ethyl acetate and isopropyl acetate). The solid state of obtained particles was investigated by differential scanning calorimetry (DSC) and Fourier transform infrared (FT-IR) spectroscopy. The agglomerated were also evaluated in term of production yield, distribution of particles and dissolution behavior. Results: The results showed that the effectiveness of stabilizer in terms of particle size and particle size distribution is specific to each solvent candidate. A stabilizer with a lower HLB value is preferred which actually increased its effectiveness with the solvent candidates with higher lipophilicity. HPMC appeared to be the most versatile stabilizer because it showed a better stabilizing effect compared to other stabilizers in all solvents used. Conclusion: This study demonstrated that the efficiency of stabilizers in forming the celecoxib agglomerates by QESD was influenced by the HLB of the stabilizer and lipophilicity of the solvents. PMID:28101468
Agglomeration of Celecoxib by Quasi Emulsion Solvent Diffusion Method: Effect of Stabilizer.
Maghsoodi, Maryam; Nokhodchi, Ali
2016-12-01
Purpose: The quasi-emulsion solvent diffusion (QESD) has evolved into an effective technique to manufacture agglomerates of API crystals. Although, the proposed technique showed benefits, such as cost effectiveness, that is considerably sensitive to the choice of a stabilizer, which agonizes from a absence of systemic understanding in this field. In the present study, the combination of different solvents and stabilizers were compared to investigate any connections between the solvents and stabilizers. Methods: Agglomerates of celecoxib were prepared by QESD method using four different stabilizers (Tween 80, HPMC, PVP and SLS) and three different solvents (methyl acetate, ethyl acetate and isopropyl acetate). The solid state of obtained particles was investigated by differential scanning calorimetry (DSC) and Fourier transform infrared (FT-IR) spectroscopy. The agglomerated were also evaluated in term of production yield, distribution of particles and dissolution behavior. Results: The results showed that the effectiveness of stabilizer in terms of particle size and particle size distribution is specific to each solvent candidate. A stabilizer with a lower HLB value is preferred which actually increased its effectiveness with the solvent candidates with higher lipophilicity. HPMC appeared to be the most versatile stabilizer because it showed a better stabilizing effect compared to other stabilizers in all solvents used. Conclusion: This study demonstrated that the efficiency of stabilizers in forming the celecoxib agglomerates by QESD was influenced by the HLB of the stabilizer and lipophilicity of the solvents.
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.
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.
An upwind multigrid method for solving viscous flows on unstructured triangular meshes. M.S. Thesis
NASA Technical Reports Server (NTRS)
Bonhaus, Daryl Lawrence
1993-01-01
A multigrid algorithm is combined with an upwind scheme for solving the two dimensional Reynolds averaged Navier-Stokes equations on triangular meshes resulting in an efficient, accurate code for solving complex flows around multiple bodies. The relaxation scheme uses a backward-Euler time difference and relaxes the resulting linear system using a red-black procedure. Roe's flux-splitting scheme is used to discretize convective and pressure terms, while a central difference is used for the diffusive terms. The multigrid scheme is demonstrated for several flows around single and multi-element airfoils, including inviscid, laminar, and turbulent flows. The results show an appreciable speed up of the scheme for inviscid and laminar flows, and dramatic increases in efficiency for turbulent cases, especially those on increasingly refined grids.
Lee, Barry
2010-05-01
This paper presents a new multigrid method applied to the most common Sn discretizations (Petrov-Galerkin, diamond-differenced, corner-balanced, and discontinuous Galerkin) of the mono-energetic Boltzmann transport equation in the optically thick and thin regimes, and with strong anisotropic scattering. Unlike methods that use scalar DSA diffusion preconditioners for the source iteration, this multigrid method is applied directly to an integral equation for the scalar flux. Thus, unlike the former methods that apply a multigrid strategy to the scalar DSA diffusion operator, this method applies a multigrid strategy to the integral source iteration operator, which is an operator for 5 independent variables in spatial 3-d (3 in space and 2 in angle) and 4 independent variables in spatial 2-d (2 in space and 2 in angle). The core smoother of this multigrid method involves applications of the integral operator. Since the kernel of this integral operator involves the transport sweeps, applying this integral operator requires a transport sweep (an inversion of an upper triagular matrix) for each of the angles used. As the equation is in 5-space or 4-space, the multigrid approach in this paper coarsens in both angle and space, effecting efficient applications of the coarse integral operators. Although each V-cycle of this method is more expensive than a V-cycle for the DSA preconditioner, since the DSA equation does not have angular dependence, the overall computational efficiency is about the same for problems where DSA preconditioning {\\it is} effective. This new method also appears to be more robust over all parameter regimes than DSA approaches. Moreover, this new method is applicable to a variety of Sn spatial discretizations, to problems involving a combination of optically thick and thin regimes, and more importantly, to problems with anisotropic scattering cross-sections, all of which DSA approaches perform poorly or not applicable at all. This multigrid approach
Analysis of a multigrid method for the Euler equations of gas dynamics in two dimensions
NASA Astrophysics Data System (ADS)
Mulder, Wim A.
1987-04-01
The multigrid convergence rates of several relaxation schemes for the linearized upwind differenced Euler equations are estimated by two-level Fourier analysis. Strong alignment, the flow being aligned with the grid, causes the failure of schemes that use only local data, such as Point-Jacobi, Red-Black, and Block-Jacobi relaxation. Collective Symmetric Gauss-Seidel relaxation, which is global in nature, can overcome this problem. However, it still fails at or near singularities. This is confirmed by a numerical experiment for the nonlinear Euler equations, using flux-vector splitting.
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 Astrophysics Data System (ADS)
Dizaji, Farzad F.; Marshall, Jeffrey S.
2016-11-01
Modeling the response of interacting particles, droplets, or bubbles to subgrid-scale fluctuations in turbulent flows is a long-standing challenge in multiphase flow simulations using the Reynolds-Averaged Navier-Stokes approach. The problem also arises for large-eddy simulation for sufficiently small values of the Kolmogorov-scale particle Stokes number. This paper expands on a recently proposed stochastic vortex structure (SVS) method for modeling of turbulence fluctuations for colliding or otherwise interacting particles. An accelerated version of the SVS method was developed using the fast multipole expansion and local Taylor expansion approach, which reduces computation speed by two orders of magnitude compared to the original SVS method. Detailed comparisons are presented showing close agreement of the energy spectrum and probability density functions of various fields between the SVS computational model, direct numerical simulation (DNS) results, and various theoretical and experimental results found in the literature. Results of the SVS method for particle collision rate and related measures of particle interaction exhibit excellent agreement with DNS predictions for homogeneous turbulent flows. The SVS method was also used with adhesive particles to simulate formation of particle agglomerates with different values of the particle Stokes and adhesion numbers, and various measures of the agglomerate structure are compared to the DNS results.
NASA Astrophysics Data System (ADS)
Wolkov, A. V.
2010-03-01
The Galerkin method with discontinuous basis functions is adapted for solving the Euler and Navier-Stokes equations on unstructured hexahedral grids. A hybrid multigrid algorithm involving the finite element and grid stages is used as an iterative solution method. Numerical results of calculating the sphere inviscid flow, viscous flow in a bent pipe, and turbulent flow past a wing are presented. The numerical results and the computational cost are compared with those obtained using the finite volume method.
NASA Astrophysics Data System (ADS)
Rossow, C.-C.
1992-10-01
The applicability of a multigrid technique to block-structured, body-fitted meshes is examined focusing on three different strategies. In the first strategy data are exchanged between blocks in each stage of a five-stage Runge-Kutta time-stepping scheme which keeps a possible time lag between blocks to a minimum, but requires a large amount of I/O operations and storage. The second strategy is based on performing a complete Runge-Kutta cycle within a block before switching to the next. In the third strategy both a complete Runge-Kutta cycle and the residual evaluation for the restriction operator are done within a block, allowing a minimum of I/O and storage. The inviscid flow around a wing-body/engine-pylon configuration was computed on a mesh consisting of 11 computational blocks. It was found that both the first and the second strategies delivered converged results, but the third failed due to larger time lag between blocks.
Progress with Multigrid Schemes for Hypersonic Flow Problems
1991-12-01
paper, we first briefly describe the multigrid method and different execution strategies that will be considered. The multigrid approach is based on...determine their damping properties. The capabilities of the multi’grid 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
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.
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.
NASA Astrophysics Data System (ADS)
Stiller, Jörg
2016-12-01
We present a polynomial multigrid method for nodal interior penalty and local discontinuous Galerkin formulations of the Poisson equation on Cartesian grids. For smoothing we propose two classes of overlapping Schwarz methods. The first class comprises element-centered and the second face-centered methods. Within both classes we identify methods that achieve superior convergence rates, prove robust with respect to the mesh spacing and the polynomial order, at least up to P = 32. Consequent structure exploitation yields a computational complexity of O (PN), where N is the number of unknowns. Further we demonstrate the suitability of the face-centered method for element aspect ratios up to 32.
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.
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
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.
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
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.
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.
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.
Augustin, Christoph M; Neic, Aurel; Liebmann, Manfred; Prassl, Anton J; Niederer, Steven A; Haase, Gundolf; Plank, Gernot
2016-01-15
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
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
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.
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.
3D magnetospheric parallel hybrid multi-grid method applied to planet–plasma interactions
Leclercq, L.; Mancini, M.
2016-03-15
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.
A Line Search Multigrid Method for Large-Scale Convex Optimization
2007-07-03
symmetric matrix G, there exists an orthogonal matrix Q such that Q⊤g is parallel to the first coordinate direction and Q⊤GQ is a tridiagonal matrix ...Methods for PDEs. Consider solving the system of linear equa- tions (2.1) Ahxh = bh, where Ah is a symmetric positive definite matrix and h is the...Assumption 2.2. The coarser level matrix Ah−1 relates to the finer level matrix Ah through Ah−1 = RhAhPh. Given an approximate solution xh,k, a
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.
Multigrid for hypersonic inviscid flows
NASA Technical Reports Server (NTRS)
Decker, Naomi H.; Turkel, Eli
1990-01-01
The use of multigrid methods to solve the Euler equations for hypersonic flow is discussed. The steady state equations are considered with a Runge-Kutta smoother based on the time accurate equations together with local time stepping and residual smoothing. The effect of the Runge-Kutta coefficients on the convergence rate was examined considering both damping characteristics and convection properties. The importance of boundary conditions on the convergence rate for hypersonic flow is discussed. Also of importance are the switch between the second and fourth difference viscosity. Solutions are given for flow around the bump in a channel and flow around a biconic section.
Multigrid calculation of three-dimensional turbomachinery flows
NASA Technical Reports Server (NTRS)
Caughey, David A.
1989-01-01
Research was performed in the general area of computational aerodynamics, with particular emphasis on the development of efficient techniques for the solution of the Euler and Navier-Stokes equations for transonic flows through the complex blade passages associated with turbomachines. In particular, multigrid methods were developed, using both explicit and implicit time-stepping schemes as smoothing algorithms. The specific accomplishments of the research have included: (1) the development of an explicit multigrid method to solve the Euler equations for three-dimensional turbomachinery flows based upon the multigrid implementation of Jameson's explicit Runge-Kutta scheme (Jameson 1983); (2) the development of an implicit multigrid scheme for the three-dimensional Euler equations based upon lower-upper factorization; (3) the development of a multigrid scheme using a diagonalized alternating direction implicit (ADI) algorithm; (4) the extension of the diagonalized ADI multigrid method to solve the Euler equations of inviscid flow for three-dimensional turbomachinery flows; and also (5) the extension of the diagonalized ADI multigrid scheme to solve the Reynolds-averaged Navier-Stokes equations for two-dimensional turbomachinery flows.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
New multigrid approach for three-dimensional unstructured, adaptive grids
NASA Technical Reports Server (NTRS)
Parthasarathy, Vijayan; Kallinderis, Y.
1994-01-01
A new multigrid method with adaptive unstructured grids is presented. The three-dimensional Euler equations are solved on tetrahedral grids that are adaptively refined or coarsened locally. The multigrid method is employed to propagate the fine grid corrections more rapidly by redistributing the changes-in-time of the solution from the fine grid to the coarser grids to accelerate convergence. A new approach is employed that uses the parent cells of the fine grid cells in an adapted mesh to generate successively coaser levels of multigrid. This obviates the need for the generation of a sequence of independent, nonoverlapping grids as well as the relatively complicated operations that need to be performed to interpolate the solution and the residuals between the independent grids. The solver is an explicit, vertex-based, finite volume scheme that employs edge-based data structures and operations. Spatial discretization is of central-differencing type combined with a special upwind-like smoothing operators. Application cases include adaptive solutions obtained with multigrid acceleration for supersonic and subsonic flow over a bump in a channel, as well as transonic flow around the ONERA M6 wing. Two levels of multigrid resulted in reduction in the number of iterations by a factor of 5.
New multigrid approach for three-dimensional unstructured, adaptive grids
NASA Astrophysics Data System (ADS)
Parthasarathy, Vijayan; Kallinderis, Y.
1994-05-01
A new multigrid method with adaptive unstructured grids is presented. The three-dimensional Euler equations are solved on tetrahedral grids that are adaptively refined or coarsened locally. The multigrid method is employed to propagate the fine grid corrections more rapidly by redistributing the changes-in-time of the solution from the fine grid to the coarser grids to accelerate convergence. A new approach is employed that uses the parent cells of the fine grid cells in an adapted mesh to generate successively coarser levels of multigrid. This obviates the need for the generation of a sequence of independent, nonoverlapping grids as well as the relatively complicated operations that need to be performed to interpolate the solution and the residuals between the independent grids. The solver is an explicit, vertex-based, finite volume scheme that employs edge-based data structures and operations. Spatial discretization is of central-differencing type combined with special upwind-like smoothing operators. Application cases include adaptive solutions obtained with multigrid acceleration for supersonic and subsonic flow over a bump in a channel, as well as transonic flow around the ONERA M6 wing. Two levels of multigrid resulted in reduction in the number of iterations by a factor of 5.
New multigrid approach for three-dimensional unstructured, adaptive grids
NASA Astrophysics Data System (ADS)
Parthasarathy, Vijayan; Kallinderis, Y.
1994-05-01
A new multigrid method with adaptive unstructured grids is presented. The three-dimensional Euler equations are solved on tetrahedral grids that are adaptively refined or coarsened locally. The multigrid method is employed to propagate the fine grid corrections more rapidly by redistributing the changes-in-time of the solution from the fine grid to the coarser grids to accelerate convergence. A new approach is employed that uses the parent cells of the fine grid cells in an adapted mesh to generate successively coaser levels of multigrid. This obviates the need for the generation of a sequence of independent, nonoverlapping grids as well as the relatively complicated operations that need to be performed to interpolate the solution and the residuals between the independent grids. The solver is an explicit, vertex-based, finite volume scheme that employs edge-based data structures and operations. Spatial discretization is of central-differencing type combined with a special upwind-like smoothing operators. Application cases include adaptive solutions obtained with multigrid acceleration for supersonic and subsonic flow over a bump in a channel, as well as transonic flow around the ONERA M6 wing. Two levels of multigrid resulted in reduction in the number of iterations by a factor of 5.
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.
NASA Astrophysics Data System (ADS)
Mascarenhas, Brendan S.; Helenbrook, Brian T.; Atkins, Harold L.
2010-05-01
An improved p-multigrid algorithm for discontinuous Galerkin (DG) discretizations of convection-diffusion problems is presented. The general p-multigrid algorithm for DG discretizations involves a restriction from the p=1 to p=0 discontinuous polynomial solution spaces. This restriction is problematic and has limited the efficiency of the p-multigrid method. For purely diffusive problems, Helenbrook and Atkins have demonstrated rapid convergence using a method that restricts from a discontinuous to continuous polynomial solution space at p=1. It is shown that this method is not directly applicable to the convection-diffusion (CD) equation because it results in a central-difference discretization for the convective term. To remedy this, ideas from the streamwise upwind Petrov-Galerkin (SUPG) formulation are used to devise a transition from the discontinuous to continuous space at p=1 that yields an upwind discretization. The results show that the new method converges rapidly for all Peclet numbers.
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.
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.
An improved theoretical model of acoustic agglomeration
Song, L. ); Koopmann, G.H. . Center for Acoustics and Vibration); Hoffmann, T.L. )
1994-04-01
An improved theoretical model is developed to describe the acoustic agglomeration of particles entrained in a gas medium. The improvements to the present theories are twofold: first, wave scattering is included in the orthokinetic interaction of particles and second, hydrodynamic interaction, shown to be an important agglomeration mechanism for certain operation conditions, is incorporated into the model. The influence of orthokinetic and hydrodynamic interactions introduce associated convergent velocities that cause particles to approach each other and collide. The convergent velocities are related with an acoustic agglomeration frequency function (AAFF) through a semi-statistical method. This function is the key parameter for the theoretical simulation of acoustic agglomeration.
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.
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.
Textbook Multigrid Efficiency for the Steady Euler Equations
NASA Technical Reports Server (NTRS)
Roberts, Thomas W.; Sidilkover, David; Swanson, R. C.
2004-01-01
A fast multigrid solver for the steady incompressible Euler 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. Solvers for both unstructured triangular grids and structured quadrilateral grids have been written. Computations for channel flow and flow over a nonlifting airfoil have computed. Using Gauss-Seidel relaxation ordered in the flow direction, textbook multigrid convergence rates of nearly one order-of-magnitude residual reduction per multigrid cycle are achieved, independent of the grid spacing. This approach also may be applied to the compressible Euler equations and the incompressible Navier-Stokes equations.
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.
NASA Technical Reports Server (NTRS)
Cannizzaro, Frank E.; Ash, Robert L.
1992-01-01
A state-of-the-art computer code has been developed that incorporates a modified Runge-Kutta time integration scheme, upwind numerical techniques, multigrid acceleration, and multi-block capabilities (RUMM). A three-dimensional thin-layer formulation of the Navier-Stokes equations is employed. For turbulent flow cases, the Baldwin-Lomax algebraic turbulence model is used. Two different upwind techniques are available: van Leer's flux-vector splitting and Roe's flux-difference splitting. Full approximation multi-grid plus implicit residual and corrector smoothing were implemented to enhance the rate of convergence. Multi-block capabilities were developed to provide geometric flexibility. This feature allows the developed computer code to accommodate any grid topology or grid configuration with multiple topologies. The results shown in this dissertation were chosen to validate the computer code and display its geometric flexibility, which is provided by the multi-block structure.
NASA Astrophysics Data System (ADS)
Gravemeier, Volker; Kronbichler, Martin; Gee, Michael W.; Wall, Wolfgang A.
2011-02-01
This article studies three aspects of the recently proposed algebraic variational multiscale-multigrid method for large-eddy simulation of turbulent flow. First, the method is integrated into a second-order-accurate generalized-α time-stepping scheme. Second, a Fourier analysis of a simplified model problem is performed to assess the impact of scale separation on the overall performance of the method. The analysis reveals that scale separation implemented by projective operators provides modeling effects very close to an ideal small-scale subgrid viscosity, that is, it preserves low frequencies, in contrast to non-projective scale separations. Third, the algebraic variational multiscale-multigrid method is applied to turbulent flow past a square-section cylinder. The computational results obtained with the method reveal, on the one hand, the good accuracy achievable for this challenging test case already at a rather coarse discretization and, on the other hand, the superior computing efficiency, e.g., compared to a traditional dynamic Smagorinsky modeling approach.
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.
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.
Multi-grid for structures analysis
NASA Technical Reports Server (NTRS)
Kascak, Albert F.
