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  • Numerical Methods  (4)
  • Viscous flow  (3)
  • Navier-Stokes  (2)
  • 65N15  (1)
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  • 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
    A regularization-stabilization technique for nonlinear conservation equation computations (1988)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 4 (1988), S. 165-171 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Mathematics and Statistics ; Numerical Methods
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A regularization procedure for nonlinear conservation equations is introduced and demonstrated to have a stabilizing effect on the numerical solution of the associated approximate problem. Representative results for a least-squares finite-element method are given, and the numerical performance of the stabilization procedure explored. The effect of the regularization term is similar to a local numerical dissipation dependent on the numerical itegration time step.
    Zusätzliches Material: 4 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/num.1690040302
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  • 5
    Digitale Medien
    Digitale Medien
    Superconvergence phenomena in nonlinear two-point boundary-value problems (1993)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 9 (1993), S. 561-577 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Mathematics and Statistics ; Numerical Methods
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Superconvergence estimates are derived for a class of strongly nonlinear two-point boundary-value problems. The analysis considers solution and gradient superconvergence points as well as flux postprocessing formulas. Finally, the extension to parabolic problems is considered. © 1993 John Wiley & Sons, Inc.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/num.1690090506
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  • 6
    Digitale Medien
    Digitale Medien
    Least-squares finite element approximation of Fisher's reaction-diffusion equation (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 11 (1995), S. 175-186 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Mathematics and Statistics ; Numerical Methods
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Fisher's equation is a classical diffusion-reaction type of problem describing diffusion and nonlinear reproduction of a species. In the present study we develop a least-squares finite element formulation of Fisher's equation and carry out supporting numerical studies. Of particular interest are questions associated with the approximation of progressive wave solutions with minimum speed and the viability of the least-squares approach for this class of problem. © 1995 John Wiley & Sons, Inc.
    Zusätzliches Material: 7 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/num.1690110206
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  • 7
    Digitale Medien
    Digitale Medien
    Natural and postprocessed superconvergence in semilinear problems (1991)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 7 (1991), S. 245-259 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Mathematics and Statistics ; Numerical Methods
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Superconvergence error estimates are established for a class of semilinear problems defined by a linear elliptic operator with a nonlinear forcing term. The analysis is for rectangular biquadratic elements, and we prove superconvergence of the derivative components along associated lines through the Gauss points. Derivative postprocessing formula and formulas for integrals are also considered and similar superconvergence estimates proven.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/num.1690070304
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  • 8
    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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  • 9
    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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  • 10
    Digitale Medien
    Digitale Medien
    Performance of iterative methods for Newtonian and generalized Newtonian flows (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 127-150 
    Details
    ISSN: 0271-2091
    Schlagwort(e): Iterative solution ; Viscous flow ; Generalized conjugate gradient ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Maschinenbau
    Notizen: We consider the use of accelerated gradient-type iterative methods for solution of Newtonian and certain non-Newtonian (power-law and Bingham models) viscous flow problems. The formulations are based on penalty and mixed finite element methods, and such factors as the effect of the penalty parameter, asymmetry, continuation and preconditioning are examined.
    Zusätzliches Material: 19 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/fld.1650090202
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