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  • 1
    Electronic Resource
    Electronic Resource
    AN ADAPTIVE FINITE ELEMENT SCHEME FOR HYDRAULIC FRACTURING WITH PROPPANT TRANSPORT (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 645-670 
    Details
    ISSN: 0271-2091
    Keywords: hydraulic fracturing ; finite elements ; moving adaptive grids ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A mathematical model and adaptive finite element scheme are developed for describing the distribution of proppant in a propagating hydraulic fracture. The governing equation for proppant concentration is derived by applying the conservation law of mass to the proppant and to the proppant-laden fluid. Shah's empirical equation, which relates the proppant concentration and the indices of the non-Newtonian fluid, is used to describe the proppant-laden fluid. The proppant distribution inside a hydraulic fracture can then be obtained by solving the proppant concentration equation together with the governing equations of fluid and elasticity for a hydraulic fracturing. A novel moving grid scheme is developed that combines grid point insertion with redistribution. Four examples corresponding to different in situ stress distributions are computed to demonstrate the scheme. © 1997 by John Wiley & Sons, Ltd.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 2
    Electronic Resource
    Electronic Resource
    FINITE ELEMENT ANALYSIS OF ANISOTROPIC FLUID SUSPENSIONS (1996)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 11-27 
    Details
    ISSN: 0271-2091
    Keywords: finite elements ; liquid crystal ; nematic ; anisotropic ; electro rheological ; 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 orientation tensor L is introduced to construct a modified Leslie-Ericksen model for the viscous, incompressible flow of anisotropic suspensions (including electric field effects). This is then utilized to develop a weak variational formulation and finite element scheme for computing the flow and orientation fields. Numerical results are presented for exploratory test problems.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 3
    Electronic Resource
    Electronic Resource
    Coupled heat transfer and viscous flow, and magnetic effects in weld pool analysis (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 713-730 
    Details
    ISSN: 0271-2091
    Keywords: Viscous flow ; Heat transfer ; Phase change ; Finite elements ; Magnetic field ; 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 finite element formulation and analysis is developed to study coupled heat transfer and viscous flow in a weld pool. The thermal effects generate not only buoyancy forces but also a variation in the surface tension which acts to drive the viscous flow in the molten weld pool. A moving phase boundary separates molten and solid material. Numerical experiments reveal the nature of the highly convective flow in the weld pool and the associated thermal profiles. The relative importance of buoyancy, surface tension, phase change, convection, etc. are examined. We also consider the sensitivity of the solution to the finite element mesh and related non-linear numerical instabilities. Of particular interest is the coupling of the thermal and viscous flow fields for the case when radial flow is inward or outward.
    Additional Material: 20 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650090605
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  • 4
    Electronic Resource
    Electronic Resource
    Periodic viscous flow: A bench-mark problem (1990)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 11 (1990), S. 87-97 
    Details
    ISSN: 0271-2091
    Keywords: Periodic ; Unsteady ; Viscous flow ; Finite elements ; 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 double-transform technique provides a semi-analytic solution in the form of a series expansion for unsteady axisymmetric Stokes flow in the entrance region of a semi-infinite rigid cylindrical tube. This in turn offers an appropriate bench-mark problem for evaluating the quality of numerical approximations. To illustrate this, periodic axial flow in a circular cylinder is considered. Some aspects of the bench-mark problem that are of interest include the reverse flow in the wall layers, the accuracy of the approximate method in different flow regimes and the mesh grading. This bench-mark problem and the numerical study provide some insight into practical issues pertinent to the approximate solution of unsteady and periodic flows.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650110106
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    A least squares finite element method for viscoelastic fluid flow problems (1993)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 17 (1993), S. 943-953 
    Details
    ISSN: 0271-2091
    Keywords: Viscoelastic ; Least squares ; Finite elements ; 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: Viscoelastic flows remain a demanding class of problems for approximate analysis, particularly at increasing Weissenberg numbers. Part of the difficulty stems from the convective behavior and in the treatment of the stress field as a primary unknown. This latter aspect has led to the use of higher-order piecewise approximations for the stress approximation spaces in recent finite element research. The computational complexity of the discretized problem is increased significantly by this approach but at present it appears the most viable technique for solving these problems. Motivated by recent success in treating mixed systems and convective problems, we formulate here a least squares finite element method for the viscoelastic flow problem. Numerical experiments are conducted to test the method and examine its strengths and limitations. Some difficulties and open issues are identified through the numerical experiments. We consider the use of high degree elements (p refinement) to improve performance and accuracy.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650171103
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    Paper (German National Licenses)
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  • 6
    Electronic Resource
    Electronic Resource
    AN ENTROPY VARIABLE FORMULATION AND APPLICATIONS FOR THE TWO-DIMENSIONAL SHALLOW WATER EQUATIONS (1996)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 23 (1996), S. 29-46 
    Details
    ISSN: 0271-2091
    Keywords: shallow water equations ; entropy variables ; streamline upwind Petrov-Galerkin ; symmetric formulations ; finite elements ; 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 symmetric formulation of the two-dimensional shallow water equations and a streamline upwind Petrov-Galerkin (SUPG) scheme are developed and tested. The symmetric formulation is constructed by means of a transformation of dependent variables derived from the relation for the total energy of the water column. This symmetric form is well suited to the SUPG approach as seen in analogous treatments of gas dynamics problems based on entropy variables. Particulars related to the construction of the upwind test functions and an appropriate discontinuity-capturing operator are included. A formal extension to the viscous, dissipative problem and a stability analysis are also presented. Numerical results for shallow water flow in a channel with (a) a step transition, (b) a curved wall transition and (c) a straight wall transition are compared with experimental and other computational results from the literature.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 7
    Electronic Resource
    Electronic Resource
    Least-squares finite elements for fluid flow and transport (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 27 (1998), S. 97-107 
    Details
    ISSN: 0271-2091
    Keywords: least-squares ; finite elements ; flow ; transport ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The least-squares mixed finite element method is concisely described and supporting error estimates and computational results for linear elliptic (steady diffusion) problems are briefly summarized. The extension to the stationary Navier-Stokes problems for Newtonian, generalized Newtonian and viscoelastic fluids is then considered. Results of numerical studies are presented for the driven cavity problem and for a stick-slip problem. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
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