1989-01-01
In structural analysis the amount of computational time necessary for a solution is proportional to the number of degrees of freedom times the bandwidth squared. In implicit time analysis, this must be done at each discrete point in time. If, in addition, the problem is nonlinear, then this solution must be iterated at each point in time. If the bandwidth is large, the size of the problem that can be analyzed is severely limited. The multi-grid method is a possible algorithm which can make this solution much more computationally efficient. This method has been used for years in computational fluid mechanics. It works on the fact that relaxation is very efficient on the high frequency components of the solution (nearest neighbor interactions) and not very good on low frequency components of the solution (far interactions). The multi-grid method is then to relax the solution on a particular model until the residual stops changing. This indicates that the solution contains the higher frequency components. A coarse model is then generated for the lower frequency components to the solution. The model is then relaxed for the lower frequency components of the solution. These lower frequency components are then interpolated to the fine model. In computational fluid mechanics the equations are usually expressed as finite differences.
The algebraic multigrid projection for eigenvalue problems; backrotations and multigrid fixed points
NASA Technical Reports Server (NTRS)
Costiner, Sorin; Taasan, Shlomo
1994-01-01
The periods of the theorem for the algebraic multigrid projection (MGP) for eigenvalue problems, and of the multigrid fixed point theorem for multigrid cycles combining MGP with backrotations, are presented. The MGP and the backrotations are central eigenvector separation techniques for multigrid eigenvalue algorithms. They allow computation on coarse levels of eigenvalues of a given eigenvalue problem, and are efficient tools in the computation of eigenvectors.
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.
On the parallel efficiency of the Frederickson-McBryan multigrid
NASA Technical Reports Server (NTRS)
Decker, Naomi H.
1990-01-01
To take full advantage of the parallelism in a standard multigrid algorithm requires as many processors as points. However, since coarse grids contain fewer points, most processors are idle during the coarse grid iterations. Frederickson and McBryan claim that retaining all points on all grid levels (using all processors) can lead to a superconvergent algorithm. The purpose of this work is to show that the parellel superconvergent multigrid (PSMG) algorithm of Frederickson and McBryan, though it achieves perfect processor utilization, is no more efficient than a parallel implementation of standard multigrid methods. PSMG is simply a new and perhaps simpler way of achieving the same results.
NASA Astrophysics Data System (ADS)
Puthen Veettil, Binesh; König, Dirk; Huang, Shujuan; Patterson, Robert; Conibeer, Gavin
2017-02-01
Silicon nanocrystals embedded in a dielectric matrix have been considered a potential candidate for many optoelectronic and photovoltaic applications and have been under vigorous study in recent years. One of the main properties of interest in this application is the absorption bandgap, which is determined by the quantum confinement of silicon nanocrystals. The ability to predict the absorption bandgap is a key step in designing an optimum solar cell using this material. Although several higher level algorithms are available to predict the electronic confinement in these nanocrystals, most of them make regular-shape assumptions for the ease of computation. In this work, we present a model for the accurate prediction of the quantum confinement in silicon nanocrystals of non-regular shape by employing an efficient, self-consistent Full-Multi-Grid method. Confined energies in spherical, elongated, and arbitrarily shaped nanocrystals are calculated. The excited level calculations quantify the wavefunction coupling and energy level splitting arising due to the proximity of dots. The splitting magnitude was found to be as high as 0.1 eV for the 2 nm size silicon quantum dots. The decrease in confinement energy due to the elongation of dots was found to be more than 0.2 eV, and the trend was similar for different dielectric materials. Theoretical predictions were compared to the results from optical and structural characterisation and found to be in agreement. The loss of degeneracy in highly asymmetric quantum dots, such as a "horse-shoe" shaped quantum dot, significantly affects the excited state energies.
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.
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.
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.
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).
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).
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.
Tuminaro, Raymond S.; Perego, Mauro; Tezaur, Irina Kalashnikova; Salinger, Andrew G.; Price, Stephen
2016-10-06
A multigrid method is proposed that combines ideas from matrix dependent multigrid for structured grids and algebraic multigrid for unstructured grids. It targets problems where a three-dimensional mesh can be viewed as an extrusion of a two-dimensional, unstructured mesh in a third dimension. Our motivation comes from the modeling of thin structures via finite elements and, more specifically, the modeling of ice sheets. Extruded meshes are relatively common for thin structures and often give rise to anisotropic problems when the thin direction mesh spacing is much smaller than the broad direction mesh spacing. Within our approach, the first few multigrid hierarchy levels are obtained by applying matrix dependent multigrid to semicoarsen in a structured thin direction fashion. After sufficient structured coarsening, the resulting mesh contains only a single layer corresponding to a two-dimensional, unstructured mesh. Algebraic multigrid can then be employed in a standard manner to create further coarse levels, as the anisotropic phenomena is no longer present in the single layer problem. The overall approach remains fully algebraic, with the minor exception that some additional information is needed to determine the extruded direction. Furthermore, this facilitates integration of the solver with a variety of different extruded mesh applications.
An adaptive multigrid model for hurricane track prediction
NASA Technical Reports Server (NTRS)
Fulton, Scott R.
1993-01-01
This paper describes a simple numerical model for hurricane track prediction which uses a multigrid method to adapt the model resolution as the vortex moves. The model is based on the modified barotropic vorticity equation, discretized in space by conservative finite differences and in time by a Runge-Kutta scheme. A multigrid method is used to solve an elliptic problem for the streamfunction at each time step. Nonuniform resolution is obtained by superimposing uniform grids of different spatial extent; these grids move with the vortex as it moves. Preliminary numerical results indicate that the local mesh refinement allows accurate prediction of the hurricane track with substantially less computer time than required on a single uniform grid.
Efficient relaxed-Jacobi smoothers for multigrid on parallel computers
NASA Astrophysics Data System (ADS)
Yang, Xiang; Mittal, Rajat
2017-03-01
In this Technical Note, we present a family of Jacobi-based multigrid smoothers suitable for the solution of discretized elliptic equations. These smoothers are based on the idea of scheduled-relaxation Jacobi proposed recently by Yang & Mittal (2014) [18] and employ two or three successive relaxed Jacobi iterations with relaxation factors derived so as to maximize the smoothing property of these iterations. The performance of these new smoothers measured in terms of convergence acceleration and computational workload, is assessed for multi-domain implementations typical of parallelized solvers, and compared to the lexicographic point Gauss-Seidel smoother. The tests include the geometric multigrid method on structured grids as well as the algebraic grid method on unstructured grids. The tests demonstrate that unlike Gauss-Seidel, the convergence of these Jacobi-based smoothers is unaffected by domain decomposition, and furthermore, they outperform the lexicographic Gauss-Seidel by factors that increase with domain partition count.
FINAL REPORT: Multigrid for Systems and Time-Dependent PDEs
Jones, J. E.
2016-08-02
This report has two sections. The first section is the motivation for looking at differing discretizations on coarse grids for solving a parabolic equation using multigrid in time. The second section contains selected numerical results from the many experiments conducted. The most interesting result is that for explicit fine grid discretizations, the best coarse discretization (i.e. smallest convergence rates) is a weighting between implicit and explicit methods.
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
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.
Backscattering of agglomerate particles
NASA Astrophysics Data System (ADS)
Zubko, Evgenij; Ovcharenko, Andrey; Bondarenko, Sergey; Shkuratov, Yuriy; Scotto, Cathy S.; Merritt, Charles; Hart, Matthew B.; Eversole, Jay D.; Videen, Gorden W.
2004-12-01
We examine how aggregation affects the light-scattering signatures, especially the polarization in the near-backward-scattering direction. We use the discrete dipole approximation (DDA) to study the backscatter of agglomerate particles consisting of oblong monomers. We examine the effects of monomer number and packing structure on the resulting negative polarization branch at small phase angle. We find large a dependence on the orientation of the monomers within the agglomerate and a smaller dependence on the number of monomers, suggesting that the mechanism producing the negative polarization minimum depends strongly on the interactions between the individual monomers. We also examine experimental measurements of substrates composed of biological cells. We find that the light-scattering signatures in the backward direction are not only different for different spore species, but for spores that have been prepared using different methodologies. These signatures are reproducible in different substrates composed of the spores from the same batches.
Anisotropic seismic inversion using a multigrid Monte Carlo approach
NASA Astrophysics Data System (ADS)
Mewes, Armin; Kulessa, Bernd; McKinley, John D.; Binley, Andrew M.
2010-10-01
We propose a new approach for the inversion of anisotropic P-wave data based on Monte Carlo methods combined with a multigrid approach. Simulated annealing facilitates objective minimization of the functional characterizing the misfit between observed and predicted traveltimes, as controlled by the Thomsen anisotropy parameters (ɛ, δ). Cycling between finer and coarser grids enhances the computational efficiency of the inversion process, thus accelerating the convergence of the solution while acting as a regularization technique of the inverse problem. Multigrid perturbation samples the probability density function without the requirements for the user to adjust tuning parameters. This increases the probability that the preferred global, rather than a poor local, minimum is attained. Undertaking multigrid refinement and Monte Carlo search in parallel produces more robust convergence than does the initially more intuitive approach of completing them sequentially. We demonstrate the usefulness of the new multigrid Monte Carlo (MGMC) scheme by applying it to (a) synthetic, noise-contaminated data reflecting an isotropic subsurface of constant slowness, horizontally layered geologic media and discrete subsurface anomalies; and (b) a crosshole seismic data set acquired by previous authors at the Reskajeage test site in Cornwall, UK. Inverted distributions of slowness (s) and the Thomson anisotropy parameters (ɛ, δ) compare favourably with those obtained previously using a popular matrix-based method. Reconstruction of the Thomsen ɛ parameter is particularly robust compared to that of slowness and the Thomsen δ parameter, even in the face of complex subsurface anomalies. The Thomsen ɛ and δ parameters have enhanced sensitivities to bulk-fabric and fracture-based anisotropies in the TI medium at Reskajeage. Because reconstruction of slowness (s) is intimately linked to that ɛ and δ in the MGMC scheme, inverted images of phase velocity reflect the integrated
In vitro dosimetry of agglomerates
NASA Astrophysics Data System (ADS)
Hirsch, V.; Kinnear, C.; Rodriguez-Lorenzo, L.; Monnier, C. A.; Rothen-Rutishauser, B.; Balog, S.; Petri-Fink, A.
2014-06-01
Agglomeration of nanoparticles in biological fluids is a pervasive phenomenon that leads to difficulty in the interpretation of results from in vitro exposure, primarily due to differing particokinetics of agglomerates to nanoparticles. Therefore, well-defined small agglomerates were designed that possessed different particokinetic profiles, and their cellular uptake was compared to a computational model of dosimetry. The approach used here paves the way for a better understanding of the impact of agglomeration on the nanoparticle-cell interaction.Agglomeration of nanoparticles in biological fluids is a pervasive phenomenon that leads to difficulty in the interpretation of results from in vitro exposure, primarily due to differing particokinetics of agglomerates to nanoparticles. Therefore, well-defined small agglomerates were designed that possessed different particokinetic profiles, and their cellular uptake was compared to a computational model of dosimetry. The approach used here paves the way for a better understanding of the impact of agglomeration on the nanoparticle-cell interaction. Electronic supplementary information (ESI) available: ITC data for tiopronin/Au-NP interactions, agglomeration kinetics at different pHs for tiopronin-coated Au-NPs, UV-Vis spectra in water, PBS and DMEM and temporal correlation functions for single Au-NPs and corresponding agglomerates, calculation of diffusion and sedimentation parameters, modelling of relative cell uptake based on the ISDD model and cytotoxicity of single Au-NPs and their agglomerates, and synthesis and cell uptake of large spherical Au-NPs. See DOI: 10.1039/c4nr00460d
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; 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
Multigrid convergence of inviscid fixed- and rotary-wing flows
NASA Astrophysics Data System (ADS)
Allen, C. B.
2002-05-01
The affect of multigrid acceleration implemented within an upwind-biased Euler method is presented, and applied to fixed-wing and rotary-wing flows. The convergence of fixed- and rotary-wing computations is shown to be vastly different, and multigrid is shown to be less effective for rotary-wing flows. The flow about a hovering rotor suffers from very slow convergence of the inner blade region, where the flow is effectively incompressible. Furthermore, the vortical wake must develop over several turns before convergence is achieved, whereas for fixed-wing computations the far-field grid and solution have little significance. Results are presented for single mesh and two, three, four, and five level multigrid, and using five levels a reduction in required CPU time of over 80 per cent is demonstrated for rotary-wing computations, but 94 per cent for fixed-wing computations. It is found that a simple V-cycle is the most effective, smoothing in the decreasing mesh density direction only, with a relaxed trilinear prolongation operator. Copyright
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.
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.
A Multigrid Algorithm for Steady Transonic Potential Flows Around Aerofoils Using Newton Iteration
NASA Astrophysics Data System (ADS)
Boerstoel, J. W.
1982-12-01
The application of multigrid relaxation to transonic potential-flow calculation was investigated. Fully conservative potential flows around aerofoils were taken as test problems. The solution algorithm was based on Newton iteration. In each Newton iteration step, multigrid relaxation was used to calculate correction potentials. It was found that the iteration to the circulation has to be kept outside the multigrid algorithm. In order to obtain meaningful norms of residuals (to be used in termination tests of loops), difference formulas with asymptotic scaling were introduced. Nonlinear instability problems were solved by upwind differencing using mass-flux-vector splitting instead of artificial viscosity or artificial density. It was also found that the multigrid method cannot efficiently update shock positions due to the (mainly) linear character of individual multigrid relaxation cycles. For subsonic flows, the algorithm is quite efficient. For transonic flows, the algorithm was found robust; it efficiency should be increased by improving the iteration on the shock positions; this is a highly nonlinear process.
Analysis of p-multigrid solution schemes for discontinuous Galerkin discretizations of flow problems
NASA Astrophysics Data System (ADS)
Mascarenhas, Brendan S.
p-multigrid is a 'multigrid-like' algorithm used to obtain solutions to high-order hp-finite element discretizations. In this method convergence is accelerated by using coarse levels constructed by reducing the order, p, of the approximating polynomial. We have investigated p-multigrid coupled with preconditioned block relaxation schemes to obtain the steady-state solution to discontinuous Galerkin (DG) discretizations of the Euler equations. Block-diagonal, -line, and sweeping preconditioners, and also the alternate direction implicit (ADI), and the incomplete lower-upper (ILU(0)) preconditioners are considered. Relaxation schemes that approximately-invert (AI) the steady-state stiffness matrix and implicit psuedo time-advancing (ITA) schemes are Fourier analyzed and compared. In general, for orders of approximating polynomial p ≥ 2, the AI schemes perform better than the similarly preconditioned ITA schemes. The results show that p-multigrid iterations of the AI-ILU(0) scheme with under-relaxation o = 1/2 converge fastest and are the most robust of the schemes studied. Similar to prior observations by Helenbrook and Atkins p-multigrid was observed to behave anomalously when p transitions from 1 to 0. Using ideas from Helenbrook and Atkins correction for diffusion, and the streamwise upwind Petrov-Galerkin (SUPG) formulation, this anomalous behavior is corrected for the 1D convection equation. The correction is then extended to the 1D convection-diffusion equation.
Tuminaro, Raymond S.; Perego, Mauro; Tezaur, Irina Kalashnikova; ...
2016-10-06
A multigrid method is proposed that combines ideas from matrix dependent multigrid for structured grids and algebraic multigrid for unstructured grids. It targets problems where a three-dimensional mesh can be viewed as an extrusion of a two-dimensional, unstructured mesh in a third dimension. Our motivation comes from the modeling of thin structures via finite elements and, more specifically, the modeling of ice sheets. Extruded meshes are relatively common for thin structures and often give rise to anisotropic problems when the thin direction mesh spacing is much smaller than the broad direction mesh spacing. Within our approach, the first few multigridmore » hierarchy levels are obtained by applying matrix dependent multigrid to semicoarsen in a structured thin direction fashion. After sufficient structured coarsening, the resulting mesh contains only a single layer corresponding to a two-dimensional, unstructured mesh. Algebraic multigrid can then be employed in a standard manner to create further coarse levels, as the anisotropic phenomena is no longer present in the single layer problem. The overall approach remains fully algebraic, with the minor exception that some additional information is needed to determine the extruded direction. Furthermore, this facilitates integration of the solver with a variety of different extruded mesh applications.« less
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.
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
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
Multigrid techniques for the solution of the passive scalar advection-diffusion equation
NASA Technical Reports Server (NTRS)
Phillips, R. E.; Schmidt, F. W.
1985-01-01
The solution of elliptic passive scalar advection-diffusion equations is required in the analysis of many turbulent flow and convective heat transfer problems. The accuracy of the solution may be affected by the presence of regions containing large gradients of the dependent variables. The multigrid concept of local grid refinement is a method for improving the accuracy of the calculations in these problems. In combination with the multilevel acceleration techniques, an accurate and efficient computational procedure is developed. In addition, a robust implementation of the QUICK finite-difference scheme is described. Calculations of a test problem are presented to quantitatively demonstrate the advantages of the multilevel-multigrid method.
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.
Gao, Hao; Phan, Lan; Lin, Yuting
2012-09-01
A graphics processing unit-based parallel multigrid solver for a radiative transfer equation with vacuum boundary condition or reflection boundary condition is presented for heterogeneous media with complex geometry based on two-dimensional triangular meshes or three-dimensional tetrahedral meshes. The computational complexity of this parallel solver is linearly proportional to the degrees of freedom in both angular and spatial variables, while the full multigrid method is utilized to minimize the number of iterations. The overall gain of speed is roughly 30 to 300 fold with respect to our prior multigrid solver, which depends on the underlying regime and the parallelization. The numerical validations are presented with the MATLAB codes at https://sites.google.com/site/rtefastsolver/.
Fast and High Accuracy Multigrid Solution of the Three Dimensional Poisson Equation
NASA Astrophysics Data System (ADS)
Zhang, Jun
1998-07-01
We employ a fourth-order compact finite difference scheme (FOS) with the multigrid algorithm to solve the three dimensional Poisson equation. We test the influence of different orderings of the grid space and different grid-transfer operators on the convergence and efficiency of our high accuracy algorithm. Fourier smoothing analysis is conducted to show that FOS has a smaller smoothing factor than the traditional second-order central difference scheme (CDS). A new method of Fourier smoothing analysis is proposed for the partially decoupled red-black Gauss-Seidel relaxation with FOS. Numerical results are given to compare the computed accuracy and the computational efficiency of FOS with multigrid against CDS with multigrid.
Phan, Lan; Lin, Yuting
2012-01-01
Abstract. A graphics processing unit–based parallel multigrid solver for a radiative transfer equation with vacuum boundary condition or reflection boundary condition is presented for heterogeneous media with complex geometry based on two-dimensional triangular meshes or three-dimensional tetrahedral meshes. The computational complexity of this parallel solver is linearly proportional to the degrees of freedom in both angular and spatial variables, while the full multigrid method is utilized to minimize the number of iterations. The overall gain of speed is roughly 30 to 300 fold with respect to our prior multigrid solver, which depends on the underlying regime and the parallelization. The numerical validations are presented with the MATLAB codes at https://sites.google.com/site/rtefastsolver/. PMID:23085905
Conjugate gradient coupled with multigrid for an indefinite problem
NASA Technical Reports Server (NTRS)
Gozani, J.; Nachshon, A.; Turkel, E.
1984-01-01
An iterative algorithm for the Helmholtz equation is presented. This scheme was based on the preconditioned conjugate gradient method for the normal equations. The preconditioning is one cycle of a multigrid method for the discrete Laplacian. The smoothing algorithm is red-black Gauss-Seidel and is constructed so it is a symmetric operator. The total number of iterations needed by the algorithm is independent of h. By varying the number of grids, the number of iterations depends only weakly on k when k(3)h(2) is constant. Comparisons with a SSOR preconditioner are presented.
