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  • Finite elements  (3)
  • Navier-Stokes  (2)
  • 65L10  (1)
  • 65N15  (1)
  • 1
    Digitale Medien
    Digitale Medien
    Convergence analysis of least-squares mixed finite elements (1993)
    Springer
    Computing 51 (1993), S. 111-123 
    Details
    ISSN: 1436-5057
    Schlagwort(e): 65N30 ; 65N15 ; 65L10 ; Least-squares ; mixed finite element method ; superconvergence
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik
    Beschreibung / Inhaltsverzeichnis: Zusammenfassung Die Methode der kleinsten Fehlerquadrate wird bei gemischten finiten Elementen für die Differentialgleichungen erster Ordnung angewandt, die den linearen elliptischen 1-D Randwertaufgaben zweiter Ordnung entsprechen. Es werden theoretische Untersuchungen vorgestellt und Fehlerabschätzungen vorgenommen. Diese sind mit den früther von Carey and Shen [5] veröffentlichten numerischen Analysen konsistent. Die LBB Bedingung ist nicht notwendig und es werden Abschätzungen für verschiedene Grade der Austatz-Polynome vorgenommen. Superkonvergente Abschätzungen werden ebenso vorgestellt.
    Notizen: Abstract The least-squares finite element method for first order systems corresponding to second order linear two-point boundary value problems is considered. A theoretical analysis and error estimates are developed and the estimates are seen to be consistent with our previous numerical studies in Carey and Shen [5]. The method is not subject to the LBB condition and we consider, in particular, the estimates when the polynomial degree differs for the corresponding variables. Superconvergence estimates are also developed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02243846
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  • 2
    Digitale Medien
    Digitale Medien
    A vector-parallel scheme for Navier-Stokes computations at multi-gigaflop performance rates (1995)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 21 (1995), S. 445-466 
    Details
    ISSN: 0271-2091
    Schlagwort(e): vector-parallel computing ; Navier-Stokes ; Runge-Kutta ; domain decompostion ; CFD ; gigaflop ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Maschinenbau
    Notizen: A class of vector-parallel schemes for solution of steady compressible or incompressible viscous flow is developed and performance studies carried out. The algorithms employ an artificial transient treatment that permits rapid integration to a steady state. In the present work a four-stage explicit Runge-Kutta scheme employing variable local step size is utilized for the ODE system integration. The RK-4 scheme is restructured to allow vectorization and enhance concurrency in the calculation for a streamfunction-vorticity formulation of the flow problem. The parameters of the resulting RK scheme can be selected to accelerate convergence of the RK recursion. Four main procedures are considered which permit vector-parallel solution: a Jacobi update, a hybrid of the Jacobi and Gauss-Seidel method, red-black ordering and domain decomposition. Numerical performance studies are conducted with a representative viscous incompressible flow calculation. Results indicate that a scheme involving domain decomposition with a Gauss-Seidel type of update for the RK four-stage scheme is most effective and provides performance in excess of 8 Gflops on the Cray C-90.
    Zusätzliches Material: 13 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/fld.1650210602
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  • 3
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): Navier-Stokes ; high-order difference ; compact scheme ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: 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.
    Zusätzliches Material: 10 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nme.1620382008
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  • 4
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): Viscous flow ; Heat transfer ; Phase change ; Finite elements ; Magnetic field ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Maschinenbau
    Notizen: 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.
    Zusätzliches Material: 20 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/fld.1650090605
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  • 5
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): Periodic ; Unsteady ; Viscous flow ; Finite elements ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Maschinenbau
    Notizen: 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.
    Zusätzliches Material: 3 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/fld.1650110106
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  • 6
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): Viscoelastic ; Least squares ; Finite elements ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Maschinenbau
    Notizen: 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.
    Zusätzliches Material: 5 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/fld.1650171103
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