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Projection Methods (projection + methods)
Selected AbstractsA spectral projection method for the analysis of autocorrelation functions and projection errors in discrete particle simulationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2008André Kaufmann Abstract Discrete particle simulation is a well-established tool for the simulation of particles and droplets suspended in turbulent flows of academic and industrial applications. The study of some properties such as the preferential concentration of inertial particles in regions of high shear and low vorticity requires the computation of autocorrelation functions. This can be a tedious task as the discrete point particles need to be projected in some manner to obtain the continuous autocorrelation functions. Projection of particle properties on to a computational grid, for instance, the grid of the carrier phase, is furthermore an issue when quantities such as particle concentrations are to be computed or source terms between the carrier phase and the particles are exchanged. The errors committed by commonly used projection methods are often unknown and are difficult to analyse. Grid and sampling size limit the possibilities in terms of precision per computational cost. Here, we present a spectral projection method that is not affected by sampling issues and addresses all of the above issues. The technique is only limited by computational resources and is easy to parallelize. The only visible drawback is the limitation to simple geometries and therefore limited to academic applications. The spectral projection method consists of a discrete Fourier-transform of the particle locations. The Fourier-transformed particle number density and momentum fields can then be used to compute the autocorrelation functions and the continuous physical space fields for the evaluation of the projection methods error. The number of Fourier components used to discretize the projector kernel can be chosen such that the corresponding characteristic length scale is as small as needed. This allows to study the phenomena of particle motion, for example, in a region of preferential concentration that may be smaller than the cell size of the carrier phase grid. The precision of the spectral projection method depends, therefore, only on the number of Fourier modes considered. Copyright © 2008 John Wiley & Sons, Ltd. [source] Semi-coupled air/water immersed boundary approach for curvilinear dynamic overset grids with application to ship hydrodynamicsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2008Juntao Huang Abstract For many problems in ship hydrodynamics, the effects of air flow on the water flow are negligible (the frequently called free surface conditions), but the air flow around the ship is still of interest. A method is presented where the water flow is decoupled from the air solution, but the air flow uses the unsteady water flow as a boundary condition. The authors call this a semi-coupled air/water flow approach. The method can be divided into two steps. At each time step the free surface water flow is computed first with a single-phase method assuming constant pressure and zero stress on the interface. The second step is to compute the air flow assuming the free surface as a moving immersed boundary (IB). The IB method developed for Cartesian grids (Annu. Rev. Fluid Mech. 2005; 37:239,261) is extended to curvilinear grids, where no-slip and continuity conditions are used to enforce velocity and pressure boundary conditions for the air flow. The forcing points close to the IB can be computed and corrected under a sharp interface condition, which makes the computation very stable. The overset implementation is similar to that of the single-phase solver (Comput. Fluids 2007; 36:1415,1433), with the difference that points in water are set as IB points even if they are fringe points. Pressure,velocity coupling through pressure implicit with splitting of operators or projection methods is used for water computations, and a projection method is used for the air. The method on each fluid is a single-phase method, thus avoiding ill-conditioned numerical systems caused by large differences of fluid properties between air and water. The computation is only slightly slower than the single-phase version, with complete absence of spurious velocity oscillations near the free surface, frequently present in fully coupled approaches. Validations are performed for laminar Couette flow over a wavy boundary by comparing with the analytical solution, and for the surface combatant model David Taylor Model Basin (DTMB) 5512 by comparing with Experimental Fluid Dynamics (EFD) and the results of two-phase level set computations. Complex flow computations are demonstrated for the ONR Tumblehome DTMB 5613 with superstructure subject to waves and wind, including 6DOF motions and broaching in SS7 irregular waves and wind. Copyright © 2008 John Wiley & Sons, Ltd. [source] LS-DYNA and the 8:1 differentially heated cavityINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 8 2002Mark A. Christon Abstract This paper presents results computed using LS-DYNA's new incompressible flow solver for a differentially heated cavity with an 8:1 aspect ratio at a slightly super-critical Rayleigh number. Three Galerkin-based solution methods are applied to the 8:1 thermal cavity on a sequence of four grids. The solution methods include an explicit time-integration algorithm and two second-order projection methods,one semi-implicit and the other fully implicit. A series of ad hoc modifications to the basic Galerkin finite element method are shown to result in degraded solution quality with the most serious effects introduced by row-sum lumping the mass matrix. The inferior accuracy of a lumped mass matrix relative to a consistent mass matrix is demonstrated with the explicit algorithm which fails to obtain a transient solution on the coarsest grid and exhibits a general trend to under-predict oscillation amplitudes. The best results are obtained with semi-implicit and fully implicit second-order projection methods where the fully implicit method is used in conjunction with a ,smart' time integrator. Copyright © 2002 John Wiley & Sons, Ltd. [source] Independent comparative study of PCA, ICA, and LDA on the FERET data setINTERNATIONAL JOURNAL OF IMAGING SYSTEMS AND TECHNOLOGY, Issue 5 2005Kresimir Delac Abstract Face recognition is one of the most successful applications of image analysis and understanding and has gained much attention in recent years. Various algorithms