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.
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.
Tweed Relaxation: a new multigrid smoother for stretched structured grids
NASA Astrophysics Data System (ADS)
Bewley, Thomas; Mashayekhi, Alireza
2012-11-01
In DNS/LES of the NSE using a fractional step method, one must accurately solve a Poisson equation for the pressure update at each timestep. This step often represents a significant fraction of the overall computational burden and, when Fourier methods are unavailable, geometric multigrid methods are a preferred choice. When working on an unstretched Cartesian grid, the red-black Gauss-Seidel method is the most efficient multigrid smoother available. When working on a Cartesian grid that is stretched in 1 coordinate direction to provide grid clustering near a wall, zebra relaxation, on sets of lines perpendicular to the wall, is most efficient. When working on a structured grid that is stretched in 2 or 3 coordinate directions, however, one is forced to alternate the directions that the zebra relaxation is applied in order to pass information quickly across all regions of grid clustering. A new relaxation method is introduced which is shown to significantly outperform such alternating direction line smoothers. This new method is implicit along sets of lines that branch and form 90° corners, like the stripes at the shoulder of a tweed shirt, to stay everywhere perpendicular to the nearest wall, thus passing information quickly across all regions of grid clustering.
Multigrid properties of upwind-biased data reconstructions
NASA Astrophysics Data System (ADS)
Warren, Gary P.; Roberts, Thomas W.
1993-11-01
The multigrid properties of two data reconstruction methods used for achieving second-order spatial accuracy when solving the two-dimensional Euler equations are examined. The data reconstruction methods are used with an implicit upwind algorithm which uses linearized backward-Euler time-differencing. The solution of the resulting linear system is performed by an iterative procedure. In the present study only regular quadrilateral grids are considered, so a red-black Gauss-Seidel iteration is used. Although the Jacobian is approximated by first-order upwind extrapolation, two alternative data reconstruction techniques for the flux integral that yield higher-order spatial accuracy at steady state are examined. The first method, probably most popular for structured quadrilateral grids, is based on estimating the cell gradients using one-dimensional reconstruction along curvilinear coordinates. The second method is based on Green's theorem. Analysis and numerical results for the two dimensional Euler equations show that data reconstruction based on Green's theorem has superior multigrid properties as compared to the one-dimensional data reconstruction method.
Multigrid properties of upwind-biased data reconstructions
NASA Technical Reports Server (NTRS)
Warren, Gary P.; Roberts, Thomas W.
1993-01-01
The multigrid properties of two data reconstruction methods used for achieving second-order spatial accuracy when solving the two-dimensional Euler equations are examined. The data reconstruction methods are used with an implicit upwind algorithm which uses linearized backward-Euler time-differencing. The solution of the resulting linear system is performed by an iterative procedure. In the present study only regular quadrilateral grids are considered, so a red-black Gauss-Seidel iteration is used. Although the Jacobian is approximated by first-order upwind extrapolation, two alternative data reconstruction techniques for the flux integral that yield higher-order spatial accuracy at steady state are examined. The first method, probably most popular for structured quadrilateral grids, is based on estimating the cell gradients using one-dimensional reconstruction along curvilinear coordinates. The second method is based on Green's theorem. Analysis and numerical results for the two dimensional Euler equations show that data reconstruction based on Green's theorem has superior multigrid properties as compared to the one-dimensional data reconstruction method.
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.
Multigrid Reduction in Time for Nonlinear Parabolic Problems
Falgout, R. D.; Manteuffel, T. A.; O'Neill, B.; Schroder, J. B.
2016-01-04
The need for parallel-in-time is being driven by changes in computer architectures, where future speed-ups will be available through greater concurrency, but not faster clock speeds, which are stagnant.This leads to a bottleneck for sequential time marching schemes, because they lack parallelism in the time dimension. Multigrid Reduction in Time (MGRIT) is an iterative procedure that allows for temporal parallelism by utilizing multigrid reduction techniques and a multilevel hierarchy of coarse time grids. MGRIT has been shown to be effective for linear problems, with speedups of up to 50 times. The goal of this work is the efficient solution of nonlinear problems with MGRIT, where efficient is defined as achieving similar performance when compared to a corresponding linear problem. As our benchmark, we use the p-Laplacian, where p = 4 corresponds to a well-known nonlinear diffusion equation and p = 2 corresponds to our benchmark linear diffusion problem. When considering linear problems and implicit methods, the use of optimal spatial solvers such as spatial multigrid imply that the cost of one time step evaluation is fixed across temporal levels, which have a large variation in time step sizes. This is not the case for nonlinear problems, where the work required increases dramatically on coarser time grids, where relatively large time steps lead to worse conditioned nonlinear solves and increased nonlinear iteration counts per time step evaluation. This is the key difficulty explored by this paper. We show that by using a variety of strategies, most importantly, spatial coarsening and an alternate initial guess to the nonlinear time-step solver, we can reduce the work per time step evaluation over all temporal levels to a range similar with the corresponding linear problem. This allows for parallel scaling behavior comparable to the corresponding linear problem.
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 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.
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.
NONLINEAR MULTIGRID SOLVER EXPLOITING AMGe COARSE SPACES WITH APPROXIMATION PROPERTIES
Christensen, Max La Cour; Villa, Umberto E.; Engsig-Karup, Allan P.; Vassilevski, Panayot S.
2016-01-22
The paper introduces a nonlinear multigrid solver for mixed nite element discretizations based on the Full Approximation Scheme (FAS) and element-based Algebraic Multigrid (AMGe). The main motivation to use FAS for unstruc- tured problems is the guaranteed approximation property of the AMGe coarse spaces that were developed recently at Lawrence Livermore National Laboratory. These give the ability to derive stable and accurate coarse nonlinear discretization problems. The previous attempts (including ones with the original AMGe method, [5, 11]), were less successful due to lack of such good approximation properties of the coarse spaces. With coarse spaces with approximation properties, our FAS approach on un- structured meshes should be as powerful/successful as FAS on geometrically re ned meshes. For comparison, Newton's method and Picard iterations with an inner state-of-the-art linear solver is compared to FAS on a nonlinear saddle point problem with applications to porous media ow. It is demonstrated that FAS is faster than Newton's method and Picard iterations for the experiments considered here. Due to the guaranteed approximation properties of our AMGe, the coarse spaces are very accurate, providing a solver with the potential for mesh-independent convergence on general unstructured meshes.
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.
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.
NASA Astrophysics Data System (ADS)
Kaus, Boris; Popov, Anton; Püsök, Adina
2014-05-01
In order to solve high-resolution 3D problems in computational geodynamics it is crucial to use multigrid solvers in combination with parallel computers. A number of approaches are currently in use in the community, which can broadly be divided into coupled and decoupled approaches. In the decoupled approach, an algebraic or geometric multigrid method is used as a preconditioner for the velocity equations only while an iterative approach such as Schur complement reduction used to solve the outer velocity-pressure equations. In the coupled approach, on the other hand, a multigrid approach is applied to both the velocity and pressure equations. The coupled multigrid approaches are typically employed in combination with staggered finite difference discretizations, whereas the decoupled approach is the method of choice in many of the existing finite element codes. Yet, it is unclear whether there are differences in speed between the two approaches, and if so, how this depends on the initial guess. Here, we implemented both approaches in combination with a staggered finite difference discretization and test the robustness of the two approaches with respect to large jumps in viscosity contrast, as well as their computational efficiency as a function of the initial guess. Acknowledgements. Funding was provided by the European Research Council under the European Community's Seventh Framework Program (FP7/2007-2013) / ERC Grant agreement #258830. Numerical computations have been performed on JUQUEEN of the Jülich high-performance computing center.
Development of multigrid algorithms for problems from fluid dynamics
NASA Astrophysics Data System (ADS)
Becker, K.; Trottenberg, U.
Multigrid algorithms are developed to demonstrate multigrid technique efficiency for complicated fluid dynamics problems regarding error reduction and discretization accuracy. Subsonic potential 2-D flow around a profile is studied as well as rotation-symmetric flow in a slot between two rotating spheres and the flow in the combustion chamber of Otto engines. The study of the 2-D subsonic potential flow around a profile with the multigrid algorithm is discussed.
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.
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 solutions to quasi-elliptic schemes
NASA Technical Reports Server (NTRS)
Brandt, A.; Taasan, S.
1985-01-01
Quasi-elliptic schemes arise from central differencing or finite element discretization of elliptic systems with odd order derivatives on non-staggered grids. They are somewhat unstable and less accurate then corresponding staggered-grid schemes. When usual multigrid solvers are applied to them, the asymptotic algebraic convergence is necessarily slow. Nevertheless, it is shown by mode analyses and numerical experiments that the usual FMG algorithm is very efficient in solving quasi-elliptic equations to the level of truncation errors. Also, a new type of multigrid algorithm is presented, mode analyzed and tested, for which even the asymptotic algebraic convergence is fast. The essence of that algorithm is applicable to other kinds of problems, including highly indefinite ones.
Multigrid shallow water equations on an FPGA
NASA Astrophysics Data System (ADS)
Jeffress, Stephen; Duben, Peter; Palmer, Tim
2015-04-01
A novel computing technology for multigrid shallow water equations is investigated. As power consumption begins to constrain traditional supercomputing advances, weather and climate simulators are exploring alternative technologies that achieve efficiency gains through massively parallel and low power architectures. In recent years FPGA implementations of reduced complexity atmospheric models have shown accelerated speeds and reduced power consumption compared to multi-core CPU integrations. We continue this line of research by designing an FPGA dataflow engine for a mulitgrid version of the 2D shallow water equations. The multigrid algorithm couples grids of variable resolution to improve accuracy. We show that a significant reduction of precision in the floating point representation of the fine grid variables allows greater parallelism and thus improved overall peformance while maintaining accurate integrations. Preliminary designs have been constructed by software emulation. Results of the hardware implementation will be presented at the conference.
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.
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.
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.
Advanced Multigrid Solvers for Fluid Dynamics
NASA Technical Reports Server (NTRS)
Brandt, Achi
1999-01-01
The main objective of this project has been to support the development of multigrid techniques in computational fluid dynamics that can achieve "textbook multigrid efficiency" (TME), which is several orders of magnitude faster than current industrial CFD solvers. Toward that goal we have assembled a detailed table which lists every foreseen kind of computational difficulty for achieving it, together with the possible ways for resolving the difficulty, their current state of development, and references. We have developed several codes to test and demonstrate, in the framework of simple model problems, several approaches for overcoming the most important of the listed difficulties that had not been resolved before. In particular, TME has been demonstrated for incompressible flows on one hand, and for near-sonic flows on the other hand. General approaches were advanced for the relaxation of stagnation points and boundary conditions under various situations. Also, new algebraic multigrid techniques were formed for treating unstructured grid formulations. More details on all these are given below.
Grid optimization and multigrid techniques for fluid flow and transport problems
NASA Astrophysics Data System (ADS)
Pardhanani, Anand L.
1992-01-01
Special numerical techniques for the efficient and accurate solution of fluid flow and certain other transport processes are investigated. These include adaptive redistribution and optimization of computational grids, multigrid techniques for convection-diffusion problems, and multigrid time-marching methods for non-stationary and nonlinear problems. The grid optimization strategy is based on constructing and minimizing a mathematical objective function which defines the desired grid properties. For convection-diffusion problems, it is demonstrated that standard multigrid techniques fail when the coarse grids violate mesh-size restrictions. A variety of alternate multigrid strategies are explored, including artificial dissipation, fine grid pre-elimination, self-adjoint formulation, defect correction, and combination with grid redistribution. Multilevel techniques are also developed for time-dependent problems, including evolution problems with non-steady or transient solutions, and steady-state problems solved with artificial time-marching. Both explicit and implicit integration schemes are investigated, and it is shown that significant performance improvements can be gained with the use of multigrid. These techniques are implemented and tested on representative model problems as well as practical applications of current research interest. The grid investigations involve optimization in model problems, and in large-scale 3-D aircraft wing-body configurations. The multigrid applications range from model convection-diffusion problems, to time-dependent problems, to coupled nonlinear problems in two major application areas. The first application involves simulating spatio-temporal patterns in a coupled, nonlinear, reaction-diffusion problem that models the behavior of the Belousov-Zhabotinskii reaction. This multi-species reaction, which exhibits intricate patterns in laboratory experiments, has attracted considerable interest in the field of nonlinear dynamics. The
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.
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.
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.
Local block refinement with a multigrid flow solver
NASA Astrophysics Data System (ADS)
Lange, C. F.; Schäfer, M.; Durst, F.
2002-01-01
A local block refinement procedure for the efficient computation of transient incompressible flows with heat transfer is presented. The procedure uses patched structured grids for the blockwise refinement and a parallel multigrid finite volume method with colocated primitive variables to solve the Navier-Stokes equations. No restriction is imposed on the value of the refinement rate and non-integer rates may also be used. The procedure is analysed with respect to its sensitivity to the refinement rate and to the corresponding accuracy. Several applications exemplify the advantages of the method in comparison with a common block structured grid approach. The results show that it is possible to achieve an improvement in accuracy with simultaneous significant savings in computing time and memory requirements. Copyright
NASA Astrophysics Data System (ADS)
Huseynov, Elchin M.
2017-04-01
Nanocrystalline 3C-SiC particles irradiated by neutron flux during 20 h in TRIGA Mark II light water pool type research reactor. Silicon carbide nanoparticles were analyzed by Scanning Electron Microscope (SEM) and Transmission Electron Microscopy (TEM) devices before and after neutron irradiation. The agglomeration of nanoparticles was studied comparatively before and after neutron irradiation. After neutron irradiation the amorphous layer surrounding the nanoparticles was analyzed in TEM device. Neutron irradiation defects in the 3C-SiC nanoparticles and other effects investigated by TEM device. The effect of irradiation on the crystal structure of the nanomaterial was studied by selected area electron diffraction (SAED) and electron diffraction patterns (EDP) analysis.
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.
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.
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.
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 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.
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 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 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.
Algebraic multigrid domain and range decomposition (AMG-DD / AMG-RD)*
Bank, R.; Falgout, R. D.; Jones, T.; ...
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
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.
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.
MGGHAT: Elliptic PDE software with adaptive refinement, multigrid and high order finite elements
NASA Technical Reports Server (NTRS)
Mitchell, William F.
1993-01-01
MGGHAT (MultiGrid Galerkin Hierarchical Adaptive Triangles) is a program for the solution of linear second order elliptic partial differential equations in two dimensional polygonal domains. This program is now available for public use. It is a finite element method with linear, quadratic or cubic elements over triangles. The adaptive refinement via newest vertex bisection and the multigrid iteration are both based on a hierarchical basis formulation. Visualization is available at run time through an X Window display, and a posteriori through output files that can be used as GNUPLOT input. In this paper, we describe the methods used by MGGHAT, define the problem domain for which it is appropriate, illustrate use of the program, show numerical and graphical examples, and explain how to obtain the software.
Multigrid acceleration and turbulence models for computations of 3D turbulent jets in crossflow
NASA Technical Reports Server (NTRS)
Demuren, A. O.
1992-01-01
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 to be obtained with both turbulence models. 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 equation in the latter may be responsible. Computed results with both turbulence models are compared to experimental data for a pair of opposed jets in crossflow. Both models yield reasonable agreement for the mean flow velocity, but RSM yields better predictions of the Reynolds stresses.
Application of the multigrid solution technique to hypersonic entry vehicles
NASA Astrophysics Data System (ADS)
Greene, Francis A.
1994-09-01
Multigrid techniques have been incorporated into an existing hypersonic flow analysis code, 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-deg blunted sphere-cone and a blended-wing body, are presented. It is shown that the algorithm predicts heating rates accurately, and computes solutions in one-third the computational time of the nonmultigrid algorithm.
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.
Agglomeration tendency in dry pharmaceutical granular systems.
Lachiver, Emilie DesRosiers; Abatzoglou, Nicolas; Cartilier, Louis; Simard, Jean-Sébastien
2006-10-01
The agglomeration tendency of dry pharmaceutical mixtures containing various concentrations of Xylitab 100 (Xylitol), calcium carbonate precipitated (CCP) and magnesium stearate (MgSt) was evaluated statistically as a function of mixing time. A Ro-Tap tester was employed to mix the three pharmaceutical components, and the agglomerates formed were measured with respect to their weight and size. An experimental design was devised and applied to structure and then statistically analyze the results. Xylitab was found not to be influential in the formation of agglomerates, but aided in deagglomeration when mixed with other components. CCP and MgSt formed agglomerates over time and showed positive interactions favouring agglomeration. The agglomerates started to fracture when they reached a critical size, at which stage the particles' attraction forces (cohesion forces) were weaker than both gravity and inertia. It has been shown and quantitatively demonstrated that the mixing time and ingredient concentrations of a three-component pharmaceutical mixture can affect agglomeration tendency.
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.
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.
Multigrid iteration solution procedure for solving two-dimensional sets of coupled equations. [HTGR
Vondy, D.R.
1984-07-01
A procedure of iterative solution was coded in Fortran to apply the multigrid scheme of iteration to a set of coupled equations for solving two-dimensional sets of coupled equations. 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 not always competitive with simple overrelaxation. Implementing an effective and flexible procedure is a time-consuming task. Absolute error level evaluation was found to be essential to support methods assessment. A code source listing is presented to allow simple 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.
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.
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.
Zonal multigrid solution of compressible flow problems on unstructured and adaptive meshes
NASA Technical Reports Server (NTRS)
Mavriplis, Dimitri J.
1989-01-01
The simultaneous use of adaptive meshing techniques with a multigrid strategy for solving the 2-D Euler equations in the context of unstructured meshes is studied. To obtain optimal efficiency, methods capable of computing locally improved solutions without recourse to global recalculations are pursued. A method for locally refining an existing unstructured mesh, without regenerating a new global mesh is employed, and the domain is automatically partitioned into refined and unrefined regions. Two multigrid strategies are developed. In the first, time-stepping is performed on a global fine mesh covering the entire domain, and convergence acceleration is achieved through the use of zonal coarse grid accelerator meshes, which lie under the adaptively refined regions of the global fine mesh. Both schemes are shown to produce similar convergence rates to each other, and also with respect to a previously developed global multigrid algorithm, which performs time-stepping throughout the entire domain, on each mesh level. However, the present schemes exhibit higher computational efficiency due to the smaller number of operations on each level.
NASA Astrophysics Data System (ADS)
Kifonidis, K.; Müller, E.
