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  • 1
    Electronic Resource
    Electronic Resource
    On a finite element CFD algorithm for compressible, viscous and turbulent aerodynamic flowsBased as an invited lecture. (1987)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 7 (1987), S. 1235-1259 
    Details
    ISSN: 0271-2091
    Keywords: Fluid Mechanics ; CFD ; Finite Element ; Accuracy/Convergence ; Stability ; PNS/TLNS ; Turbulent ; 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: This paper develops and analyses individual construction aspects of an efficient and accurate finite element algorithm for prediction of viscous and turbulent flow fields of impact in aerodynamics. The theoretical construction employs a Taylor weak statement (TWS) for coincident embedding of stability mechanisms within a classic Galerkin finite element formulation of semi-discrete approximation error orthogonalization. A wide variety of the stabilizing mechanisms of independently derived CFD algorithms are contained within the TWS theory. An implicit construction that meets the requirement of efficient convergence to steady state is developed. The theoretical asymptotic error estimates of the TWS finite element algorithm for supersonic and viscous boundary layer flows are verified. Application to a three-dimensional turbulent flow is cited.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650071107
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  • 2
    Electronic Resource
    Electronic Resource
    A globally well-posed finite element algorithm for aerodynamics applications (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 12 (1991), S. 407-441 
    Details
    ISSN: 0271-2091
    Keywords: Compressible Navier-Stokes equations ; Taylor weak statement ; Curvilinear co-ordinate dissipation ; Lyapunov stability theory ; Well-posed boundary conditions ; Finite element semi-discretization ; Implicit Rosenbrock-Runge-Kutta scheme ; Tensor matrix product factorization ; 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 CFD algorithm is developed for Euler and Navier-Stokes aerodynamic applications. For the linear basis, the resultant approximation is at least second-order-accurate in time and space for synergistic use of three procedures: (1) a Taylor weak statement, which provides for derivation of companion conservation law systems with embedded dispersion-error control mechanisms; (2) a stiffly stable second-order-accurate implicit Rosenbrock-Runge-Kutta temporal algorithm; and (3) a matrix tensor product factorization that permits efficient numerical linear algebra handling of the terminal large-matrix statement. Thorough analyses are presented regarding well-posed boundary conditions for inviscid and viscous flow specifications. Numerical solutions are generated and compared for critical evaluation of quasi-one- and two-dimensional Euler and Navier-Stokes benchmark test problems. Of critical importance, essentially non-oscillatory solutions are uniformly attained for a range of supercritical flow situations with shocks.
    Additional Material: 24 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650120502
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  • 3
    Electronic Resource
    Electronic Resource
    Determination of the critical slip surface in slope stability computations (1980)
    New York, NY [u.a.] : Wiley-Blackwell
    International Journal for Numerical and Analytical Methods in Geomechanics 4 (1980), S. 333-359 
    Details
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: The analysis of the stability of slopes using limiting equilibrium considerations necessitates the determination of the critical slip surface which yields the minimal factor of safety. The numerous methods currently available for slope stability analysis provide a procedure for assigning a factor of safety to a given slip surface, but do not consider the problem of identifying the critical conditions.This paper presents an effective minimization procedure based on dynamic programming by which the minimal factor of safety, and the corresponding surface, are determined simultaneously. This procedure SSDP (Slope Stability by Dynamic Programming), couples the minimization scheme with Spencer's method of slope stability analysis. It may be applied to slopes of any geometry, layering, pore pressure and external load distributions. No arbitrary restrictions are placed on the shape of the slip surfaces, and the analysis satisfies all equilibrium equations.Application of the procedure to slope stability problems reported in the literature shows that for a given slip surface the procedure yields factors of safety which are almost identical to those reported, but in every case a more critical slip surface, with a lower factor of safety, may be found.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nag.1610040405
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  • 4
    Electronic Resource
    Electronic Resource
    Consequences of deviatoric normality in plasticity with isotropic strain hardening (1982)
    New York, NY [u.a.] : Wiley-Blackwell
    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 383-390 
    Details
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: For many soils experimental evidence suggests that deviation from normality between the plastic strain increments and the yield function is exhibited mainly in the volumetric behaviour, whereas the deviatoric behaviour exhibits normality. An analysis of the consequence of this observation is presented, and it leads to an expression for the plastic potential function as composed of two functions, a yield function and another dependent only on the hydrostatic pressure; the latter is considered to constitute the concept of correction functions presented recently by Desai and Siriwardane13.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nag.1610060308
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  • 5
    Electronic Resource
    Electronic Resource
    Slope stability analysis for undrained loading conditions (1993)
    New York, NY [u.a.] : Wiley-Blackwell
    International Journal for Numerical and Analytical Methods in Geomechanics 17 (1993), S. 15-43 
    Details
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: The current state of art for limit equilibrium analysis of slope stability problems lacks a satisfactory procedure for stability evaluation under general, rapid (undrained) loading conditions. Some procedures are available for the analysis of rapid drawdown, but these suffer from several shortcomings and, furthermore, are not applicable to other types of rapid loading. An approach is presented which overcomes these limitations. The approach integrates four components-establishment of soil behaviour on the basis of laboratory testing, estimation of steady-state conditions in the slope using a boundary value analysis, estimation of distribution of undrained strength in the slope using undrained stress paths, and identification of the critical slip surface followed by calculation of its factor of safety. The approach is illustrated through its application to the stability analysis of an earth dam under rapid drawdown and earthquake conditions.