were proposed and research groups across the world reported different and often contradictory results when comparing them. The aim of this paper is to present an independent, comparative study of three most popular appearance-based face recognition projection methods (PCA, ICA, and LDA) in completely equal working conditions regarding preprocessing and algorithm implementation. We are motivated by the lack of direct and detailed independent comparisons of all possible algorithm implementations (e.g., all projection,metric combinations) in available literature. For consistency with other studies, FERET data set is used with its standard tests (gallery and probe sets). Our results show that no particular projection,metric combination is the best across all standard FERET tests and the choice of appropriate projection,metric combination can only be made for a specific task. Our results are compared to other available studies and some discrepancies are pointed out. As an additional contribution, we also introduce our new idea of hypothesis testing across all ranks when comparing performance results. © 2006 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 15, 252,260, 2005 [source] On Helmholtz decompositions and their generalizations,An overviewMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 4 2010W. Sprössig Abstract Helmholtz' theorem initiates a remarkable development in the theory of projection methods that are adapted to the numerical solution of equations in fluid dynamics and elasticity. There is a dense connection with Hodge-de Rham decompositions of smooth 1-forms. We give an overview of this type of decompositions and discuss their applications to vector, quaternionic and Clifford-valued boundary value problems in the corresponding Hilbert,Sobolev spaces. Copyright © 2009 John Wiley & Sons, Ltd. [source] Smoothed Particle Magnetohydrodynamics , III.MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 2 2005Multidimensional tests, ·B= 0 constraint ABSTRACT In two previous papers (Papers I and II), we have described an algorithm for solving the equations of Magnetohydrodynamics (MHD) using the Smoothed Particle Hydrodynamics (SPH) method. The algorithm uses dissipative terms in order to capture shocks and has been tested on a wide range of one-dimensional problems in both adiabatic and isothermal MHD. In this paper, we investigate multidimensional aspects of the algorithm, refining many of the aspects considered in Papers I and II and paying particular attention to the code's ability to maintain the ,·B= 0 constraint associated with the magnetic field. In particular, we implement a hyperbolic divergence cleaning method recently proposed by Dedner et al. in combination with the consistent formulation of the MHD equations in the presence of non-zero magnetic divergence derived in Papers I and II. Various projection methods for maintaining the divergence-free condition are also examined. Finally, the algorithm is tested against a wide range of multidimensional problems used to test recent grid-based MHD codes. A particular finding of these tests is that in Smoothed Particle Magnetohydrodynamics (SPMHD), the magnitude of the divergence error is dependent on the number of neighbours used to calculate a particle's properties and only weakly dependent on the total number of particles. Whilst many improvements could still be made to the algorithm, our results suggest that the method is ripe for application to problems of current theoretical interest, such as that of star formation. [source] Multivariate data analysis on historical IPV production data for better process understanding and future improvementsBIOTECHNOLOGY & BIOENGINEERING, Issue 1 2010Yvonne E. Thomassen Abstract Historical manufacturing data can potentially harbor a wealth of information for process optimization and enhancement of efficiency and robustness. To extract useful data multivariate data analysis (MVDA) using projection methods is often applied. In this contribution, the results obtained from applying MVDA on data from inactivated polio vaccine (IPV) production runs are described. Data from over 50 batches at two different production scales (700-L and 1,500-L) were available. The explorative analysis performed on single unit operations indicated consistent manufacturing. Known outliers (e.g., rejected batches) were identified using principal component analysis (PCA). The source of operational variation was pinpointed to variation of input such as media. Other relevant process parameters were in control and, using this manufacturing data, could not be correlated to product quality attributes. The gained knowledge of the IPV production process, not only from the MVDA, but also from digitalizing the available historical data, has proven to be useful for troubleshooting, understanding limitations of available data and seeing the opportunity for improvements. Biotechnol. Bioeng. 2010;107: 96,104. © 2010 Wiley Periodicals, Inc. [source] A Kronecker product approximate preconditioner for SANsNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 8-9 2004Amy N. Langville Abstract Many very large Markov chains can be modelled efficiently as stochastic automata networks (SANs). A SAN is composed of individual automata which, for the most part, act independently, requiring only infrequent interaction. SANs represent the generator matrix Q of the underlying Markov chain compactly as the sum of Kronecker products of smaller matrices. Thus, storage savings are immediate. The benefit of a SAN's compact representation, known as the descriptor, is often outweighed by its tendency to make analysis of the underlying Markov chain tough. While iterative or projections methods have been used to solve the system ,Q=0, the time until these methods converge to the stationary solution , is still unsatisfactory. SAN's compact representation has made the next logical research step of preconditioning thorny. Several preconditioners for SANs have been proposed and tested, yet each has enjoyed little or no success. Encouraged by the recent success of approximate inverses as preconditioners, we have explored their potential as SAN preconditioners. One particularly relevant finding on approximate inverse preconditioning is the nearest Kronecker product approximation discovered by Pitsianis and Van Loan. In this paper, we extend the nearest Kronecker product technique to approximate the Q matrix for an SAN with a Kronecker product, A1 , A2 ,,, AN. Then, we take M = A , A ,,, A as our SAN NKP preconditioner. Copyright © 2004 John Wiley & Sons, Ltd. [source] | ||||||||||