2012-08-01
Aims: We describe and study a family of new multigrid iterative solvers for the multidimensional, implicitly discretized equations of hydrodynamics. Schemes of this class are free of the Courant-Friedrichs-Lewy condition. They are intended for simulations in which widely differing wave propagation timescales are present. A preferred solver in this class is identified. Applications to some simple stiff test problems that are governed by the compressible Euler equations, are presented to evaluate the convergence behavior, and the stability properties of this solver. Algorithmic areas are determined where further work is required to make the method sufficiently efficient and robust for future application to difficult astrophysical flow problems. Methods: The basic equations are formulated and discretized on non-orthogonal, structured curvilinear meshes. Roe's approximate Riemann solver and a second-order accurate reconstruction scheme are used for spatial discretization. Implicit Runge-Kutta (ESDIRK) schemes are employed for temporal discretization. The resulting discrete equations are solved with a full-coarsening, non-linear multigrid method. Smoothing is performed with multistage-implicit smoothers. These are applied here to the time-dependent equations by means of dual time stepping. Results: For steady-state problems, our results show that the efficiency of the present approach is comparable to the best implicit solvers for conservative discretizations of the compressible Euler equations that can be found in the literature. The use of red-black as opposed to symmetric Gauss-Seidel iteration in the multistage-smoother is found to have only a minor impact on multigrid convergence. This should enable scalable parallelization without having to seriously compromise the method's algorithmic efficiency. For time-dependent test problems, our results reveal that the multigrid convergence rate degrades with increasing Courant numbers (i.e. time step sizes). Beyond a
Multigrid-based reconstruction algorithm for quantitative photoacoustic tomography
Li, Shengfu; Montcel, Bruno; Yuan, Zhen; Liu, Wanyu; Vray, Didier
2015-01-01
This paper proposes a multigrid inversion framework for quantitative photoacoustic tomography reconstruction. The forward model of optical fluence distribution and the inverse problem are solved at multiple resolutions. A fixed-point iteration scheme is formulated for each resolution and used as a cost function. The simulated and experimental results for quantitative photoacoustic tomography reconstruction show that the proposed multigrid inversion can dramatically reduce the required number of iterations for the optimization process without loss of reliability in the results. PMID:26203371
Morphological characterization of diesel soot agglomerates based on the Beer-Lambert law
NASA Astrophysics Data System (ADS)
Lapuerta, Magín; Martos, Francisco J.; José Expósito, Juan
2013-03-01
A new method is proposed for the determination of the number of primary particles composing soot agglomerates emitted from diesel engines as well as their individual fractal dimension. The method is based on the Beer-Lambert law and it is applied to micro-photographs taken in high resolution transmission electron microscopy. Differences in the grey levels of the images lead to a more accurate estimation of the geometry of the agglomerate (in this case radius of gyration) than other methods based exclusively on the planar projections of the agglomerates. The method was validated by applying it to different images of the same agglomerate observed from different angles of incidence, and proving that the effect of the angle of incidence is minor, contrary to other methods. Finally, the comparisons with other methods showed that the size, number of primary particles and fractal dimension (the latter depending on the particle size) are usually underestimated when only planar projections of the agglomerates are considered.
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.
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.
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.
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.
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.
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.
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
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.
Modeling of particle agglomeration in nanofluids
NASA Astrophysics Data System (ADS)
Krishna, K. Hari; Neti, S.; Oztekin, A.; Mohapatra, S.
2015-03-01
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.
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.
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.
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.
A multiblock multigrid three-dimensional Euler equation solver
NASA Technical Reports Server (NTRS)
Cannizzaro, Frank E.; Elmiligui, Alaa; Melson, N. Duane; Vonlavante, E.
1990-01-01
Current aerodynamic designs are often quite complex (geometrically). Flexible computational tools are needed for the analysis of a wide range of configurations with both internal and external flows. In the past, geometrically dissimilar configurations required different analysis codes with different grid topologies in each. The duplicity of codes can be avoided with the use of a general multiblock formulation which can handle any grid topology. Rather than hard wiring the grid topology into the program, it is instead dictated by input to the program. In this work, the compressible Euler equations, written in a body-fitted finite-volume formulation, are solved using a pseudo-time-marching approach. Two upwind methods (van Leer's flux-vector-splitting and Roe's flux-differencing) were investigated. Two types of explicit solvers (a two-step predictor-corrector and a modified multistage Runge-Kutta) were used with multigrid acceleration to enhance convergence. A multiblock strategy is used to allow greater geometric flexibility. A report on simple explicit upwind schemes for solving compressible flows is included.
Algebraic Multigrid by Smoothed Aggregation for Second and Fourth Order Elliptic Problems
NASA Technical Reports Server (NTRS)
Vanek, Petr; Mandel, Jan; Brezina, Marian
1996-01-01
Multigrid methods are very efficient iterative solvers for system of algebraic equations arising from finite element and finite difference discretization of elliptic boundary value problems. The main principle of multigrid methods is to complement the local exchange of information in point-wise iterative methods by a global one utilizing several related systems, called coarse levels, with a smaller number of variables. The coarse levels are often obtained as a hierarchy of discretizations with different characteristic meshsizes, but this requires that the discretization is controlled by the iterative method. To solve linear systems produced by existing finite element software, one needs to create an artificial hierarchy of coarse problems. The principal issue is then to obtain computational complexity and approximation properties similar to those for nested meshes, using only information in the matrix of the system and as little extra information as possible. Such algebraic multigrid method that uses the system matrix only was developed by Ruge. The prolongations were based on the matrix of the system by partial solution from given values at selected coarse points. The coarse grid points were selected so that each point would be interpolated to via so-called strong connections. Our approach is based on smoothed aggregation introduced recently by Vanek. First the set of nodes is decomposed into small mutually disjoint subsets. A tentative piecewise constant interpolation (in the discrete sense) is then defined on those subsets as piecewise constant for second order problems, and piecewise linear for fourth order problems. The prolongation operator is then obtained by smoothing the output of the tentative prolongation and coarse level operators are defined variationally.
A simplified analysis of the multigrid V-cycle as a fast elliptic solver
NASA Technical Reports Server (NTRS)
Decker, Naomi H.; Taasan, Shlomo
1988-01-01
For special model problems, Fourier analysis gives exact convergence rates for the two-grid multigrid cycle and, for more general problems, provides estimates of the two-grid convergence rates via local mode analysis. A method is presented for obtaining mutigrid convergence rate estimates for cycles involving more than two grids (using essentially the same analysis as for the two-grid cycle). For the simple cast of the V-cycle used as a fast Laplace solver on the unit square, the k-grid convergence rate bounds obtained by this method are sharper than the bounds predicted by the variational theory. Both theoretical justification and experimental evidence are presented.
Percolative fragmentation and spontaneous agglomeration
Hurt, R.; Davis, K.
1999-03-01
Captive particle imaging experiments were performed on over 200 coal and char particles in the pulverized size range from four coals of various rank at oxygen concentration from 3--19 mol% and at gas temperatures of about 1250 K. Despite wide variations in single-particle behavior, the data set reveals two clear trends that provide new information on the nature of char combustion. First, the low-rank coal chars are observed to maintain their high reactivity through the late stages of combustion, thus avoiding the near-extinction events and long burnout tails observed for bituminous coal chars. Secondly, percolative fragmentation in the late stages of combustion is a rare event under these conditions. Some particles reach a percolation threshold rate in combustion, but typically undergo spontaneous agglomeration rather than liberation of the incipient fragments. It is concluded that percolative fragmentation behavior in the pulverized size range is determined not only by solid-phase connectivity, but also by a real competition between disruptive and cohesive forces present at the time of formation of the colloidal-sized incipient fragments.
A robust multi-grid pressure-based algorithm for multi-fluid flow at all speeds
NASA Astrophysics Data System (ADS)
Darwish, M.; Moukalled, F.; Sekar, B.
2003-04-01
This paper reports on the implementation and testing, within a full non-linear multi-grid environment, of a new pressure-based algorithm for the prediction of multi-fluid flow at all speeds. The algorithm is part of the mass conservation-based algorithms (MCBA) group in which the pressure correction equation is derived from overall mass conservation. The performance of the new method is assessed by solving a series of two-dimensional two-fluid flow test problems varying from turbulent low Mach number to supersonic flows, and from very low to high fluid density ratios. Solutions are generated for several grid sizes using the single grid (SG), the prolongation grid (PG), and the full non-linear multi-grid (FMG) methods. The main outcomes of this study are: (i) a clear demonstration of the ability of the FMG method to tackle the added non-linearity of multi-fluid flows, which is manifested through the performance jump observed when using the non-linear multi-grid approach as compared to the SG and PG methods; (ii) the extension of the FMG method to predict turbulent multi-fluid flows at all speeds. The convergence history plots and CPU-times presented indicate that the FMG method is far more efficient than the PG method and accelerates the convergence rate over the SG method, for the problems solved and the grids used, by a factor reaching a value as high as 15.
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
Multigrid solution of internal flows using unstructured solution adaptive meshes
NASA Technical Reports Server (NTRS)
Smith, Wayne A.; Blake, Kenneth R.
1992-01-01
This is the final report of the NASA Lewis SBIR Phase 2 Contract Number NAS3-25785, Multigrid Solution of Internal Flows Using Unstructured Solution Adaptive Meshes. The objective of this project, as described in the Statement of Work, is to develop and deliver to NASA a general three-dimensional Navier-Stokes code using unstructured solution-adaptive meshes for accuracy and multigrid techniques for convergence acceleration. The code will primarily be applied, but not necessarily limited, to high speed internal flows in turbomachinery.
An Upwind Multigrid Algorithm for Calculating Flows on Unstructured Grids
NASA Technical Reports Server (NTRS)
Bonhaus, Daryl L.
1993-01-01
An algorithm is described that calculates inviscid, laminar, and turbulent flows on triangular meshes with an upwind discretization. A brief description of the base solver and the multigrid implementation is given, followed by results that consist mainly of convergence rates for inviscid and viscous flows over a NACA four-digit airfoil section. The results show that multigrid does accelerate convergence when the same relaxation parameters that yield good single-grid performance are used; however, larger gains in performance can be realized by doing less work in the relaxation scheme.
Multigrid Particle-in-cell Simulations of Plasma Microturbulence
J.L.V. Lewandowski
2003-06-17
A new scheme to accurately retain kinetic electron effects in particle-in-cell (PIC) simulations for the case of electrostatic drift waves is presented. The splitting scheme, which is based on exact separation between adiabatic and on adiabatic electron responses, is shown to yield more accurate linear growth rates than the standard df scheme. The linear and nonlinear elliptic problems that arise in the splitting scheme are solved using a multi-grid solver. The multi-grid particle-in-cell approach offers an attractive path, both from the physics and numerical points of view, to simulate kinetic electron dynamics in global toroidal plasmas.
AMG (Algebraic Multigrid): Basic Development, Applications and Theory.
1987-01-07
NAME OF RESPONSIBLE INDIVIDUAL 22b. TELEPHONE NUMBER 22c OFFICE SYMBOL I n iude .4 re4 Code Captain Thomas (202) 767-5025 NM DO FORM 1473.83 APR...31 (1977), 333-390, ICASE Report 76-27. (B2) A. Brandt; "Algebraic multigrid: theory", Proc. Int’l M3onf., Copper 1.buntain., C), Aprol, 1983. (B3) A... Copper Mtn., OD, April 1983. (Dl) J.E. Dendy, Jr.; "Black box multigrid," LA-UR-Sl-2337 Los Alamos National Laboratory, Los Alamos, New Mexico, J. Ccn
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.
NASA Astrophysics Data System (ADS)
Langer, Stefan
2013-03-01
For unstructured finite volume methods, we present a line implicit Runge-Kutta method applied as smoother in an agglomerated multigrid algorithm to significantly improve the reliability and convergence rate to approximate steady-state solutions of the Reynolds-averaged Navier-Stokes equations. To describe turbulence, we consider a one-equation Spalart-Allmaras turbulence model. The line implicit Runge-Kutta method extends a basic explicit Runge-Kutta method by a preconditioner given by an approximate derivative of the residual function. The approximate derivative is only constructed along predetermined lines which resolve anisotropies in the given grid. Therefore, the method is a canonical generalisation of point implicit methods. Numerical examples demonstrate the improvements of the line implicit Runge-Kutta when compared with explicit Runge-Kutta methods accelerated with local time stepping.
Bed material agglomeration during fluidized bed combustion
Brown, R.C.; Dawson, M.R.; Noble, S.
1993-02-01
The purpose of this project is to determine the physical and chemical reactions which led to the undesired agglomeration of bed material during fluidized bed combustion and to relate these reactions to specific causes. Survey of industrial-scale fluidized bed combustors is being conducted to determine the occurrence of bed agglomeration and the circumstances under which agglomeration took place. This task should be finished by the end of February. Samples of bed material, agglomerate material, and boiler deposits are being requested from boiler operators as part of the survey. Once received, these sample will be analyzed to determine chemical and mineralogic composition. The bulk chemical determination will be performed using x-ray fluorescence and inductively coupled plasma-optical emission (ICP). Mineralogy will be detected by x-ray diffraction (XRD). Chemical and mineral reactions will be determined by scanning electron microscopy, optical microscopy, and electron microprobe.
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.
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.
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 solution of the nonlinear Poisson-Boltzmann equation and calculation of titration curves.
Oberoi, H; Allewell, N M
1993-01-01
Although knowledge of the pKa values and charge states of individual residues is critical to understanding the role of electrostatic effects in protein structure and function, calculating these quantities is challenging because of the sensitivity of these parameters to the position and distribution of charges. Values for many different proteins which agree well with experimental results have been obtained with modified Tanford-Kirkwood theory in which the protein is modeled as a sphere (reviewed in Ref. 1); however, convergence is more difficult to achieve with finite difference methods, in which the protein is mapped onto a grid and derivatives of the potential function are calculated as differences between the values of the function at grid points (reviewed in Ref. 6). Multigrid methods, in which the size of the grid is varied from fine to coarse in several cycles, decrease computational time, increase rates of convergence, and improve agreement with experiment. Both the accuracy and computational advantage of the multigrid approach increase with grid size, because the time required to achieve a solution increases slowly with grid size. We have implemented a multigrid procedure for solving the nonlinear Poisson-Boltzmann equation, and, using lysozyme as a test case, compared calculations for several crystal forms, different refinement procedures, and different charge assignment schemes. The root mean square difference between calculated and experimental pKa values for the crystal structure which yields best agreement with experiment (1LZT) is 1.1 pH units, with the differences in calculated and experimental pK values being less than 0.6 pH units for 16 out of 21 residues. The calculated titration curves of several residues are biphasic. Images FIGURE 8 PMID:8369451
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.
Multigrid Strategies for Viscous Flow Solvers on Anisotropic Unstructured Meshes
NASA Technical Reports Server (NTRS)
Movriplis, Dimitri J.
1998-01-01
Unstructured multigrid techniques for relieving the stiffness associated with high-Reynolds number viscous flow simulations on extremely stretched grids are investigated. One approach consists of employing a semi-coarsening or directional-coarsening technique, based on the directions of strong coupling within the mesh, in order to construct more optimal coarse grid levels. An alternate approach is developed which employs directional implicit smoothing with regular fully coarsened multigrid levels. The directional implicit smoothing is obtained by constructing implicit lines in the unstructured mesh based on the directions of strong coupling. Both approaches yield large increases in convergence rates over the traditional explicit full-coarsening multigrid algorithm. However, maximum benefits are achieved by combining the two approaches in a coupled manner into a single algorithm. An order of magnitude increase in convergence rate over the traditional explicit full-coarsening algorithm is demonstrated, and convergence rates for high-Reynolds number viscous flows which are independent of the grid aspect ratio are obtained. Further acceleration is provided by incorporating low-Mach-number preconditioning techniques, and a Newton-GMRES strategy which employs the multigrid scheme as a preconditioner. The compounding effects of these various techniques on speed of convergence is documented through several example test cases.
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.
NASA Astrophysics Data System (ADS)
Mitchell, Lawrence; Müller, Eike Hermann
2016-12-01
The implementation of efficient multigrid preconditioners for elliptic partial differential equations (PDEs) is a challenge due to the complexity of the resulting algorithms and corresponding computer code. For sophisticated (mixed) finite element discretisations on unstructured grids an efficient implementation can be very time consuming and requires the programmer to have in-depth knowledge of the mathematical theory, parallel computing and optimisation techniques on manycore CPUs. In this paper we show how the development of bespoke multigrid preconditioners can be simplified significantly by using a framework which allows the expression of the each component of the algorithm at the correct abstraction level. Our approach (1) allows the expression of the finite element problem in a language which is close to the mathematical formulation of the problem, (2) guarantees the automatic generation and efficient execution of parallel optimised low-level computer code and (3) is flexible enough to support different abstraction levels and give the programmer control over details of the preconditioner. We use the composable abstractions of the Firedrake/PyOP2 package to demonstrate the efficiency of this approach for the solution of strongly anisotropic PDEs in atmospheric modelling. The weak formulation of the PDE is expressed in Unified Form Language (UFL) and the lower PyOP2 abstraction layer allows the manual design of computational kernels for a bespoke geometric multigrid preconditioner. We compare the performance of this preconditioner to a single-level method and hypre's BoomerAMG algorithm. The Firedrake/PyOP2 code is inherently parallel and we present a detailed performance analysis for a single node (24 cores) on the ARCHER supercomputer. Our implementation utilises a significant fraction of the available memory bandwidth and shows very good weak scaling on up to 6,144 compute cores.
Diffusion and reaction in microbead agglomerates.
Nunes Kirchner, Carolina; Träuble, Markus; Wittstock, Gunther
2010-04-01
Scanning electrochemical microscopy has been used to analyze the flux of p-aminonophenol (PAP) produced by agglomerates of polymeric microbeads modified with galactosidase as a model system for the bead-based heterogeneous immunoassays. With the use of mixtures of enzyme-modified and bare beads in defined ratio, agglomerates with different saturation levels of the enzyme modification were produced. The PAP flux depends on the intrinsic kinetics of the galactosidase, the local availability of the substrate p-aminophenyl-beta-D-galactopyranoside (PAPG), and the external mass transport conditions in the surrounding of the agglomerate and the internal mass transport within the bead agglomerate. The internal mass transport is influenced by the diffusional shielding of the modified beads by unmodified beads. SECM in combination with optical microscopy was used to determine experimentally the external flux. These data are in quantitative agreement with boundary element simulation considering the SECM microelectrode as an interacting probe and treating the Michaelis-Menten kinetics of the enzyme as nonlinear boundary conditions with two independent concentration variables [PAP] and [PAPG]. The PAPG concentration at the surface of the bead agglomerate was taken as a boundary condition for the analysis of the internal mass transport condition as a function of the enzyme saturation in the bead agglomerate. The results of this analysis are represented as PAP flux per contributing modified bead and the flux from freely suspended galactosidase-modified beads. These numbers are compared to the same number from the SECM experiments. It is shown that depending on the enzyme saturation level a different situation can arise where either beads located at the outer surface of the agglomerate dominate the contribution to the measured external flux or where the contribution of buried beads cannot be neglected for explaining the measured external flux.
Aluminum Agglomeration and Trajectory in Solid Rocket Motors
2007-08-30
cinematography data from China Lake. Task 2.2, Aluminum Agglomeration Model Selection (SEA/BYU/ATK Task) Part of the model selection task has already been... Manual . Software and Engineering Associates, Inc. 1802 N. Carson Street, Suite 200, Carson City, NV 89701. 2005. [DCF-2005b] S. S. Dunn, D. E. Coats, and J...C. French, SPP Standard Stability Prediction Method for Solid Rocket Motors; Axial Mode Computer Program User’s Manual . Software and Engineering
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.
Modifying drug release and tablet properties of starch acetate tablets by dry powder agglomeration.
Mäki, Riikka; Suihko, Eero; Rost, Susanne; Heiskanen, Minna; Murtomaa, Matti; Lehto, Vesa-Pekka; Ketolainen, Jarkko
2007-02-01
In this study three model drugs (N-acetyl-D-glucosamine (NAG), anhydrous caffeine, and propranolol hydrochloride) were agglomerated with starch acetate (SA) by mixing the binary powders on a stainless steel (SS) plate. Agglomeration was induced by triboelectrification of the particles during mixing, and it was evaluated as a method to achieve controlled drug release rate. These agglomerates, mixed with different amounts of a disintegrant, were compressed into tablets whose dissolution characteristics were determined. Triboelectric measurements showed that when the drugs were in contact with SS, charges of the opposite polarity were generated to SA (+) and caffeine and NAG (-) promoting adhesion. Instead, propranolol HCl was charged with the same polarity as SA. SEM micrographs showed that smaller caffeine particles, in spite of their larger negative charge, agglomerated less efficiently with SA than larger NAG particles. This emphasizes the importance of particle size in the agglomeration process. Propranolol HCl did not form agglomerates with SA since their particle sizes and charges were identical. As a result, agglomeration of powders prior to tablet compression allows for modification and control of the release rate of the drugs from the SA matrix tablets as well as the tensile strength of the tablets.