    Additional Material: 17 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nag.1610170103
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  • 6
    Electronic Resource
    Electronic Resource
    On Taylor weak statement finite element methods for computational fluid dynamics (1995)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 21 (1995), S. 273-294 
    Details
    ISSN: 0271-2091
    Keywords: finite element ; finite volume ; Taylor weak statement ; Taylor-Galerkin method ; phase velocity ; 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 Taylor series augmentation of a weak statement (a ‘Taylor weak statement’ or ‘Taylor-Galerkin’ method) is used to systematically reduce the dispersion error in a finite element approximation of the one-dimensional transient advection equation. A frequency analysis is applied to determine the phase velocity of semi-implicit linear, quadratic and cubic basis one-dimensional finite element methods and of several comparative finite difference/finite volume algorithms. The finite element methods analysed include both Galerkin and Taylor weak statements. The frequency analysis is used to obtain an improved linear basis Taylor weak statement finite element algorithm. Solutions are reported for verification problems in one and two dimensions and are compared with finite volume solutions. The improved finite element algorithms have sufficient phase accuracy to achieve highly accurate linear transient solutions with little or no artificial diffusion.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650210402
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  • 7
    Electronic Resource
    Electronic Resource
    A taylor weak-statement algorithm for hyperbolic conservation laws (1987)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 7 (1987), S. 489-520 
    Details
    ISSN: 0271-2091
    Keywords: CFD Algorithm ; Weak Statement ; Hyperbolic ; Parabolic ; Dissipation ; Dispersion ; 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: Finite element analysis, applied to computational fluid dynamics (CFD) problem classes, presents a formal procedure for establishing the ingredients of a discrete approximation numerical solution algorithm. A classical Galerkin weak-statement formulation, formed on a Taylor series extension of the conservation law system, is developed herein that embeds a set of parameters eligible for constraint according to specification of suitable norms. The derived family of Taylor weak statements is shown to contain, as special cases, over one dozen independently derived CFD algorithms published over the past several decades for the high speed flow problem class. A theoretical analysis is completed that facilitates direct qualitative comparisons. Numerical results for definitive linear and non-linear test problems permit direct quantitative performance comparisons.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650070505
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  • 8
    Electronic Resource
    Electronic Resource
    Comparison of magnetic fields computed by finite element and classical series methods (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 271-280 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The finite element reduced scalar potential method of calculating magnetic fields is investigated by comparing it with a classical series method. Both methods are applied to two problems having a current band surrounding a ferromagnetic shell. The magnetic field distributions obtained by both methods are shown to be in generally good agreement.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620190208
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  • 9
    Electronic Resource
    Electronic Resource
    Accelerated bisection techniques for tri- and quindiagonal matrices (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 35 (1992), S. 203-218 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper considers accelerated bisection methods for calculating the eigenvalues of symmetric tridiagonal and quindiagonal matrices using cubic polynomial interpolation, as well as first and second order Newton iteration. Recursive relations based on the Sturm sequences are presented for the Newton type methods. The relations use a convenient scaling which retains the relative magnitudes in the iterative schemes but which avoids numerical overflow. Numerical examples show a significant increase in convergence rate.
    Additional Material: 3 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620350113
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  • 10
    Electronic Resource
    Electronic Resource
    Finite element solution algorithm for viscous incompressible fluid dynamics (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 89-101 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical solution algorithm employing the finite element concept of solid mechanics is derived for the transient laminar two-dimensional flow of an incompressible viscous fluid. Through dependent variable transformation, the problem is uniformly recast into the solution of a quasi-linear elliptic boundary value-problem, for which the finite element solution theory is established. The algorithm is uniquely user-oriented in accepting the generalized elliptic boundary condition specification of any non-coordinate-surface solution do main closure segment and on employing an arbitrarily irregular computational latticc. Numerical results are presented for several problems in internal flow illustrating solution accuracy, convergence, versatility and the ability to predict imbedded regions of recirculating flow.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620060110
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