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Digitale Medien

A non-linearly stable implicit finite element algorithm for hypersonic aerodynamics (1992)

Iannelli, G. S. ; Baker, A. J.

Chichester [u.a.] : Wiley-Blackwell

International Journal for Numerical Methods in Engineering 34 (1992), S. 419-441

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ISSN: 0029-5981

Schlagwort(e): Engineering ; Engineering General

Quelle: Wiley InterScience Backfile Collection 1832-2000

Thema: Mathematik , Technik allgemein

Notizen: A generalized curvilinear co-ordinate Taylor weak statement implicit finite element algorithm is developed for the two-dimensional and axisymmetric compressible Navier-Stokes equations for ideal and reacting gases. For accurate hypersonic simulation, air is modelled as a mixture of five perfect gases, i.e. molecular and atomic oxygen and nirogen as well as nitric oxide. The associated pressure is then determined via Newton solution of the classical chemical equilibrium equation system. The directional semi-discretization is achieved using an optimal metric data Galerkin finite element weak statement, on a developed ‘companion conservation law system’, permitting classical test and trial space definitions. Utilizing an implicit Runge-Kutta scheme, the terminal algorithm is then non-linearly stable, and second-order accurate in space and time on arbitrary curvilinear co-ordinates. Subsequently, a matrix tensor product factorization procedure permits an efficient numerical linear algebra handling for large Courant numbers. For ideal- and real-gas hypersonic flows, the algorithm generates essentially non-oscillatory numerical solutions in the presence of strong detached shocks and boundary layer inviscid flow interactions.

Zusätzliches Material: 9 Ill.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1002/nme.1620340203

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Digitale Medien

Shape reconstruction and volume meshing for complex solids (1991)

Baker, Timothy J.

Chichester [u.a.] : Wiley-Blackwell

International Journal for Numerical Methods in Engineering 32 (1991), S. 665-675

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ISSN: 0029-5981

Schlagwort(e): Engineering ; Engineering General

Quelle: Wiley InterScience Backfile Collection 1832-2000

Thema: Mathematik , Technik allgemein

Notizen: The reconstruction of a solid surface from a series of cross-sections and the generation of a volume mesh that conforms with a prescribed surface are issues that arise in numerous applications. We describe an approach to both these problems that is based on the generation of a tetrahedral mesh which automatically captures a triangulation of the surface points. A simple algorithm for introducing a set of interior points permits a simple partition of the volume mesh into two disjoint sets of tetrahedra such that one set determines the interior of the solid while the second determines the exterior.

Zusätzliches Material: 10 Ill.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1002/nme.1620320404

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Digitale Medien

Accelerated bisection techniques for tri- and quindiagonal matrices (1992)

Baker, Graham

Chichester [u.a.] : Wiley-Blackwell

International Journal for Numerical Methods in Engineering 35 (1992), S. 203-218

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ISSN: 0029-5981

Schlagwort(e): Engineering ; Engineering General

Quelle: Wiley InterScience Backfile Collection 1832-2000

Thema: Mathematik , Technik allgemein

Notizen: 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.

Zusätzliches Material: 3 Tab.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1002/nme.1620350113

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Digitale Medien

Slope stability analysis for undrained loading conditions (1993)

Baker, R. ; Frydman, S. ; Talesnick, M.

New York, NY [u.a.] : Wiley-Blackwell

International Journal for Numerical and Analytical Methods in Geomechanics 17 (1993), S. 15-43

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ISSN: 0363-9061

Schlagwort(e): Engineering ; Engineering General

Quelle: Wiley InterScience Backfile Collection 1832-2000

Thema: Architektur, Bauingenieurwesen, Vermessung , Geologie und Paläontologie

Notizen: 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.

Zusätzliches Material: 17 Ill.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1002/nag.1610170103

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Digitale Medien

A globally well-posed finite element algorithm for aerodynamics applications (1991)

Iannelli, G. S. ; Baker, A. J.

Chichester : Wiley-Blackwell

International Journal for Numerical Methods in Fluids 12 (1991), S. 407-441

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ISSN: 0271-2091

Schlagwort(e): 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

Quelle: Wiley InterScience Backfile Collection 1832-2000

Thema: Maschinenbau

Notizen: 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.

Zusätzliches Material: 24 Ill.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1002/fld.1650120502

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