Performance investigation of multigrid optimization for DNS-based optimal control problems
NASA Astrophysics Data System (ADS)
Nita, Cornelia; Vandewalle, Stefan; Meyers, Johan
2016-11-01
Optimal control theory in Direct Numerical Simulation (DNS) or Large-Eddy Simulation (LES) of turbulent flow involves large computational cost and memory overhead for the optimization of the controls. In this context, the minimization of the cost functional is typically achieved by employing gradient-based iterative methods such as quasi-Newton, truncated Newton or non-linear conjugate gradient. In the current work, we investigate the multigrid optimization strategy (MGOpt) in order to speed up the convergence of the damped L-BFGS algorithm for DNS-based optimal control problems. The method consists in a hierarchy of optimization problems defined on different representation levels aiming to reduce the computational resources associated with the cost functional improvement on the finest level. We examine the MGOpt efficiency for the optimization of an internal volume force distribution with the goal of reducing the turbulent kinetic energy or increasing the energy extraction in a turbulent wall-bounded flow; problems that are respectively related to drag reduction in boundary layers, or energy extraction in large wind farms. Results indicate that in some cases the multigrid optimization method requires up to a factor two less DNS and adjoint DNS than single-grid damped L-BFGS. The authors acknowledge support from OPTEC (OPTimization in Engineering Center of Excellence, KU Leuven, Grant No PFV/10/002).
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.
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.
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
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.
Multigrid time-accurate integration of Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Arnone, Andrea; Liou, Meng-Sing; Povinelli, Louis A.
1993-01-01
Efficient acceleration techniques typical of explicit steady-state solvers are extended to time-accurate calculations. Stability restrictions are greatly reduced by means of a fully implicit time discretization. A four-stage Runge-Kutta scheme with local time stepping, residual smoothing, and multigridding is used instead of traditional time-expensive factorizations. Some applications to natural and forced unsteady viscous flows show the capability of the procedure.
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.
Soft- and hard-agglomerate aerosols made at high temperatures.
Tsantilis, Stavros; Pratsinis, Sotiris E
2004-07-06
Criteria for aerosol synthesis of soft-agglomerate, hard-agglomerate, or even nonagglomerate particles are developed on the basis of particle sintering and coalescence. Agglomerate (or aggregate) particles are held together by weak, physical van der Waals forces (soft agglomerates) or by stronger chemical or sintering bonds (hard agglomerates). Accounting for simultaneous gas phase chemical reaction, coagulation, and sintering during the formation and growth of silica (SiO2) nanoparticles by silicon tetrachloride (SiCl4) oxidation and neglecting the spread of particle size distribution, the onset of hard-agglomerate formation is identified at the end of full coalescence, while the onset of soft-agglomerate formation is identified at the end of sintering. Process conditions such as the precursor initial volume fraction, maximum temperature, residence time, and cooling rate are explored, identifying regions for the synthesis of particles with a controlled degree of agglomeration (ratio of collision to primary particle diameters).
Chander, S.; Hogg, R.
1993-07-01
The goals of this research program are to demonstrate the technical and economic feasibility of a micro-agglomerate flotation process and to establish the essential criteria for reagent selection and system design and operation. 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 {mu}m) 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. We are investigating the use of a hybrid process -- Micro-agglomerate flotation -- which is a combination of oil agglomeration and froth flotation. The basic concept is to use small quantities of oil to promote the formation of dense micro-agglomerates.
Adaptive Methods for Compressible Flow
1994-03-01
convergence while requiring little additional storage. In addition, multigrid can be used in conjunction with any convergent base scheme, with adequate care ...coarse grids can be obtained with the agglomeration technique, although care must be taken to ensure that the coarse grid operator is convergent on these... care - those cells that intersect the surface. DT- ful programming, many of these geometri- NURBS does not currently provide the ca- cal computations can
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
2012-12-07
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.
Chander, S.; Hogg, R.
1995-01-01
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. We are investigating the use of a hybrid process - micro-agglomerate flotation - which is a combination of oil-agglomeration and froth flotation. The basic concept is to use small quantities of oil to promote the formation of dense micro-agglomerates with minimal entrapment of water and mineral particles, and to use froth flotation to extract these micro-agglomerates from the water/dispersed-mineral phase. Since the floating units are agglomerates (about 30-50 mm in size) rather than individual coal particles (1-10 mm) the problems of froth overload and water/mineral carryover should be significantly alleviated. Micro-agglomerate flotation has considerable potential for the practical deep cleaning of coal on a commercial scale.
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.
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.
Rapidly converging multigrid reconstruction of cone-beam tomographic data
NASA Astrophysics Data System (ADS)
Myers, Glenn R.; Kingston, Andrew M.; Latham, Shane J.; Recur, Benoit; Li, Thomas; Turner, Michael L.; Beeching, Levi; Sheppard, Adrian P.
2016-10-01
In the context of large-angle cone-beam tomography (CBCT), we present a practical iterative reconstruction (IR) scheme designed for rapid convergence as required for large datasets. The robustness of the reconstruction is provided by the "space-filling" source trajectory along which the experimental data is collected. The speed of convergence is achieved by leveraging the highly isotropic nature of this trajectory to design an approximate deconvolution filter that serves as a pre-conditioner in a multi-grid scheme. We demonstrate this IR scheme for CBCT and compare convergence to that of more traditional techniques.
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.
Wei, Feng; Zhang, Jun-ying; Zheng, Chu-guang
2005-01-01
In order to remove efficiently haled-particles emissions from coal combustions, a new way was used to put forward the process of agglomeration and the atomization was produced by the nozzle and then sprayed into the flue before precipitation devices of power station boiler in order to make inhaled-particles agglomerate into bigger particles, which can be easily removed but not change existing running conditions of boiler. According to this idea, a model is set up to study agglomeration rate and effect forces between fly ash inhaled-particles and atomized agglomerator particles. The developed agglomeration rate was expressed by relative particle number decreasing speed per unit volume. The result showed that viscosity force and flow resistance force give main influences on agglomeration effect of inhaled-particles, while springiness force and gravity have little effect on agglomeration effect of theirs. Factors influencing the agglomeration rate and effect forces are studied, including agglomerator concentration, agglomerator flux and agglomerator density, atomized-particles diameters and inhaled-particles diameter and so on.
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
Rakcheev, Denis; Philippe, Allan; Schaumann, Gabriele E
2013-11-19
Studying the environmental fate of engineered or natural colloids requires efficient methods for measuring their size and quantifying them in the environment. For example, an ideal method should maintain its correctness, accuracy, reproducibility, and robustness when applied to samples contained in complex matrixes and distinguish the target particles from the natural colloidal background signals. Since it is expected that a large portion of nanoparticles will form homo- or heteroagglomerates when released into environmental media, it is necessary to differentiate agglomerates from primary particles. At present, most sizing techniques do not fulfill these requirements. In this study, we used online coupling of two promising complementary sizing techniques: hydrodynamic chromatography (HDC) and single-particle ICPMS analysis to analyze gold nanoparticles agglomerated under controlled conditions. We used the single-particle mode of the ICPMS detector to detect single particles eluted from an HDC-column and determine a mass and an effective diameter for each particle using a double calibration approach. The average agglomerate relative density and fractal dimension were calculated using these data and used to follow the morphological evolution of agglomerates over time during the agglomeration process. The results demonstrate the ability of HDC coupled to single-particle analysis to identify and characterize nanoparticle homoagglomerates and is a very promising technique for the analysis of colloids in complex media.
NASA Astrophysics Data System (ADS)
Ao, Wen; Liu, Peijin; Yang, Wenjing
2016-12-01
In solid propellants, aluminum is widely used to improve the performance, however the condensed combustion products especially the large agglomerates generated from aluminum combustion significantly affect the combustion and internal flow inside the solid rocket motor. To clarify the properties of the condensed combustion products of aluminized propellants, a constant-pressure quench vessel was adopted to collect the combustion products. The morphology and chemical compositions of the collected products, were then studied by using scanning electron microscopy coupled with energy dispersive (SEM-EDS) method. Various structures have been observed in the condensed combustion products. Apart from the typical agglomerates or smoke oxide particles observed before, new structures including the smoke oxide clusters, irregular agglomerates and carbon-inclusions are discovered and investigated. Smoke oxide particles have the highest amount in the products. The highly dispersed oxide particle is spherical with very smooth surface and is on the order of 1-2 μm, but due to the high temperature and long residence time, these small particles will aggregate into smoke oxide clusters which are much larger than the initial particles. Three types of spherical agglomerates have been found. As the ambient gas temperature is much higher than the boiling point of Al2O3, the condensation layer inside which the aluminum drop is burning would evaporate quickly, which result in the fact that few "hollow agglomerates" has been found compared to "cap agglomerates" and "solid agglomerates". Irregular agglomerates usually larger than spherical agglomerates. The formation of irregular agglomerates likely happens by three stages: deformation of spherical aluminum drops; combination of particles with various shape; finally production of irregular agglomerates. EDS results show the ratio of O to Al on the surface of agglomerates is lower in comparison to smoke oxide particles. C and O account for
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.
Atif, Rasheed; Inam, Fawad
2016-01-01
One of the main issues in the production of polymer nanocomposites is the dispersion state of filler as multilayered graphene (MLG) and carbon nanotubes (CNTs) tend to agglomerate due to van der Waals forces. The agglomeration can be avoided by using organic solvents, selecting suitable dispersion and production methods, and functionalizing the fillers. Another proposed method is the use of hybrid fillers as synergistic effects can cause an improvement in the dispersion state of the fillers. In this review article, various aspects of each process that can help avoid filler agglomeration and improve dispersion state are discussed in detail. This review article would be helpful for both current and prospective researchers in the field of MLG- and CNT-based polymer nanocomposites to achieve maximum enhancement in mechanical, thermal, and electrical properties of produced polymer nanocomposites.
Reasons and remedies for the agglomeration of multilayered graphene and carbon nanotubes in polymers
Atif, Rasheed
2016-01-01
Summary One of the main issues in the production of polymer nanocomposites is the dispersion state of filler as multilayered graphene (MLG) and carbon nanotubes (CNTs) tend to agglomerate due to van der Waals forces. The agglomeration can be avoided by using organic solvents, selecting suitable dispersion and production methods, and functionalizing the fillers. Another proposed method is the use of hybrid fillers as synergistic effects can cause an improvement in the dispersion state of the fillers. In this review article, various aspects of each process that can help avoid filler agglomeration and improve dispersion state are discussed in detail. This review article would be helpful for both current and prospective researchers in the field of MLG- and CNT-based polymer nanocomposites to achieve maximum enhancement in mechanical, thermal, and electrical properties of produced polymer nanocomposites. PMID:27826492
Fast GPU-based computation of spatial multigrid multiframe LMEM for PET.
Nassiri, Moulay Ali; Carrier, Jean-François; Després, Philippe
2015-09-01
Significant efforts were invested during the last decade to accelerate PET list-mode reconstructions, notably with GPU devices. However, the computation time per event is still relatively long, and the list-mode efficiency on the GPU is well below the histogram-mode efficiency. Since list-mode data are not arranged in any regular pattern, costly accesses to the GPU global memory can hardly be optimized and geometrical symmetries cannot be used. To overcome obstacles that limit the acceleration of reconstruction from list-mode on the GPU, a multigrid and multiframe approach of an expectation-maximization algorithm was developed. The reconstruction process is started during data acquisition, and calculations are executed concurrently on the GPU and the CPU, while the system matrix is computed on-the-fly. A new convergence criterion also was introduced, which is computationally more efficient on the GPU. The implementation was tested on a Tesla C2050 GPU device for a Gemini GXL PET system geometry. The results show that the proposed algorithm (multigrid and multiframe list-mode expectation-maximization, MGMF-LMEM) converges to the same solution as the LMEM algorithm more than three times faster. The execution time of the MGMF-LMEM algorithm was 1.1 s per million of events on the Tesla C2050 hardware used, for a reconstructed space of 188 x 188 x 57 voxels of 2 x 2 x 3.15 mm3. For 17- and 22-mm simulated hot lesions, the MGMF-LMEM algorithm led on the first iteration to contrast recovery coefficients (CRC) of more than 75 % of the maximum CRC while achieving a minimum in the relative mean square error. Therefore, the MGMF-LMEM algorithm can be used as a one-pass method to perform real-time reconstructions for low-count acquisitions, as in list-mode gated studies. The computation time for one iteration and 60 millions of events was approximately 66 s.
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.
Multigrid calculation of internal flows in complex geometries
NASA Technical Reports Server (NTRS)
Smith, K. M.; Vanka, S. P.
1992-01-01
The development, validation, and application of a general purpose multigrid solution algorithm and computer program for the computation of elliptic flows in complex geometries is presented. This computer program combines several desirable features including a curvilinear coordinate system, collocated arrangement of the variables, and Full Multi-Grid/Full Approximation Scheme (FMG/FAS). Provisions are made for the inclusion of embedded obstacles and baffles inside the flow domain. The momentum and continuity equations are solved in a decoupled manner and a pressure corrective equation is used to update the pressures such that the fluxes at the cell faces satisfy local mass continuity. Despite the computational overhead required in the restriction and prolongation phases of the multigrid cycling, the superior convergence results in reduced overall CPU time. The numerical scheme and selected results of several validation flows are presented. Finally, the procedure is applied to study the flowfield in a side-inlet dump combustor and twin jet impingement from a simulated aircraft fuselage.
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.
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.
Brown, R.C.; Dawson, M.R.; Smeenk, J.L.
1995-04-01
Experiments performed support the hypothesis that a reducing atmosphere during fluidized bed coal combustion contributes to the formation of agglomerates. Reducing conditions are imposed by controlling the amount of combustion air supplied to the combustor, 50% of theoretical in these experiments. These localized reducing conditions may arise from either poor lateral bed mixing or oxygen-starved conditions due to the coal feed locations. Deviations from steady-state operating conditions in bed pressure drop may be used to detect agglomerate formation. Interpretation of the bed pressure drop was made more straightforward by employing a moving average difference method. During steady-state operation, the difference between the moving point averages should be close to zero, within {plus_minus}0.03 inches of water. Instability within the combustor, experienced once agglomerates begin to form, can be recognized as larger deviations from zero, on the magnitude of {plus_minus}0.15 inches of water.
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
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.
Solving the Fluid Pressure Poisson Equation Using Multigrid - Evaluation and Improvements.
Dick, Christian; Rogowsky, Marcus; Westermann, Ruediger
2015-12-23
In many numerical simulations of fluids governed by the incompressible Navier-Stokes equations, the pressure Poisson equation needs to be solved to enforce mass conservation. Multigrid solvers show excellent convergence in simple scenarios, yet they can converge slowly in domains where physically separated regions are combined at coarser scales. Moreover, existing multigrid solvers are tailored to specific discretizations of the pressure Poisson equation, and they cannot easily be adapted to other discretizations. In this paper we analyze the convergence properties of existing multigrid solvers for the pressure Poisson equation in different simulation domains, and we show how to further improve the multigrid convergence rate by using a graph-based extension to determine the coarse grid hierarchy. The proposed multigrid solver is generic in that it can be applied to different kinds of discretizations of the pressure Poisson equation, by using solely the specification of the simulation domain and pre-assembled computational stencils. We analyze the proposed solver in combination with finite difference and finite volume discretizations of the pressure Poisson equation. Our evaluations show that, despite the common assumption, multigrid schemes can exploit their potential even in the most complicated simulation scenarios, yet this behavior is obtained at the price of higher memory consumption.
Solving the Fluid Pressure Poisson Equation Using Multigrid-Evaluation and Improvements.
Dick, Christian; Rogowsky, Marcus; Westermann, Rudiger
2016-11-01
In many numerical simulations of fluids governed by the incompressible Navier-Stokes equations, the pressure Poisson equation needs to be solved to enforce mass conservation. Multigrid solvers show excellent convergence in simple scenarios, yet they can converge slowly in domains where physically separated regions are combined at coarser scales. Moreover, existing multigrid solvers are tailored to specific discretizations of the pressure Poisson equation, and they cannot easily be adapted to other discretizations. In this paper we analyze the convergence properties of existing multigrid solvers for the pressure Poisson equation in different simulation domains, and we show how to further improve the multigrid convergence rate by using a graph-based extension to determine the coarse grid hierarchy. The proposed multigrid solver is generic in that it can be applied to different kinds of discretizations of the pressure Poisson equation, by using solely the specification of the simulation domain and pre-assembled computational stencils. We analyze the proposed solver in combination with finite difference and finite volume discretizations of the pressure Poisson equation. Our evaluations show that, despite the common assumption, multigrid schemes can exploit their potential even in the most complicated simulation scenarios, yet this behavior is obtained at the price of higher memory consumption.
Multigrid Methods on Parallel Computers: A Survey on Recent Developments
1990-12-01
multi- color (red-black, four color etc.) order- ing of the grid points. Clearly, computation of defects, interpolation and restriction can be also...73716 72555 .984 85750 82919 95800 85206 .889 113086 97406 16406 16383 .999 22042 21845 23024 21853 .949 31668 29143 Table 6: Evaluated time
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 Methods in Network Optimization: Overview and Appraisal
1994-03-01
Tucker ( KKT ) optimality conditions . These are necessary and sufficient for linear programming problems. The case of equality constraints is specifically...8 C. KARUSH-KUHN-TUCKER ( KKT ) OPTIMALITY CONDITIONS ....... 8 D. OPTIMALITY CONDITIONS IN NETWORKS...considered. A key result in establishing the KKT conditions is the lemma presented in section B. Finally, in section D we specialize the optimality
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. 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. This project is concerned with a hydrid process, micro-agglomerate flotation, which is a combination of oil agglomeration and froth flotation.
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.
Soot agglomeration in isolated, free droplet combustion
NASA Technical Reports Server (NTRS)
Choi, M. Y.; Dryer, F. L.; Green, G. J.; Sangiovanni, J. J.
1993-01-01
Under the conditions of an isolated, free droplet experiment, hollow, carbonaceous structures, called soot spheres, were observed to form during the atmospheric pressure, low Reynolds number combustion of 1-methylnaphthalene. These structures which are agglomerates composed of smaller spheroidal units result from both thermophoretic effects induced by the envelope flame surrounding each drop and aerodynamic effects caused by changes in the relative gas/drop velocities. A chemically reacting flow model was used to analyze the process of sootshell formation during microgravity droplet combustion. The time-dependent temperature and gas property field surrounding the droplet was determined, and the soot cloud location for microgravity combustion of n-heptane droplets was predicted. Experiments showed that the sooting propensity of n-alkane fuel droplets can be varied through diluent substitution, oxygen-index variations, and ambient pressure reductions.
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.
Overpopulated, Underdeveloped Urban Agglomerations: Tomorrow’s Unstable Operating Environment
2012-05-08
DATES COVERED (From - To) 4. TITLE AND SUBTITLE Overpopulated , Underdeveloped Urban Agglomerations: Tomorrow’s 5a. CONTRACT NUMBER...ABSTRACT This paper asserts that a unique future operational environment is developing: overpopulated , underdeveloped urban agglomerations. A...proposed definition for this operating environment is (or would be) an overpopulated urban area which is located within a developing or underdeveloped
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.
