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  • 1
    Electronic Resource
    Electronic Resource
    Editorial preface for the second decade of Communications in Numerical Methods in Engineering (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. iii 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640110102
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  • 2
    Electronic Resource
    Electronic Resource
    Some conformal map constructs for numerical grids (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 127-135 
    Details
    ISSN: 1069-8299
    Keywords: conformal mapping ; numerical grids ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We develop some special conformal maps and related strategies for grid generation in certain ‘difficult’ domains. Of particular interest are non-convex domains, and domains with corners and cusps.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640110206
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  • 3
    Electronic Resource
    Electronic Resource
    A note on Richardson extrapolation as an error estimator for non-linear reaction-diffusion problems (1997)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 13 (1997), S. 533-540 
    Details
    ISSN: 1069-8299
    Keywords: extrapolation ; non-linear potential equation ; reaction-diffusion ; semiconductors ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We develop and test a 6th-order Richardson extrapolation scheme as an error estimator for reaction-diffusion problems. Supporting numerical experiments are presented. © 1997 John Wiley & Sons, Ltd.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 4
    Electronic Resource
    Electronic Resource
    Higher-order compact mixed methods (1997)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 13 (1997), S. 553-564 
    Details
    ISSN: 1069-8299
    Keywords: mixed methods ; high-order finite differences ; compact stencils ; superconvergence ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We develop a class of higher-order mixed finite difference methods for elliptic partial differential equations. The problem is recast as a first-order mixed system and the higher-order compact schemes follow as a natural extension of the formulations we developed previously for the scalar PDE problem. Since the flux appears explicitly in the mixed formulation we obtain higher-order (nodal superconvergent) solutions in both the primary solution field and also the flux. Some supporting numerical experiments are included to demonstrate the superconvergent rates. © 1997 John Wiley & Sons, Ltd.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 5
    Electronic Resource
    Electronic Resource
    Galerkin and collocation-Galerkin methods with superconvergence and optimal fluxes (1981)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 17 (1981), S. 939-950 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Finite element methods are formulated and investigated for the effectiveness factor problem for heat and mass transfer with chemical reactions in catalyst pellet models. A Galerkin finite element method is compared with a previous C1 collocation method7. A scheme that is conceptually intermediate between these two methods and accordingly has been termed collocation-Galerkin is formulated and numerical experiments considered. Of particular interest here are superconvergence results at the Gauss and Jacobi points, respectively. Numerical studies of superconvergence in the presence of a nonlinear reaction-rate term are presented. An integral formula is devised and used to compute the flux at the pellet surface to optimal accuracy. Numerical experiments are conducted to demonstrate the improvement in computed fluxes.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620170610
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  • 6
    Electronic Resource
    Electronic Resource
    Variable upwinding and adaptive mesh refinement in convection-diffusion (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 341-353 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An analysis of the stability and oscillation properties of upwind finite element methods for convection-diffusion is given and used to develop a variable upwinding formulation. This formulation is particularly well suited to problems with nonconstant coefficients, nonlinearity or non-uniform meshes. We present the theoretical analysis and numerical studies for a standard steady-state and transient model one-dimensional convection-diffusion problem. The variable upwind strategy can also be used to significant advantage in conjunction with adaptive mesh refinement. Numerical results for the steady-state case in which convection dominates and the mesh is adaptively refined into a boundary layer confirm the efficacy of the scheme.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620190304
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  • 7
    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)
  • 8
    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)
  • 9
    Electronic Resource
    Electronic Resource
    Free-surface flow over curved surfaces: Part I: Perturbation analysis (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 28 (1998), S. 191-200 
    Details
    ISSN: 0271-2091
    Keywords: curved surface ; shallow water ; non-hydrostatic ; spillway ; finite element ; 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 standard two-dimensional shallow water equation formulation assumes a mild bed slope and no curvature effect. These assumptions limit the applicability of these equations for some important classes of problems. In particular, flow over a spillway is affected by the bed curvature via a decidedly non-hydrostatic pressure distribution. A detailed derivation of a more general equation set is given here in Part I. The method relies upon a perturbation expansion to simplify a bed-fitted co-ordinate configuration of the three-dimensional Euler equations. The resulting equations are essentially the equivalent of the two-dimensional shallow water equations but with curvature included and without the mild slope assumption. A finite element analysis and flume result are given in Part II. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    High-order compact scheme for the steady stream-function vorticity equations (1995)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 38 (1995), S. 3497-3512 
    Details
    ISSN: 0029-5981
    Keywords: Navier-Stokes ; high-order difference ; compact scheme ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A higher-order compact scheme that is O(h4) on the nine-point 2-D stencil is formulated for the steady stream-function vorticity form of the Navier-Stokes equations. The resulting stencil expressions are presented and hence this new scheme can be easily incorporated into existing industrial software. We also show that special treatment of the wall boundary conditions is required. The method is tested on representative model problems and compares very favourably with other schemes in the literature.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620382008
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