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  • 1
    Electronic Resource
    Electronic Resource
    Towards generalization and optimization of implicit methods (1985)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985), S. 357-380 
    Details
    ISSN: 0271-2091
    Keywords: Iterative Methods ; Implicit Procedures ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A general implicit (GI) method for solving iteratively the algebraic system arising from a finite difference approximation of an elliptic partial differential equation is formulated. Under certain assumptions this method can be reduced to the already known implicit techniques. It is shown that the GI method has a very special physical meaning when solving fluid flow problems. It is shown also how this method can be optimized to achieve the maximum rate of convergence. Finally it is shown how this new strategy is applied by solving some classical numerical fluid dynamics problems.
    Additional Material: 21 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650050406
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    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    The parametrized strongly implicit method for solving elliptic difference equations (1985)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985), S. 381-391 
    Details
    ISSN: 0271-2091
    Keywords: Matrix Iterative Methods ; Strongly Implicit Procedure ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A new method for solving elliptic difference equations is derived based on the strongly implicit method. This parametrized strongly implicit method has three free parameters which may be functions of the field's nodal point. The method has some resemblance to the SOR techniques, but in the present method the off-diagonal entries are also over-relaxed. The main application of this method is for transport equations such as those governing the fluid flow and heat transfer fields.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650050407
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Stable second-order accurate iterative solutions for second-order elliptic problems (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 583-598 
    Details
    ISSN: 0271-2091
    Keywords: Upwind ; Second order ; Stable schemes ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The paper describes a numerical scheme for solving a convection-diffusion elliptic system with very small diffusion coefficients. This iterative numerical procedure is unconditionally stable and converges very rapidly. Although only linear equations are considered here, this technique can be easily extended to non-linear equations, while keeping its main features as for the linear case. The numerical experiments presented are quite general and confirm most of these features. These examples also show a good way of implementing this scheme.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650090508
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Solving numerically the Navier-Stokes equations on parallel systems (1990)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 10 (1990), S. 907-923 
    Details
    ISSN: 0271-2091
    Keywords: Parallel computing ; Parallel iterative methods ; Numerical splitting techniques ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A new general approach for numerically computing flow fields on parallel computing environments is presented, discussed and analysed. The hierarchy presented here is based on a parallel split of operators. A portion of the theory is presented together with its application to two- and three-dimensional flows. This strategy is applied to a two-dimensional problem for which a specific parallel split, called a parabolized split, is given. The parallel algorithm that results from this split is analysed, leading to reasonably good parallel efficiency, which is close to 50%. Actual experiments lead to similar conclusions. This parallel strategy can also be used together with other parallel computing algorithms, such as domain decomposition, to give an optimal-type parallel algorithm for the Navier-Stokes equations.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650100805
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    Paper (German National Licenses)
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  • 5
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    Stimulated-Rock Characteristics and Behavior in Multistage Hydraulic-Fracturing Treatment (2015)
    Society of Petroleum Engineers
    Details
    Publication Date: 2015-08-01
    Print ISSN: 1086-055X
    Electronic ISSN: 1930-0220
    Topics: Geosciences , Chemistry and Pharmacology
    Published by Society of Petroleum Engineers
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    PAPER CURRENT
  • 6
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    Numerical analysis of confined turbulent flow (1982)
    Elsevier
    Details
    Publication Date: 1982-01-01
    Print ISSN: 0045-7930
    Electronic ISSN: 1879-0747
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
    Published by Elsevier
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    PAPER CURRENT
  • 7
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    High order parallel numerical schemes for solving incompressible flows (1992)
    In:  CASI
    Details
    Publication Date: 2013-08-29
    Description: The use of parallel computers for numerically solving flow fields has gained much importance in recent years. This paper introduces a new high order numerical scheme for computational fluid dynamics (CFD) specifically designed for parallel computational environments. A distributed MIMD system gives the flexibility of treating different elements of the governing equations with totally different numerical schemes in different regions of the flow field. The parallel decomposition of the governing operator to be solved is the primary parallel split. The primary parallel split was studied using a hypercube like architecture having clusters of shared memory processors at each node. The approach is demonstrated using examples of simple steady state incompressible flows. Future studies should investigate the secondary split because, depending on the numerical scheme that each of the processors applies and the nature of the flow in the specific subdomain, it may be possible for a processor to seek better, or higher order, schemes for its particular subcase.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Computational Fluid Dynamics; p 115-131
    Format: text
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    NASA TECHNICAL REPORTS
  • 8
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    Parallel algorithms for boundary value problems (1990)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: A general approach to solve boundary value problems numerically in a parallel environment is discussed. The basic algorithm consists of two steps: the local step where all the P available processors work in parallel, and the global step where one processor solves a tridiagonal linear system of the order P. The main advantages of this approach are two fold. First, this suggested approach is very flexible, especially in the local step and thus the algorithm can be used with any number of processors and with any of the SIMD or MIMD machines. Secondly, the communication complexity is very small and thus can be used as easily with shared memory machines. Several examples for using this strategy are discussed.
    Keywords: NUMERICAL ANALYSIS
    Type: NASA-TM-102498 , ICOMP-90-03 , E-5292 , NAS 1.15:102498
    Format: application/pdf
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    NASA TECHNICAL REPORTS
  • 9
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    Parallel solution of high-order numerical schemes for solving incompressible flows (1993)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: A new parallel numerical scheme for solving incompressible steady-state flows is presented. The algorithm uses a finite-difference approach to solving the Navier-Stokes equations. The algorithms are scalable and expandable. They may be used with only two processors or with as many processors as are available. The code is general and expandable. Any size grid may be used. Four processors of the NASA LeRC Hypercluster were used to solve for steady-state flow in a driven square cavity. The Hypercluster was configured in a distributed-memory, hypercube-like architecture. By using a 50-by-50 finite-difference solution grid, an efficiency of 74 percent (a speedup of 2.96) was obtained.
    Keywords: COMPUTER SYSTEMS
    Type: NASA-TM-4451 , E-7345 , NAS 1.15:4451
    Format: application/pdf
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    NASA TECHNICAL REPORTS
  • 10
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    On the mathematical modeling of the Reynolds stress's equations (1990)
    In:  Other Sources
    Details
    Publication Date: 2019-06-28
    Description: By considering the Reynolds stress equations as a possible descriptor of complex turbulent fields, pressure-velocity interaction and turbulence dissipation are studied as two of the main physical contributions to Reynolds stress balancing in turbulent flow fields. It is proven that the pressure interaction term contains turbulence generation elements. However, the usual 'return to isotropy' element appears more weakly than in the standard models. In addition, convection-like elements are discovered mathematically, but there is no mathematical evidence that the pressure fluctuations contribute to the turbulent transport mechanism. Calculations of some simple one-dimensional fields indicate that this extra convection, rather than the turbulent transport, is needed mathematically. Similarly, an expression for the turbulence dissipation is developed. The end result is a dynamic equation for the dissipation tensor which is based on the tensorial length scales.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: AIAA PAPER 90-0498
    Format: text
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    NASA TECHNICAL REPORTS
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