2016-02-15
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.
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).
Chander, S.; Hogg, R.
1995-04-01
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. 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. We are investigating the use of a hybrid process - Micro-agglomerate flotation which is a combination of oil-agglomeration and froth flotation. The basic concept is to use small quantities of oil to promote the formation of dense micro-agglomerates with minimal entrapment of water and mineral particles, and to use froth flotation to extract these micro-agglomerates from the water/dispersed-mineral phase. Since the floating units are agglomerates (about 30-50 mm in size) rather than individual coal particles (1-10 mm) the problems of froth overload and water/mineral carryover should be significantly alleviated. There are, however, complications. The process involves at least five phases: two or more solids (coal and mineral), two liquids (oil and water) and one gas (air). It is necessary to maintain precise control over the chemistry of the liquid phases in order to promote the interfacial reactions and interactions between phases necessary to ensure selectivity. Kinetics as well as thermodynamic factors may be critical in determining overall system response.
Choi, Young Joon Djilali, Ned
2016-01-15
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.
Dekkers, Petrus J; Friedlander, Sheldon K
2002-04-15
Gas-phase synthesis of fine solid particles leads to fractal-like structures whose transport and light scattering properties differ from those of their spherical counterparts. Self-preserving size distribution theory provides a useful methodology for analyzing the asymptotic behavior of such systems. Apparent inconsistencies in previous treatments of the self-preserving size distributions in the free molecule regime are resolved. Integro-differential equations for fractal-like particles in the continuum and near continuum regimes are derived and used to calculate the self-preserving and quasi-self-preserving size distributions for agglomerates formed by Brownian coagulation. The results for the limiting case (the continuum regime) were compared with the results of other authors. For these cases the finite difference method was in good in agreement with previous calculations in the continuum regime. A new analysis of aerosol agglomeration for the entire Knudsen number range was developed and compared with a monodisperse model; Higher agglomeration rates were found for lower fractal dimensions, as expected from previous studies. Effects of fractal dimension, pressure, volume loading and temperature on agglomerate growth were investigated. The agglomeration rate can be reduced by decreasing volumetric loading or by increasing the pressure. In laminar flow, an increase in pressure can be used to control particle growth and polydispersity. For D(f)=2, an increase in pressure from 1 to 4 bar reduces the collision radius by about 30%. Varying the temperature has a much smaller effect on agglomerate coagulation.
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
Preliminary characterization of a gas-promoted oil agglomeration process
Drzymala, J.; Wheelock, T.D.
1996-12-31
The agglomeration of aqueous suspensions of Pittsburgh No. 8 coal particles with i-octane was studied by employing a scale model mixing system which measured both agitator speed and torque. The progress of agglomeration was monitored by observing changes in agitator torque and was confirmed by examining samples of the suspension with an optical microscope. When a suspension containing 30 w/w% solids was degassed and then conditioned with 20 v/w% i-octane (20 ml i-octane/100 g coal), no agglomeration took place until a small amount of air (e.g., 9 v/w%) was introduced. Subsequent changes in agitator torque indicated that the ensuing process of agglomeration was complex and consisted of several stages involving various interactions between coal particles, oil drops, and gas bubbles. The time required to produce spherical agglomerates was determined for different experimental conditions by conducting a number of agglomeration tests involving different mixing tank sizes and different impeller sizes and speeds. The results indicate that agglomeration time decreases with increasing power input per unit volume and increasing gas concentration.
Development of a Gas-Promoted Oil Agglomeration Process
M. Shen; R. Abbott; T. D. Wheelock
1998-10-30
Two series of agglomeration tests were conducted as part of an effort to find a suitable basis for size scale-up of the mixing system used for a gas-promoted oil agglomeration process. In the first series of tests the agitator impeller diameter and speed were varied among runs so as to vary impeller tip speed and agitator power independently while keeping other conditions constant. In the second series of tests the mixing tank size and agitator speed were varied while the ratio of tank diameter to impeller diameter were held constant. All tests were conducted with finely ground Pittsburgh No. 8 coal and with i-octane as the agglomerant. The results of these tests showed that the minimum time te required to produce spherical agglomerates was predominantly a function of the agitator power input per unit volume. In addition, the size of the agglomerates produced in a given time was also strongly dependent on power input. At lower power input levels, the mean size rose as power input increased until a point was reached where agglomerate breakage became important and the mean size decreased. The results also showed that the ash content of the agglomerates produced in a given time tended to decrease with increasing power input. On the other hand, the recovery of clean coal on a dry, ash-free basis was not greatly affected by power input.
Crystal growth and agglomeration of calcium sulfite hemihydrate crystals
Tai, C.Y.; Chen, P.C.
1995-04-01
Flue gas desulfurization (FGD) processes are most commonly utilized to remove sulfur dioxide from stack gases of coal- or oil-fired plants. In the simple slurry technology, SO{sub 2} is absorbed by a slurry of lime/limestone to form calcium sulfite crystals of acicular habit and its strong agglomeration, requiring large clarifiers and filters to dewater the sludge to make an acceptable landfill. Crystal growth and agglomeration of calcium sulfite hemihydrate crystals from solution were studied by reacting Ca(OH){sub 2} with NaHSO{sub 3} in a pH-stat semibatch crystallizer. Single platelet crystals and agglomerates of platelet crystals were produced in the pH range from 5.80 to 6.80. The crystallization mechanism changed from primary nucleation to crystal growth in the progressive precipitation. Using the titration curves, the growth rate was calculated from the titration rate at the final stage of operation. The crystal growth rates of calcium sulfate hemihydrate crystals were found to obey the parabolic rate law in the low supersaturation range. Another point to be noted is that the precipitates of calcium sulfite hemihydrate in agitated suspensions have a tendency to form agglomerates. It was found that the degree of agglomeration is a weak function of relative supersaturation and magma density, while the pH value is a key factor that affects the degree of agglomeration. Addition of EDTA also has an effect on the agglomeration of calcium sulfite hemihydrates.
Sonic enhanced ash agglomeration and sulfur capture. Quarterly report, January 1996--March 1996
1996-04-01
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 (Patent No. 5,197,399) for simultaneously enhancing sulfur capture and particulate agglomeration of the combustor effluent. This application can be adapted as either a {open_quotes}hot flue gas cleanup{close_quotes} subsystem for the current concepts for combustor islands or as an alternative primary pulse combustor island in which stagging, 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.
Prediction of Agglomeration, Fouling, and Corrosion Tendency of Fuels in CFB Co-Combustion
NASA Astrophysics Data System (ADS)
Barišć, Vesna; Zabetta, Edgardo Coda; Sarkki, Juha
Prediction of agglomeration, fouling, and corrosion tendency of fuels is essential to the design of any CFB boiler. During the years, tools have been successfully developed at Foster Wheeler to help with such predictions for the most commercial fuels. However, changes in fuel market and the ever-growing demand for co-combustion capabilities pose a continuous need for development. This paper presents results from recently upgraded models used at Foster Wheeler to predict agglomeration, fouling, and corrosion tendency of a variety of fuels and mixtures. The models, subject of this paper, are semi-empirical computer tools that combine the theoretical basics of agglomeration/fouling/corrosion phenomena with empirical correlations. Correlations are derived from Foster Wheeler's experience in fluidized beds, including nearly 10,000 fuel samples and over 1,000 tests in about 150 CFB units. In these models, fuels are evaluated based on their classification, their chemical and physical properties by standard analyses (proximate, ultimate, fuel ash composition, etc.;.) alongside with Foster Wheeler own characterization methods. Mixtures are then evaluated taking into account the component fuels. This paper presents the predictive capabilities of the agglomeration/fouling/corrosion probability models for selected fuels and mixtures fired in full-scale. The selected fuels include coals and different types of biomass. The models are capable to predict the behavior of most fuels and mixtures, but also offer possibilities for further improvements.
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.
Gravitational Agglomeration of Post-HCDA LMFBR Nonspherical Aerosols.
1980-12-01
AD-AIO6 766 AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH F/B 13/7 GRAVITATIONAL AGGLOMERATION OF POST- HCDA LMF8R NONSPHFRICAL AER--ETC(U) DEC 80 R...OF REPORT & PERIOD COVERED i Gravitational Agglomeration of Post- HCDA TfIfM/DISSERTATION LMFBR Nonspherical Aerosols . ________O____O______________ S...it to: AFIT/NR Wright-Patterson AFB OH 45433 RESEARCH TITLE: Gravitational Agglomeration of Post- HCDA LMFBR Nonspherical Aerosols AUTHOR: Ronald
Performance of algebraic multi-grid solvers based on unsmoothed and smoothed aggregation schemes
NASA Astrophysics Data System (ADS)
Webster, R.
2001-08-01
A comparison is made of the performance of two algebraic multi-grid (AMG0 and AMG1) solvers for the solution of discrete, coupled, elliptic field problems. In AMG0, the basis functions for each coarse grid/level approximation (CGA) are obtained directly by unsmoothed aggregation, an appropriate scaling being applied to each CGA to improve consistency. In AMG1 they are assembled using a smoothed aggregation with a constrained energy optimization method providing the smoothing. Although more costly, smoothed basis functions provide a better (more consistent) CGA. Thus, AMG1 might be viewed as a benchmark for the assessment of the simpler AMG0. Selected test problems for D'Arcy flow in pipe networks, Fick diffusion, plane strain elasticity and Navier-Stokes flow (in a Stokes approximation) are used in making the comparison. They are discretized on the basis of both structured and unstructured finite element meshes. The range of discrete equation sets covers both symmetric positive definite systems and systems that may be non-symmetric and/or indefinite. Both global and local mesh refinements to at least one order of resolving power are examined. Some of these include anisotropic refinements involving elements of large aspect ratio; in some hydrodynamics cases, the anisotropy is extreme, with aspect ratios exceeding two orders. As expected, AMG1 delivers typical multi-grid convergence rates, which for all practical purposes are independent of mesh bandwidth. AMG0 rates are slower. They may also be more discernibly mesh-dependent. However, for the range of mesh bandwidths examined, the overall cost effectiveness of the two solvers is remarkably similar when a full convergence to machine accuracy is demanded. Thus, the shorter solution times for AMG1 do not necessarily compensate for the extra time required for its costly grid generation. This depends on the severity of the problem and the demanded level of convergence. For problems requiring few iterations, where grid
NASA Technical Reports Server (NTRS)
Nishida, Brian A.; Langhi, Ronald G.; Bencze, Daniel P.
1991-01-01
A multiblock/multigrid computation of the inviscid flow over a wing-mounted propfan transport with propwash is presented. An explicit multistage scheme drives the integral Euler equations to a steady state solution, while an actuator disk approximates the slipstream effects of the propfan blades. Practical applications of detailed surface gridding, multiple block field grids and multigrid convergence acceleration are demonstrated.
A Wavelet Technique For Multi-grid Solver For Large Linear Systems
NASA Astrophysics Data System (ADS)
Keller, W.
In general, large systems of linear equations cannot be solved directly. An iterative solver has to be applied instead. Unfortunately, iterative solvers have a notouriously slow convergence rate, which in the worst case can prevent convergence at all, due to the inavoidable rounding errors. Multi-grid iteration schemes are meant to guarantee a sufficiently high convergence rate, independent from the dimension of the linear system. The idea behind the multi-grid solvers is that the traditional iterative solvers eliminate only the short-wavelength error constituents in the initial guess for the solution. For the elimination of the remaining long-wavelength error constituents a much coarser grid is sufficient. On the coarse grid the dimension of the problem is much smaller so that the elimination can be done by a direct solver. The paper shows that wavelet techniques successfully can be applied for following steps of a multi-grid procedure: · Generation of an approximation of the proplem on a coarse grid from a given approximation on the fine grid. · Restriction of a signal on a fine grid to its approximation on a co grid. · Uplift of a signal from the coarse to the fine grid. The paper starts with a theoretical explanation of the links between wavelets and multi-grid solvers. Based on this investigation the class o operators, which are suitable for a multi-grid solution strategy can be characterized. The numerical efficiency of the approach will be tested for the Planar Stokes problem.
The improved robustness of multigrid elliptic solvers based on multiple semicoarsened grids
NASA Technical Reports Server (NTRS)
Naik, Naomi H.; Vanrosendale, John
1991-01-01
Multigrid convergence rates degenerate on problems with stretched grids or anisotropic operators, unless one uses line or plane relaxation. For 3-D problems, only plane relaxation suffices, in general. While line and plane relaxation algorithms are efficient on sequential machines, they are quite awkward and inefficient on parallel machines. A new multigrid algorithm is presented based on the use of multiple coarse grids, that eliminates the need for line or plane relaxation in anisotropic problems. This algorithm was developed and the standard multigrid theory was extended to establish rapid convergence for this class of algorithms. The new algorithm uses only point relaxation, allowing easy and efficient parallel implementation, yet achieves robustness and convergence rates comparable to line and plane relaxation multigrid algorithms. The algorithm described is a variant of Mulder's multigrid algorithm for hyperbolic problems. The latter uses multiple coarse grids to achieve robustness, but is unsuitable for elliptic problems, since its V-cycle convergence rate goes to one as the number of levels increases. The new algorithm combines the contributions from the multiple coarse grid via a local switch, based on the strength of the discrete operator in each coordinate direction.
Fully anisotropic 3-D EM modelling on a Lebedev grid with a multigrid pre-conditioner
NASA Astrophysics Data System (ADS)
Jaysaval, Piyoosh; Shantsev, Daniil V.; de la Kethulle de Ryhove, Sébastien; Bratteland, Tarjei
2016-12-01
We present a numerical algorithm for 3-D electromagnetic (EM) simulations in conducting media with general electric anisotropy. The algorithm is based on the finite-difference discretization of frequency-domain Maxwell's equations on a Lebedev grid, in which all components of the electric field are collocated but half a spatial step staggered with respect to the magnetic field components, which also are collocated. This leads to a system of linear equations that is solved using a stabilized biconjugate gradient method with a multigrid preconditioner. We validate the accuracy of the numerical results for layered and 3-D tilted transverse isotropic (TTI) earth models representing typical scenarios used in the marine controlled-source EM method. It is then demonstrated that not taking into account the full anisotropy of the conductivity tensor can lead to misleading inversion results. For synthetic data corresponding to a 3-D model with a TTI anticlinal structure, a standard vertical transverse isotropic (VTI) inversion is not able to image a resistor, while for a 3-D model with a TTI synclinal structure it produces a false resistive anomaly. However, if the VTI forward solver used in the inversion is replaced by the proposed TTI solver with perfect knowledge of the strike and dip of the dipping structures, the resulting resistivity images become consistent with the true models.
Brown, R.C.; Dawson, M.R.; Noble, S.D.
1993-04-01
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 and to relate these reactions to specific causes. A survey of agglomeration and deposit formation in industrial fluidized bed boilers is in progress. Preliminary results indicate that at least five boilers were experiencing some form of bed material agglomeration. In these instances it was observed that large particles were forming within the bed which were larger that the feed. Four operators could confirm that the larger bed particles had formed due to bed particles sticking together or agglomerating. Deposit formation was reported at nine sites with these deposits being found most commonly at coal feed locations and in cyclones. Other deposit locations included side walls and return loops. Examples of these agglomerates and deposits have been received from five of the surveyed facilities. Also during this quarter, a bulk sample of Illinois No. 6 coal was obtained from the Fossil Energy Program at Ames Laboratory here at Iowa State University and prepared for combustion tests. This sample was first ground to a top-size of 3/8`` using a jaw crusher then a size fraction of 3/8`` {times} 8 (US mesh) was then obtained by sieving using a Gilson Test-Master. This size fraction was selected for the preliminary laboratory-scale experiments designed to simulate the dense bed conditions that exist in the bottom of CFB combustors. To ensure uniformity of fuel composition among combustion runs, the sized coal was riffled using, a cone and long row method and stored in bags for each experiment. During this quarter additional modifications were made to achieve better control of fluidization regimes and to aid in monitoring the hydrodynamic and chemical conditions within the reactor.
1995-08-01
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 (Patent No. 5,197,399) for simultaneously enhancing sulfur capture and particulate agglomeration of the combustor effluent. This application can be adapted as either a {open_quotes}hot flue gas cleanup{close_quotes} 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. The goal of the program is to support the DOE mission in developing coal-fired combustion gas turbines. In particular, the MTCI proprietary process for bimodal ash agglomeration and simultaneous sulfur capture will be evaluated and developed. The technology embodiment of the invention provides for the use of standard grind, moderately beneficiated coal and WEM for firing the gas turbine with efficient sulfur capture and particulate emission control upstream of the turbine. The process also accommodates injection of alkali gettering material if necessary. The proposed technology provides for practical, reliable, and capital (and O&M) cost-effective means of protection for the gas turbine from impurities in the coal combustor effluent.
Leukocyte Agglomeration Reaction in Diagnosis of Allergy Reactions from Antibiotics,
tested in a clinic on 80 patients with serious allergic anamnesis . The results of the studies indicate that the leukocyte agglomeration reaction is a highly sensitive immunological indicator of hypersensitivity to antibiotics.
On Two Numerical Techniques for Light Scattering by Dielectric Agglomerated Structures
Lakhtakia, Akhlesh; Mulholland, George W.
1993-01-01
Smoke agglomerates are made of many soot sphcres, and their light scattering response is of interest in fire research. The numerical techniques chiefly used for theoretical scattering studies are the method of moments and the coupled dipole moment. The two methods have been obtained in this tutorial paper directly from the monochromatic Maxwell curl equations and shown to be equivalent. The effects of the finite size of the primary spheres have been numerically delineated. PMID:28053494
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.
NASA Astrophysics Data System (ADS)
Lalleman, Sophie; Bertrand, Murielle; Plasari, Edouard
2012-03-01
Oxalic precipitation is usually applied in nuclear industry to process radioactive wastes or to recover actinides from a multicomponent solution. This paper deals with the development of methods adapted to a nuclear environment in order to study the agglomeration phenomena during actinide oxalic precipitation. These methods are previously setup with harmless elements that simulate the actinide behaviour: the lanthanides. A parametric study is carried out to quantify the influence of operating parameters on the agglomeration kernel and to determine a kinetic law for this mechanism. The experimental study is performed in a continuous-MSMPR precipitator at steady-state. The method is based on the resolution of two population balances using the moment approach, one for elementary crystals and the other for agglomerates. Provided that the kinetic rates of nucleation and growth are known, the agglomeration kernel can be obtained from a mathematical treatment of the experimental particle size distributions. Results point out that experimental crystal sizes are consistent with an independent kernel. It appears that the agglomeration kernel is directly proportional to supersaturation, increases with temperature but is limited by ionic strength and shear rate.
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.
Preparation of norfloxacin spherical agglomerates using the ammonia diffusion system.
Puechagut, H G; Bianchotti, J; Chiale, C A
1998-04-01
Agglomerated crystals of norfloxacin were prepared by a spherical crystallization technique using the ammonia diffusion system (ADS). This technique makes it possible to agglomerate amphoteric drugs like norfloxacin, which cannot be agglomerated by conventional procedures. When an ammonia-water solution of norfloxacin is poured into an acetone dichloromethane mixture under agitation, a small amount of ammonia is liberated in the system. The ammonia-water solution plays a role both as a good solvent for norfloxacin and as a bridging liquid, allowing the crystals' collection to take place in one step. It has been proven that the agglomeration mechanism follows three steps: first acetone enters into the droplets of ammonia-water (this emulsion is formed because of the system characteristics); dissolved norfloxacin is consequently precipitated while the droplets collect the crystals; simultaneously, a part of the ammonia contained in the agglomerates diffuses to the outer organic solvent phase, thereby forming the norfloxacin spherical agglomerates. The correct selection of solvents has enabled us to obtain a suitable stable crystalline shape.
