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  • 1
    Electronic Resource
    Electronic Resource
    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 14 (1974), S. 177-188 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Two overriding characteristics for major applications of plastics in consumer products are: - the need for high volume production and - their exposure to hostile environments.Successful application and continued growth for plastics in these products requires knowledgeable prediction of performance in the process to produce the plastic part and in the environments to which it will be exposed during the product's lifetime. Progress on establishing relationships between material properties and structure are described with emphasis on response to melt process conditions and behavior when exposed to hostile environments.Commercial plastics and the processes by which they are converted into useful applications are complex systems. A multitude of interacting variables must be dealt with in order to achieve successful implementation in commercial products. Specific examples are discussed in the area of processing for non-Newtonian flow characteristics and overt effects in injection molding and extrusion, tailoring of polymers within established rheological limits and the influence of melt processing on physical and mechanical properties. The influence of application environments is discussed and specific examples are given for environmental stress cracking, stress-environment embrittlement and the effects of hot water solutions on polymer systems.
    Additional Material: 27 Ill.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Journal of Polymer Science: Polymer Letters Edition 13 (1975), S. 737-741 
    ISSN: 0360-6384
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
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  • 3
    Publication Date: 2019-07-13
    Description: 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.
    Keywords: Mathematical and Computer Sciences (General)
    Type: NASA/TM-2004-213037 , L-19023
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  • 4
    Publication Date: 2019-07-13
    Description: 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.
    Keywords: Mathematical and Computer Sciences (General)
    Type: AIAA Paper 2013-0863 , NF1676L-14827 , 51st AIAA Aerospace Sciences Meeting; Jan 07, 2013 - Jan 10, 2013; Grapevine, TX; United States
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  • 5
    Publication Date: 2019-07-13
    Description: 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.
    Keywords: Aerodynamics
    Type: AIAA Paper 2011-3235 , NF1676L-11822 , 41st AIAA Fluid Dynamics Conference and Exhibit; Jun 27, 2011 - Jun 30, 2011; Honolulu, HI; United States
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  • 6
    Publication Date: 2019-11-30
    Description: This manual describes the installation and execution of FUN3D version 13.6, including optional dependent packages. FUN3D is a suite of computational fluid dynamics simulation and design tools that uses mixed-element unstructured grids in a large number of formats, including structured multiblock and overset grid systems. A discretely-exact adjoint solver enables efficient gradient-based design and grid adaptation to reduce estimated discretization error. FUN3D is available with and without a reacting, real-gas capability. This generic gas option is available only for those persons that qualify for its beta release status.
    Keywords: Aerodynamics
    Type: NF1676L-34707 , NASA/TM-2019-220416
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  • 7
    Publication Date: 2019-07-13
    Description: 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.
    Keywords: Aerodynamics
    Type: NASA/TM-2004-213037 , L-19023
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  • 8
    Publication Date: 2019-07-13
    Description: New methodology for verification of computational methods using unstructured grids is presented. The discretization order properties are studied in computational windows, easily constructed within a collection of grids or a single grid. The windows can be adjusted to isolate the interior discretization, the boundary discretization, or singularities. A major component of the methodology is the downscaling test, introduced previously for studying the convergence rates of truncation and discretization errors of finite-volume discretization schemes on general unstructured grids. Demonstrations of the method are shown, including a comparative accuracy assessment of commonly-used schemes on general mixed grids and the identification of local accuracy deterioration at intersections of tangency and inflow/outflow boundaries. Recommendations for the use of the methodology in large-scale computational simulations are given.
    Keywords: Mathematical and Computer Sciences (General)
    Type: 46th AIAA Aerospace Sciences Meeting and Exhibit; Jan 07, 2008 - Jan 10, 2008; Reno, NV; United States
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  • 9
    Publication Date: 2019-07-12
    Description: 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.
    Keywords: Mathematical and Computer Sciences (General)
    Type: LF99-9141
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  • 10
    Publication Date: 2019-07-12
    Description: New methodology for verification of finite-volume computational methods using unstructured grids is presented. The discretization order properties are studied in computational windows, easily constructed within a collection of grids or a single grid. Tests are performed within each window and address a combination of problem-, solution-, and discretization/grid-related features affecting discretization error convergence. The windows can be adjusted to isolate particular elements of the computational scheme, such as the interior discretization, the boundary discretization, or singularities. Studies can use traditional grid-refinement computations within a fixed window or downscaling, a recently-introduced technique in which computations are made within windows contracting toward a focal point of interest. Grids within the windows are constrained to be consistently refined, allowing a meaningful assessment of asymptotic error convergence on unstructured grids. Demonstrations of the method are shown, including a comparative accuracy assessment of commonly-used schemes on general mixed grids and the identification of local accuracy deterioration at boundary intersections. Recommendations to enable attainment of design-order discretization errors for large-scale computational simulations are given.
    Keywords: Mathematical and Computer Sciences (General)
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