The Numerical Treatment of Differential Equations

Collatz, L.

doi:10.1007/978-3-662-24934-5

Cited by 173 publications

(230 citation statements)

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“…These solutions correspond to the case of torsion about axis 0 = O. Displacement lit/> then satisfies the equation ( [8], p. 326): ( 10) In the case of a rigid conical inclusion, the boundary condition on the surface of a cone is lit/> = O. Thus, the problem is identical to the previously solved potential theory problem of an inclusion (case a in Fig.…”

Section: Elastic Torsionmentioning

confidence: 80%

Singularities of elastic stresses and of harmonic functions at conical notches or inclusions

Bažant

Keer

1974

International Journal of Solids and Structures

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Abstract-The nature of singularities at the vertex of conical notches and inclusions is found for problems of potential theory and for elastostatic problems of torsion and of axisymmetric stress. A solution in terms of spherical harmonics and a general numerical solution based upon the field equations are used to determine the power dependence of the field quantities upon the distance from the apex of the cone. Eigenvalues representing the exponent are computed for various values of cone angle and for various Poisson ratios.

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Section: Elastic Torsionmentioning

confidence: 80%

Singularities of elastic stresses and of harmonic functions at conical notches or inclusions

Bažant

Keer

1974

International Journal of Solids and Structures

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“…The method of characteristics [16] is particularly suited for 1+1 dimensional hydrodynamical problems. First the differential equation [14] …”

Section: Numerical Resultsmentioning

confidence: 99%

Hydrodynamics of nuclear collisions with initial conditions from perturbative QCD

Eskola¹,

Kajantie²,

Ruuskanen³

1998

Eur. Phys. J. C

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“…Convergence relates to behavior of the solution as Ax and At tend to zero while stability is concerned with round-off error growth (Chaudhry 1987). There are three approaches for the analysis of convergence or stability of finite difference approximations for the solution of the water-hammer equations: derivation of convergence or stability criteria for the nonlinear equations; derivation of criteria for linearized equations; and numerical solution of the equations for a number of different ~xs and Ats and examination of results (Collatz 1960;Maudsley 1984).…”

Section: Methods For Numerical Comparison Of Models Convergence and Smentioning

confidence: 99%

Numerical Comparison of Pipe‐Column‐Separation Models

Simpson

Bergant

1994

J. Hydraul. Eng.

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ABSTRACT:Results comparing six column-separation numerical models for simulating localized vapor cavities and distributed vaporous cavitation in pipelines are presented. The discrete vaporcavity model (DVCM) is shown to be quite sensitive to selected input parameters. For short pipeline systems, the maximum pressure rise following column separation can vary markedly for small changes in wave speed, friction factor, diameter, initial velocity, length of pipe, or pipe slope. Of the six numerical models, three perform consistently over a broad number of reaches. One of them, the discrete gas-cavity model, is recommended for general use as it is least sensitive to input parameters or to the selected discretization of the pipeline. Three models provide inconsistent estimates of the maximum pressure rise as the number of reaches is increased; however, these models do give consistent results provided the ratio of maximum cavity size to reach volume is kept below 10%.

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The Numerical Treatment of Differential Equations

Cited by 173 publications

References 0 publications

Singularities of elastic stresses and of harmonic functions at conical notches or inclusions

Singularities of elastic stresses and of harmonic functions at conical notches or inclusions

Hydrodynamics of nuclear collisions with initial conditions from perturbative QCD

Numerical Comparison of Pipe‐Column‐Separation Models

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