Micro-agglomerate flotation for deep cleaning of coal
Chander, S.; Hogg, R.
1993-04-01
We are investigating the use of a hybrid process, Micro-agglomerate flotation, which is a combination of oil-agglomeration and froth flotation. The basic concept is to use small quantities of oil to promote the formation of dense micro-agglomerates with minimal entrapment of water and mineral particles, and to use froth flotation to extract these micro-agglomerates from the water/dispersed-mineral phase. Since the floating units are agglomerates (about 30--50 [mu]m in size) rather than individual coal particles (1--10 [mu]m) the problems of froth overload and water/mineral carryover should be significantly alleviated.Micro-agglomerate flotation has considerable potential for the practical deep cleaning of coal on a commercial scale. In principle, it should be possible to achieve both high selectivity and high yield at reasonable cost. The process requires only conventional, off-the-shelf equipment and reagent usage (oil, surfactants, etc.) should be small. There are, however, complications. The process involves at least five phases: two or more solids (coal and mineral), two liquids (oil and water) and one gas (air). It is necessary to maintain precise control over the chemistry of the liquid phases in order to promote the interfacial reactions and interactions between phases necessary to ensure selectivity. Kinetics as well as thermodynamic factors may be critical in determining overall system response.
Micro-agglomerate flotation for deep cleaning of coal
Chander, S.; Hogg, R.
1993-01-01
We are investigating the use of a hybrid process - Micro-agglomerate flotation - which is a combination of oil-agglomeration and froth flotation. The basic concept is to use small quantities of oil to promote the formation of dense micro-agglomerates with minimal entrapment of water and mineral particles, and to use froth flotation to extract these micro-agglomerates from the water/dispersed-mineral phase. Since the floating units are agglomerates (about 30--50 [mu]m in size) rather than individual coal particles (1--10 [mu]m) the problems of froth overload and water/mineral carryover should be significantly alleviated. Micro-agglomerate flotation has considerable potential for the practical deep cleaning of coal on a commercial scale. In principle, it should be possible to achieve both high selectivity and high yield at reasonable cost. The process requires only conventional, off-the-shelf equipment and reagent usage (oil, surfactants, etc.) should be small. There are, however, complications. The process involves at least five phases: two or more solids (coal and mineral), two liquids (oil and water) and one gas (air). It is necessary to maintain precise control over the chemistry of the liquid phases in order to promote the interfacial reactions and interactions between phases necessary to ensure selectivity. Kinetics as well as thermodynamic factors may be critical in determining overall system response.
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.
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.
Multigrid solution of the Navier-Stokes equations on triangular meshes
NASA Technical Reports Server (NTRS)
Mavriplis, Dimitri J.; Jameson, Antony; Martinelli, Luigi
1989-01-01
A Navier-Stokes algorithm for use on unstructured triangular meshes is presented. Spatial discretization of the governing equations is achieved using a finite element Galerkin approximation, which can be shown to be equivalent to a finite volume approximation for regular equilateral triangular meshes. Integration steady-state is performed using a multistage time-stepping scheme, and convergence is accelerated by means of implicit residual smoothing and an unstructured multigrid algorithm. Directional scaling of the artificial dissipation and the implicit residual smoothing operator is achieved for unstructured meshes by considering local mesh stretching vectors at each point. The accuracy of the scheme for highly stretched triangular meshes is validated by comparing computed flat-plate laminar boundary layer results with the well known similarity solution, and by comparing laminar airfoil results with those obtained from various well-established structured quadrilateral-mesh codes. The convergence efficiency of the present method is also shown to be competitive with those demonstrated by structured quadrilateral-mesh algorithms.
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
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.
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.
Optimization of refractive liquid crystal lenses using an efficient multigrid simulation.
Milton, Harry; Brimicombe, Paul; Morgan, Philip; Gleeson, Helen; Clamp, John
2012-05-07
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.
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.
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.
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.
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.
Dynamics of nanoparticle agglomeration in a magnetic fluid in a varying magnetic field
NASA Astrophysics Data System (ADS)
Usanov, D. A.; Postel'ga, A. E.; Bochkova, T. S.; Gavrilin, V. N.
2016-03-01
It is found that the dependence of the magnetic nanoparticle agglomerate length in a magnetic fluid on the applied magnetic field has three characteristic segments: a substantial increase in the agglomerate length with the magnetic field in the range of weak fields, a segment with an insignificant increase in the average length of agglomerates upon an increase in the field, and a sharp increase in the agglomerate length with a further increase in the field. It is shown that the agglomerate length increases in the range of strong magnetic fields due to a decrease in the spacing between adjacent agglomerates down to their complete coalescence. The total number of agglomerates decreases thereby.
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.
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.
Brandão, Pedro F; Ramos, Rui M; Valente, Inês M; Almeida, Paulo J; Carro, Antonia M; Lorenzo, Rosa A; Rodrigues, José A
2017-04-01
In this work, a simple methodology was developed for the extraction and determination of free formaldehyde content in cork agglomerate samples. For the first time, gas-diffusion microextraction was used for the extraction of volatile formaldehyde directly from samples, with simultaneous derivatization with acetylacetone (Hantzsch reaction). The absorbance of the coloured solution was read in a spectrophotometer at 412 nm. Different extraction parameters were studied and optimized (extraction temperature, sample mass, volume of acceptor solution, extraction time and concentration of derivatization reagent) by means of an asymmetric screening. The developed methodology proved to be a reliable tool for the determination of formaldehyde in cork agglomerates with the following suitable method features: low LOD (0.14 mg kg(-1)) and LOQ (0.47 mg kg(-1)), r (2) = 0.9994, and intraday and interday precision of 3.5 and 4.9%, respectively. The developed methodology was applied to the determination of formaldehyde in different cork agglomerate samples, and contents between 1.9 and 9.4 mg kg(-1) were found. Furthermore, formaldehyde was also determined by the standard method EN 717-3 for comparison purposes; no significant differences between the results of both methods were observed. Graphical abstract Representation of the GDME system and its main components.
Monitoring of odor nuisance in the tri-city agglomeration
NASA Astrophysics Data System (ADS)
Gebicki, Jacek; Dymerski, Tomasz; Namieśnik, Jacek
2016-11-01
The paper describes a principle of operation of odor nuisance monitoring network, which is being designed in the tri-city agglomeration. Moreover, it presents the preliminary results of an investigation on ambient air quality with respect to odour nuisance in a vicinity of the municipal landfill. The investigation was performed during spring-winter season using a prototype of electronic nose and the Nasal Ranger field olfactometers. The prototype was equipped with a set of six semiconductor sensors by FIGARO Co. and one PID-type sensor. The field olfactometers were used to determine mean concentration of odorants, which amounted from 2.2 to 30.2 ou/m3 depending on the place of measurement. In case of the investigation with the electronic nose prototype a classification of the ambient air samples with respect to the place of sampling was performed utilizing kNN algorithm supported with a cross-validation method. Correct classification of the ambient air samples was at the level of 66.7%. Performed investigation revealed that discrimination of the ambient air samples differing in concentration of odorants and place of origin was possible.
Evaluation of water security: an integrated approach applied in Wuhan urban agglomeration, China.
Shao, Dongguo; Yang, Fengshun; Xiao, Chun; Tan, Xuezhi
2012-01-01
To evaluate water security, the Water Resources Sustainability Evaluation Model has been developed. The model employs four criteria (economic development, flood control security, water supply security, and water environment security) and has 22 indicators, integrating them using their relative weights. The model is applied to evaluate the water security of Wuhan urban agglomeration, China. The values of the indicators are normalized using the exponential efficacy functions based on the law of diminishing marginal utility. The evaluation results show that, overall, the state of water security in Wuhan urban agglomeration is good, which is in good agreement with the true situation. The comparison between the results of the model and other three evaluation methods by the Spearman coefficient of rank correlation verifies the science and reliability of the developed model. Consequently, it is concluded that the model can be an effective tool for evaluating the states of water security and provide a basis on which to create policies for improving inadequacies in water security.
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.
1995-05-01
Over the years, multigrid has been demonstrated as an efficient technique for solving inviscid flow problems. However, for viscous flows, convergence...capture the boundary layer near the body. Usual techniques for generating a sequence of grids that produce proper convergence rates on isotropic...formulation on unstructured stretched triangular meshes. A coarsening strategy is proposed and results are discussed. (AN)
Effects of crossover hydrogen on platinum dissolution and agglomeration
NASA Astrophysics Data System (ADS)
Cheng, Tommy T. H.; Rogers, Erin; Young, Alan P.; Ye, Siyu; Colbow, Vesna; Wessel, Silvia
2011-10-01
The durability of catalysts in the polymer-electrolyte membrane fuel cell (PEMFC) is identified as a critical limiting factor for wide commercialization of fuel cells. Even though much progress has been made in understanding the degradation mechanisms, the phenomena of Pt dissolution and agglomeration and their contributing factors are not fully understood. In the present investigation, the effects of crossover hydrogen on Pt degradation are studied using an accelerated stress test (AST). The end-of-test (EOT) membrane-electrode-assemblies (MEAs) were characterized by X-ray diffraction (XRD), scanning-electron microscopy (SEM), and energy-dispersive X-ray (EDX). The results provided mechanistic understanding of Pt dissolution and agglomeration: Pt growth and agglomeration were found to be less severe with more crossover hydrogen due likely to the chemical reduction of Pt oxides by crossover hydrogen and the subsequently decrease in the amount of Pt ions formed via the oxide pathway.
Hierarchical agglomerates of carbon nanotubes as high-pressure cushions.
Liu, Yi; Qian, Weizhong; Zhang, Qiang; Cao, Anyuan; Li, Zhifei; Zhou, Weiping; Ma, Yang; Wei, Fei
2008-05-01
We report the cushioning behavior of highly agglomerated carbon nanotubes. The nanotube agglomerates can be repeatedly compacted to achieve large volume reduction (>50%) and expanded to nearly original volume without structural failure, like a robust porous cushion. At a higher pressure range (10-125 MPa), the energy absorbed per unit volume is 1 order of magnitude higher than conventional cushion materials such as foamy polystyrene. The structure of hierarchical agglomerates can be controlled for tailoring the cushioning properties and obtaining a lower cushioning coefficient (higher energy absorption) over a wide range of pressures (1-100 MPa). The mechanism was studied in terms of morphology evolution of the nanotube aggregates and pore size distribution during compression.
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.
NASA Astrophysics Data System (ADS)
Whizin, Akbar D.; Blum, Jürgen; Colwell, Joshua E.
2017-02-01
We performed laboratory experiments colliding 0.8–1.0 mm and 1.0–1.6 mm SiO2 dust aggregates with loosely bound centimeter-sized agglomerates of those aggregates in microgravity. This work builds on previous microgravity laboratory experiments examining the collisional properties of porous loosely bound dust aggregates. In centimeter-sized aggregates, surface forces dominate self-gravity and may play a large role in aggregate growth beyond this size range. We characterize the properties of protoplanetary aggregate analogs to help place constraints on initial formation mechanisms and environments. We determined several important physical characteristics of these aggregates in a large number of low-velocity collisions. We observed low coefficients of restitution and fragmentation thresholds near 1 m s‑1 for 1–2 cm agglomerates, which are in good agreement with previous findings in the literature. We find the accretion efficiency for agglomerates of loosely bound aggregates to be higher than that for just aggregates themselves. We find sticking thresholds of 6.6 ± 2 cm s‑1, somewhat higher than those in similar studies, which have observed few aggregates stick at speeds of under 3 cm s‑1. Even with highly dissipative collisions, loosely bound agglomerates have difficulty accreting beyond centimeter-sized bodies at typical collision speeds in the disk. Our results indicate agglomerates of porous aggregates have slightly higher sticking thresholds than previously thought, allowing possible growth to decimeter-sized bodies if velocities are low enough.
Gamble, John F; Chiu, Wing-Sin; Tobyn, Mike
2011-10-01
Microcrystalline cellulose (MCC) is regarded as one of the most versatile tablet filler binders, finding a wide use in both granulation and direct compression operations. It has been shown that MCC particle populations consist of a mixture of 'rod like' primary particles, and agglomerates, and that the proportion of these primary particles and agglomerates differs within the different grades of materials, contributing to the different bulk properties of these materials. However, the proportion of primary particles and agglomerates has not previously been fully elucidated, and their contribution to the performance factors such as flow explained. In this paper we use a novel microscopy-based characterization technique to demonstrate that the proportion of 'agglomerates' in the series of MCC grades between PH101 and PH200 is, by number, very low, but sufficient to perturb a volume-based particle size method by significant amounts.
NASA Technical Reports Server (NTRS)
Cain, Michael D.
1999-01-01
The goal of this thesis is to develop an efficient and robust locally preconditioned semi-coarsening multigrid algorithm for the two-dimensional Navier-Stokes equations. This thesis examines the performance of the multigrid algorithm with local preconditioning for an upwind-discretization of the Navier-Stokes equations. A block Jacobi iterative scheme is used because of its high frequency error mode damping ability. At low Mach numbers, the performance of a flux preconditioner is investigated. The flux preconditioner utilizes a new limiting technique based on local information that was developed by Siu. Full-coarsening and-semi-coarsening are examined as well as the multigrid V-cycle and full multigrid. The numerical tests were performed on a NACA 0012 airfoil at a range of Mach numbers. The tests show that semi-coarsening with flux preconditioning is the most efficient and robust combination of coarsening strategy, and iterative scheme - especially at low Mach numbers.
Hollaus, K; Weiss, B; Magele, Ch; Hutten, H
2004-02-01
The acceleration of the solution of the quasi-static electric field problem considering anisotropic complex conductivity simulated by tetrahedral finite elements of first order is investigated by geometric multigrid.
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…
Spherical agglomerates of lactose with enhanced mechanical properties.
Lamešić, Dejan; Planinšek, Odon; Lavrič, Zoran; Ilić, Ilija
2017-01-10
The aim of this study was to prepare spherical agglomerates of lactose and to evaluate their physicochemical properties, flow properties, particle friability and compaction properties, and to compare them to commercially available types of lactose for direct compression (spray-dried, granulated and anhydrous β-lactose). Porous spherical agglomerates of α-lactose monohydrate with radially arranged prism-like primary particles were prepared exhibiting a high specific surface area. All types of lactose analysed had passable or better flow properties, except for anhydrous β-lactose, which had poor flowability. Particle friability was more pronounced in larger granulated lactose particles; however, particle structure was retained in all samples analysed. The mechanical properties of spherical agglomerates of lactose, in terms of compressibility, established with Walker analysis, and compactibility, established with a compactibility profile, were found to be superior to any commercially available types of lactose. Higher compactibility of spherical agglomerates of lactose is ascribed to significantly higher particle surface area due to a unique internal structure with higher susceptibility to fragmentation.
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.
Frequency comparative study of coal-fired fly ash acoustic agglomeration.
Liu, Jianzhong; Wang, Jie; Zhang, Guangxue; Zhou, Junhu; Cen, Kefa
2011-01-01
Particulate pollution is main kind of atmospheric pollution. The fine particles are seriously harmful to human health and environment. Acoustic agglomeration is considered as a promising pretreatment technology for fine particle agglomeration. The mechanisms of acoustic agglomeration are very complex and the agglomeration efficiency is affected by many factors. The most important and controversial factor is frequency. Comparative studies between high-frequency and low-frequency sound source to agglomerate coal-fired fly ash were carried out to investigate the influence of frequency on agglomeration efficiency. Acoustic agglomeration theoretical analysis, experimental particle size distributions (PSDs) and orthogonal design were examined. The results showed that the 20 kHz high-frequency sound source was not suitable to agglomerate coal-fired fly ash. Only within the size ranging from 0.2 to 0.25 microm the particles agglomerated to adhere together, and the agglomerated particles were smaller than 2.5 microm. The application of low-frequency (1000-1800 Hz) sound source was proved as an advisable pretreatment with the highest agglomeration efficiency of 75.3%, and all the number concentrations within the measuring range decreased. Orthogonal design L16 (4)3 was introduced to determine the optimum frequency and optimize acoustic agglomeration condition. According to the results of orthogonal analysis, frequency was the dominant factor of coal-fired fly ash acoustic agglomeration and the optimum frequency was 1400 Hz.
Phosphate-enhanced cytotoxicity of zinc oxide nanoparticles and agglomerates.
Everett, W Neil; Chern, Christina; Sun, Dazhi; McMahon, Rebecca E; Zhang, Xi; Chen, Wei-Jung A; Hahn, Mariah S; Sue, H-J
2014-02-10
Zinc oxide (ZnO) nanoparticles (NPs) have been found to readily react with phosphate ions to form zinc phosphate (Zn3(PO4)2) crystallites. Because phosphates are ubiquitous in physiological fluids as well as waste water streams, it is important to examine the potential effects that the formation of Zn3(PO4)2 crystallites may have on cell viability. Thus, the cytotoxic response of NIH/3T3 fibroblast cells was assessed following 24h of exposure to ZnO NPs suspended in media with and without the standard phosphate salt supplement. Both particle dosage and size have been shown to impact the cytotoxic effects of ZnO NPs, so doses ranging from 5 to 50 μg/mL were examined and agglomerate size effects were investigated by using the bioinert amphiphilic polymer polyvinylpyrrolidone (PVP) to generate water-soluble ZnO ranging from individually dispersed 4 nm NPs up to micron-sized agglomerates. Cell metabolic activity measures indicated that the presence of phosphate in the suspension media can led to significantly reduced cell viability at all agglomerate sizes and at lower ZnO dosages. In addition, a reduction in cell viability was observed when agglomerate size was decreased, but only in the phosphate-containing media. These metabolic activity results were reflected in separate measures of cell death via the lactate dehydrogenase assay. Our results suggest that, while higher doses of water-soluble ZnO NPs are cytotoxic, the presence of phosphates in the surrounding fluid can lead to significantly elevated levels of cell death at lower ZnO NP doses. Moreover, the extent of this death can potentially be modulated or offset by tuning the agglomerate size. These findings underscore the importance of understanding how nanoscale materials can interact with the components of surrounding fluids so that potential adverse effects of such interactions can be controlled.
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".
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.
NASA Technical Reports Server (NTRS)
Sidilkover, David
1994-01-01
We present a new approach towards the construction of a genuinely multidimensional high-resolution scheme for computing steady-state solutions of the Euler equations of gas dynamics. The unique advantage of this approach is that the Gauss-Seidel relaxation is stable when applied directly to the high-resolution discrete equations, thus allowing us to construct a very efficient and simple multigrid steady-state solver. This is the only high-resolution scheme known to us that has this property. The two-dimensional scheme is presented in detail. It is formulated on triangular (structured and unstructured) meshes and can be interpreted as a genuinely two-dimensional extension of the Roe scheme. The quality of the solutions obtained using this scheme and the performance of the multigrid algorithm are illustrated by the numerical experiments. Construction of the three dimensional scheme is outlined briefly as well.
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.
Convergence of Defect-Correction and Multigrid Iterations for Inviscid Flows
NASA Technical Reports Server (NTRS)
Diskin, Boris; Thomas, James L.
2011-01-01
Convergence of multigrid and defect-correction iterations is comprehensively studied within different incompressible and compressible inviscid regimes on high-density grids. Good smoothing properties of the defect-correction relaxation have been shown using both a modified Fourier analysis and a more general idealized-coarse-grid analysis. Single-grid defect correction alone has some slowly converging iterations on grids of medium density. The convergence is especially slow for near-sonic flows and for very low compressible Mach numbers. Additionally, the fast asymptotic convergence seen on medium density grids deteriorates on high-density grids. Certain downstream-boundary modes are very slowly damped on high-density grids. Multigrid scheme accelerates convergence of the slow defect-correction iterations to the extent determined by the coarse-grid correction. The two-level asymptotic convergence rates are stable and significantly below one in most of the regions but slow convergence is noted for near-sonic and very low-Mach compressible flows. Multigrid solver has been applied to the NACA 0012 airfoil and to different flow regimes, such as near-tangency and stagnation. Certain convergence difficulties have been encountered within stagnation regions. Nonetheless, for the airfoil flow, with a sharp trailing-edge, residuals were fast converging for a subcritical flow on a sequence of grids. For supercritical flow, residuals converged slower on some intermediate grids than on the finest grid or the two coarsest grids.
The impact of agglomeration economies on hospital input prices.
Friedson, Andrew I; Li, Jing
2015-12-01
This paper examines the extent to which agglomeration of the hospital service industry enhances the productivity of producing health care. Specifically, we use a large set of private insurance claims from the FAIR Health database to show that an increasing spatial concentration of hospital services results in a decreased cost of obtaining intermediate medical services. We explicitly test whether the reduced cost at concentrated locations arises from the ability to share intermediate service providers. The identification relies on state variation in medical lab technician licensure requirements, which influence the cost of intermediate services only through the cost of running a lab. Our findings suggest that agglomeration of the hospital service industry attracts specialized medical labs, which in turn help to reduce the cost of producing laboratory tests.
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.
Flocculation, hydrophobic agglomeration and filtration of ultrafine coal
NASA Astrophysics Data System (ADS)
Yu, Zhimin
In coal preparation plant circuits, fine coal particles are aggregated either by oil agglomeration or by flocculation. In a new hydrophobic agglomeration process, recently developed hydrophobic latices are utilized. While the selectivity of such aggregation processes determines the beneficiation results, the degree of aggregation has a strong effect on fine coal filtration. The aim of this research was to study the fundamentals and analyze the common grounds for these processes, including the potential effect of the coal surface properties. The selective flocculation tests, in which three types of coal, which differed widely in surface wettability, and three additives (hydrophobic latices, a semi-hydrophobic flocculant and a typical hydrophilic polyelectrolyte) were utilized, showed that coal wettability plays a very important role in selective flocculation. The abstraction of a hydrophobic latex on coal and silica revealed that the latex had a much higher affinity towards hydrophobic coal than to hydrophilic mineral matter. As a result, the UBC-1 hydrophobic latex flocculated only hydrophobic coal particles while the polyelectrolyte (PAM) flocculated all the tested coal samples and minerals, showing no selectivity in the fine coal beneficiation. The oil agglomeration was tested using kerosene emulsified with various surfactants (e.g. cationic, anionic and non-ionic). Surfactants enhance not only oil emulsification, hence reducing oil consumption (down to 0.25--0.5%), but also entirely change the electrokinetic properties of the droplets and affect the interaction energy between oil droplets and coal particles. Consequently, the results found in the course of the experimental work strongly indicate that even oxidized coals can be agglomerated if cationic surfactants are used to emulsify the oil. Oil agglomeration of the Ford-4 ultrafine coal showed that even at extremely low oil consumption (0.25 to 0.5%), a clean coal product with an ash content around 5% at over
Liquid bridge agglomeration: A fundamental approach to toner deinking
Snyder, B.A.; Berg, J.C. . Chemical Engineering Dept.)
1994-05-01
An alternative agglomeration technique for deinking toner-printed furnishes has been investigated. This technique requires only the addition of an immiscible hydrocarbon oil dispersed in water at dosages of approximately 1% by weight on fiber. The addition is made during repulping: the process appears to be effective at all temperatures of interest (23 C and 70 C are tested) and requires no surfactants or additional chemicals. The result of the oil addition is the agglomeration of the toner particles into spheres of 1 mm to 1 cm in size. These spheres contain the added oil which acts as a binder, holding the toner particles together by liquid bridges. The process is ineffective when the furnish contains highly sized fibers or starched paper, and future work seeks to address these crucial problems.
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.
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
Contact mechanics of highly porous oxide nanoparticle agglomerates
NASA Astrophysics Data System (ADS)
Fabre, Andrea; Salameh, Samir; Ciacchi, Lucio Colombi; Kreutzer, Michiel T.; van Ommen, J. Ruud
2016-07-01
Efficient nanopowder processing requires knowledge of the powder's mechanical properties. Due to the large surface area to volume ratio, nanoparticles experience relatively strong attractive interactions, leading to the formation of micron-size porous structures called agglomerates. Significant effort has been directed towards the development of models and experimental procedures to estimate the elasticity of porous objects such as nanoparticle agglomerates; however, none of the existing models has been validated for solid fractions below 0.1. Here, we measure the elasticity of titania (TiO_2, 22 nm), alumina (Al_2O_3, 8 nm), and silica (SiO_2, 16 nm) nanopowder agglomerates by Atomic Force Microscopy, using a 3.75 μm glass colloid for the stress-strain experiments. Three sample preparations with varying degree of powder manipulation are assessed. The measured Young's moduli are in the same order of magnitude as those predicted by the model of Kendall et al., thus validating it for the estimation of the Young's modulus of structures with porosity above 90 %.
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.
Averett, Rodney D; Norton, David G; Fan, Natalie K; Platt, Manu O
2017-01-01
Sickle cell disease is a single point mutation disease that is known to alter the coagulation system, leading to hypercoagulable plasma conditions. These hypercoagulable conditions can lead to complications in the vasculature, caused by fibrin clots that form undesirably. There is a need to understand the morphology and structure of fibrin clots from patients with sickle cell disease, as this could lead to further discovery of treatments and life-saving therapies. In this work, a computational imaging analysis method is presented to evaluate fibrin agglomeration in the presence of erythrocytes (RBCs) homozygous for the sickle cell mutation (SS). Numerical algorithms were used to determine agglomeration of fibrin fibers within a matrix with SS RBCs to test the hypothesis that fibrin matrices with the inclusion of SS RBCs possess a more agglomerated structure than native fibrin matrices with AA RBCs. The numerical results showed that fibrin structures with SS RBCs displayed an overall higher degree of agglomeration as compared to native fibrin structures. The computational algorithm was also used to evaluate fibrin fiber overlap (aggregation) and anisotropy (orientation) in normal fibrin matrices compared to fibrin matrices polymerized around SS RBCs; however, there was no statistical difference. Ultrasound measurements of stiffness revealed rigid RBCs in the case of samples derived from homozygous SS blood, and densely evolving matrices, when compared to normal fibrin with the inclusion of AA RBCs. An agglomeration model is suggested to quantify the fibrin aggregation/clustering near RBCs for both normal fibrin matrices and for the altered structures. The results of this work are important in the sense that the understanding of aggregation and morphology in fibrin clots with incorporation of RBCs from persons living with sickle cell anemia may elucidate the complexities of comorbidities and other disease complications.
The role of agglomeration in the conductivity of carbon nanotube composites near percolation
NASA Astrophysics Data System (ADS)
Tarlton, Taylor; Sullivan, Ethan; Brown, Joshua; Derosa, Pedro A.
2017-02-01
A detailed study of agglomeration in composite materials containing carbon nanotubes (CNT) is presented. Three dimensional samples with different degrees of agglomeration were created in three different ways, leading to a wider range of geometries available to study. Virtual charges are injected into the computer-generated samples and move through these samples according to a Monte Carlo hopping algorithm. Results show that there is an optimal level of agglomeration that is actually beneficial for charge transport at low volume concentrations, lowering the percolation threshold. It is found that near percolation, a more uniform CNT distribution (less agglomeration) leads to more conductive paths, but with a lower mobility. The optimum level of agglomeration comes from a trade off between these two properties. Beyond this optimum agglomeration state, it is observed that conductivity tends to decrease as dispersion increases at all concentrations studied here. At high concentration (percolated samples), where CNT clumps merge, conductivity seems to be less sensitive to agglomeration.
NASA Astrophysics Data System (ADS)
Leclercq, L.; Modolo, R.; Leblanc, F.; Hess, S. L.; Andre, N.
2014-12-01
Ganymede is the only satellite which has its own magnetosphere, which is embedded in the Jovian magnetosphere (Kivelson et al. 1996). This peculiar interaction has been investigated by means of a 3D parallel multi-species hybrid model based on a CAM-CL algorithm (Mathews et al. 1994). In this formalism, ions have a kinetic description whereas electrons are considered as an inertialess fluid which ensures the neutrality of the plasma and contributes to the total current and electronic pressure. Maxwell's equations are solved to compute the temporal evolution of electromagnetic field. Hybrid simulations are performed on a uniform cartesian grid with a spatial resolution of about 240 km. Our results are globally consistent with other models and Galileo measurements. Nevertheless, our description of the magnetopause and the ionosphere is not satisfying enough due to the low spatial resolution. Indeed, we want to describe scale heights of 125 km in the ionosphere whereas the best spatial resolution that we are allowed to use is about 240 km. Therefore, in order to obtain more efficient and relevant results, it is necessary to improve the size of the grid. In this optic, we are introducing a multi-grids approach in order to refine the spatial resolution by a factor 2 (~120km) near Ganymede. The creation of a finer mesh in the simulation grid leads to make some peculiar computations at the interfaces between the two different grids, whether for the calculation of moments, such as charge density or current, or the computation of electromagnetic fields. Moreover, the parallelization of the code, based on domain decomposition methods, imposes us to take care of boundary conditions. In the hybrid model, macroparticules, which represent a kind of cloud of physical particles, have a volume equal to that of a grid cell. Then, the macroparticules entering into the higher spatial resolution region are splited into smaller macroparticules whose the volume corresponds to the volume
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
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.
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.
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.
Nano-sized Mn oxide/agglomerated silsesquioxane composite as a good catalyst for water oxidation.
Najafpour, Mohammad Mahdi; Madadkhani, Sepideh
2016-12-01
Water splitting to hydrogen and oxygen is an important reaction to store sustainable energies, and water oxidation is identified as the bottleneck for water splitting because it requires the high activation energy to perform. Herein a nano-sized Mn oxide/agglomerated silsesquioxane composite was used to synthesize an efficient catalyst for water oxidation. The composite was synthesized by a straightforward and simple procedure and characterized by scanning electron microscopy, transmission electron microscopy, Fourier transform infrared spectroscopy, Raman spectroscopy, dynamic light scattering, X-ray diffraction spectrometry, and electrochemical methods. Silsesquioxane causes good dispersion of Mn in the composite. The water-oxidizing activity of this composite was studied in the presence of cerium(IV) ammonium nitrate. The composite at the best calcination temperature (300 °C) shows a turnover frequency 0.3 (mmol O2/mol Mn.s). Regarding the low-cost, environmentally friendly precursors, simple synthesis, and efficiency for water oxidation, the composite is a promising catalyst that can be used in artificial photosynthetic systems for water splitting. We used Agglomerated silsesquioxane as a support for nano-sized Mn oxide to synthesize a good water-oxidizing catalyst.
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.
NASA Technical Reports Server (NTRS)
Roberts, Thomas W.; Sidilkover, David; Thomas, J. L.
2000-01-01
The second-order factorizable discretization of the compressible Euler equations developed by Sidilkover is extended to conservation form on general curvilinear body-fitted grids. The discrete equations are solved by symmetric collective Gauss-Seidel relaxation and FAS multigrid. Solutions for flow in a channel with Mach numbers ranging from 0.0001 to a supercritical Mach number are shown, demonstrating uniform convergence rates and no loss of accuracy in the incompressible limit. A solution for the flow around the leading edge of a semi-infinite parabolic body demonstrates that the scheme maintains rapid convergence for a flow containing a stagnation point.
Parallelization of a Multigrid Incompressible Viscous Cavity Flow Solver Using OpenMP
NASA Technical Reports Server (NTRS)
Roe, Kevin; Mehrotra, Piyush
1999-01-01
We describe a multigrid scheme for solving the viscous incompressible driven cavity problem that has been parallelized using OpenMP. The incremental parallelization allowed by OpenMP was of great help during the parallelization process. Results show good parallel efficiencies for reasonable problem sizes on an SGI Origin 2000. Since OpenMP allowed us to specify the number of threads (and in turn processors) at runtime, we were able to improve performance when solving on smaller/coarser meshes. This was accomplished by giving each processor a more reasonable amount of work rather than having many processors work on very small segments of the data (and thereby adding significant overhead).
Operation of dry-cleaned and agglomerated precompaction system (DAPS)
Tanaka, Shigemi; Okanishi, Kazuya; Kikuchi, Akio; Yamamura, Yuichi
1997-12-31
In order to reduce the manufacturing cost of coke, it is necessary to reduce mainly (1) the material cost and (2) operating cost. Both of these costs can be reduced by lowering the moisture of charging coal. Because dust generation increases with decreasing moisture of charging coal, however, the lower limit of charging coal moisture in the existing coke-oven equipment was about 5%, which yielded good results in coal moisture control (CMC) equipment. Nippon Steel has furthered the development of techniques for lowering the moisture of charging coal as far as possible in the existing coke ovens and has recently succeeded in developing a dry-cleaned and agglomerated precompaction system (DAPS) and incorporating this system in commercial production equipment. In this system, a coal preparation process is undertaken that involves separating coal fines, which cause dust generation, from dried charging coal and agglomerating them. The equipment incorporating this system was installed in the No. 3 and No. 4 coke batteries at Oita Works and brought into full-scale operation in September 1992. The equipment has since been operating smoothly.
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.
Selective agglomeration of a Pittsburgh Seam coal with isooctane
Lai, R.; Killmeyer, R.; Utz, B.; Richardson, A.; Sinha, K.
1992-01-01
The Pittsburgh Energy Technology Center initiated a research program in 1989 to investigate the fundamentals of selective agglomeration as applied to the cleaning of coals. The results of the initial study with Bruceton mine, Pittsburgh seam coal, using isooctane as an agglomerant, have been published. Subsequent to the successful reduction of the ash content of Bruceton coal to less than 0.9% after two cleaning stages, the study was extended to compare a coal from the same seam, but from Ohio. In the previous parameter optimization tests with Bruceton coal, particle size and slurry pH were found to be important parameters governing coal cleanability. Other researchers have obtained similar conclusions of the effects of particle size and coal slurry pH on the cleanability of various coals. In this study, the effects of these parameters on the cleanability of Powhatan coal were examined. Particle size reduction kinetics was examined first. Effects of size reduction (degree of mineral matter liberation), oil (isooctane)-to-coal ratio, and slurry pH on mineral matter rejection and combustible recovery were also examined. A petrographic comparison was conducted on the Powhatan and Bruceton coals to examine the degree of pyrite liberation as a function of particle size to elucidate why one coal from the same seam can be cleaned significantly better than another. (VC)
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.
NASA Astrophysics Data System (ADS)
Yang, Bingqiao; Song, Shaoxian
2014-05-01
Hydrophobic agglomeration is originated from the hydrophobic attraction between particles, which is essentially different from electrolyte coagulation and polymer flocculation. It is applied to mineral processing in floc-flotation process to improve the recovery of mineral fines. In this paper, the applications of this phenomenon in mineral fines were summarized, including the origin of hydrophobic agglomeration, the main factors affect hydrophobic agglomeration (particle hydrophobicity, shear rate and duration, nonpolar oil and tank geometry), as well as hydrophobic agglomeration based separation processes (carrier flotation and floc-flotation).
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.
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
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.
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.
On minimal energy dipole moment distributions in regular polygonal agglomerates
NASA Astrophysics Data System (ADS)
Rosa, Adriano Possebon; Cunha, Francisco Ricardo; Ceniceros, Hector Daniel
2017-01-01
Static, regular polygonal and close-packed clusters of spherical magnetic particles and their energy-minimizing magnetic moments are investigated in a two-dimensional setting. This study focuses on a simple particle system which is solely described by the dipole-dipole interaction energy, both without and in the presence of an in-plane magnetic field. For a regular polygonal structure of n sides with n ≥ 3 , and in the absence of an external field, it is proved rigorously that the magnetic moments given by the roots of unity, i.e. tangential to the polygon, are a minimizer of the dipole-dipole interaction energy. Also, for zero external field, new multiple local minima are discovered for the regular polygonal agglomerates. The number of found local extrema is proportional to [ n / 2 ] and these critical points are characterized by the presence of a pair of magnetic moments with a large deviation from the tangential configuration and whose particles are at least three diameters apart. The changes induced by an in-plane external magnetic field on the minimal energy, tangential configurations are investigated numerically. The two critical fields, which correspond to a crossover with the linear chain minimal energy and with the break-up of the agglomerate, respectively are examined in detail. In particular, the numerical results are compared directly with the asymptotic formulas of Danilov et al. (2012) [23] and a remarkable agreement is found even for moderate to large fields. Finally, three examples of close-packed structures are investigated: a triangle, a centered hexagon, and a 19-particle close packed cluster. The numerical study reveals novel, illuminating characteristics of these compact clusters often seen in ferrofluids. The centered hexagon is energetically favorable to the regular hexagon and the minimal energy for the larger 19-particle cluster is even lower than that of the close packed hexagon. In addition, this larger close packed agglomerate has two
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
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.
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
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.
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.
1988-08-01
Aeronautical Institute, Nanjing, Peoples Republic of China JAN MANDEL Computational Mathematics Group, University of Colorado at Denver, Den- ver, Colorado...have suffered * either from a slow convergence or from a non-reliable convergence. But most people were .I- L 2 Acceleration of a 2D Full Potential Flow...achieved within 3 cycles. For transonic flows, the discrete solution is very sensitive to small perturbations. Therefore the bad approximation quality
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.
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...
A Study of Multigrid Preconditioners Using Eigensystem Analysis
NASA Technical Reports Server (NTRS)
Roberts, Thomas W.; Swanson, R. C.
2005-01-01
The convergence properties of numerical schemes for partial differential equations are studied by examining the eigensystem of the discrete operator. This method of analysis is very general, and allows the effects of boundary conditions and grid nonuniformities to be examined directly. Algorithms for the Laplace equation and a two equation model hyperbolic system are examined.
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.
NASA Astrophysics Data System (ADS)
Radeva, Zheni; Müller, Peter; Tomas, Juergen
2013-06-01
High fraction of agglomerates and better agglomerate strength are main purpose for every agglomeration process. For optimizing the agglomeration process of industrial produced granules, using liquid binders, it is necessary to understand the microinteractions between primary particles and binder and the marcointeractions between the agglomerates themselves. In order to investigate the influence of the rotational velocity of the pan pelletizer and the primary particle size on the fraction of agglomerates and the mechanical properties of the produced agglomerates, the obtained structures have to be basically analyzed. Agglomeration of industrial produced Alumina Oxide (γ-Al2O3) granules is carried out in a rotating pan pelletizer. A 6 mass-% solution of viscoelastic polymer - hydroxypropyl methylcellulose (HPMC) is used as binder. The rotational velocity of the pelletizer pan is previously measured and calibrated. By changing the rotational velocity of the process chamber it was found that there are critical speed limits for the pan. The minimum critical velocity of the pelletizer plate does not provide enough contact collisions between the particles and the necessary kinetic level for agglomeration cannot be reached. The maximum critical velocity leads to higher rotational kinetic energy and this causes breakages of the agglomerates. It was also proven that the breakage strength of the agglomerates decreases with the reduction of the agglomerate size. The conclusions from the experimental work help us to understand the basics of agglomeration process and tend to develop and facilitate the operating with particle collectives in science and industry.
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)
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.
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.