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  • 1
    Electronic Resource
    Electronic Resource
    Solution techniques for the vorticity-streamfunction formulation of two-dimensional unsteady incompressible flows (1990)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 11 (1990), S. 515-539 
    Details
    ISSN: 0271-2091
    Keywords: Vorticity-streamfunction ; Unsteady incompressible flows ; 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 review of our solution techniques for the vorticity-streamfunction formulation of two-dimensional incompressible flows is presented. While both the viscous and inviscid cases are considered, the derivation of the proper finite element formulations for multiply connected domains is emphasized. In all formulations associated with the vorticity transport equation, the streamline upwind/Petrov-Galerkin method is used. The adaptive implicit-explicit and grouped element-by-element solution strategies are employed to maximize the computational efficiency. The solutions obtained in all test cases compare well with solutions from previously published investigations. The convergence and benchmark studies performed in this paper show that the solution techniques presented are accurate, reliable and efficient.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650110505
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    Paper (German National Licenses)
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  • 2
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    Numerical simulation of electrophoresis separation processes (1986)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: A new Petrov-Galerkin finite element formulation has been proposed for transient convection-diffusion problems. Most Petrov-Galerkin formulations take into account the spatial discretization, and the weighting functions so developed give satisfactory solutions for steady state problems. Though these schemes can be used for transient problems, there is scope for improvement. The schemes proposed here, which consider temporal as well as spatial discretization, provide improved solutions. Electrophoresis, which involves the motion of charged entities under the influence of an applied electric field, is governed by equations similiar to those encountered in fluid flow problems, i.e., transient convection-diffusion equations. Test problems are solved in electrophoresis and fluid flow. The results obtained are satisfactory. It is also expected that these schemes, suitably adapted, will improve the numerical solutions of the compressible Euler and the Navier-Stokes equations.
    Keywords: INORGANIC AND PHYSICAL CHEMISTRY
    Type: NASA-CR-180124 , NAS 1.26:180124
    Format: application/pdf
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  • 3
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    Unsteady incompressible flow computations with the finite-element method (1992)
    In:  Other Sources
    Details
    Publication Date: 2019-06-28
    Description: While the methods thus far developed for vorticity-streamfunction formulation are thus far restricted to 2D flows, they are applicable to both viscous and inviscid flows, including problems with multiply-connected domains. The present solution techniques for the velocity-pressure formulation can be extended to 3D problems. Attention is given to (1) two multistep formulations that use piecewise bilinear functions for the velocity and piecewise constant functions for the pressure, and (2) a novel multistep velocity-pressure formulation based on the equal-order interpolation of velocity and pressure.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: In: Finite elements in fluids. Vol. 8 (A93-45962 19-34); p. 177-209.
    Format: text
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  • 4
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    Incompressible flow computations based on the vorticity-stream function and velocity-pressure formulations (1990)
    In:  Other Sources
    Details
    Publication Date: 2019-07-12
    Description: Finite element procedures and computations based on the velocity-pressure and vorticity-stream function formulations of incompressible flows are presented. Two new multistep velocity-pressure formulations are proposed and compared with the vorticity-stream function and one-step formulations. The example problems chosen are the standing vortex problem and flow past a circular cylinder. Benchmark quality computations are performed for the cylinder problem. The numerical results indicate that the vorticity-stream function formulation and one of the two new multistep formulations involve much less numerical dissipation than the one-step formulation.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Computers and Structures (ISSN 0045-7949); 35; 4 19
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  • 5
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    Solution techniques for the vorticity-streamfunction formulation of two-dimensional unsteady incompressible flows (1990)
    In:  Other Sources
    Details
    Publication Date: 2019-07-12
    Description: A review of the solution techniques of Tezduyar et al. (1988 and 1989) for the vorticity-streamfunction formulation of two-dimensional incompressible flows is presented. While both the viscous and inviscid cases are considered, the derivation of the proper finite-element formulations for multiply connected domains is emphasized. In all formulations associated with the vorticity transport equation, the streamline upwind/Petrov-Galerkin method is used. The adaptive implicit-explicit and grouped element-by-element solution strategies are employed to maximize the computational efficiency. The solutions obtained in all test cases compare well with solutions from previously published investigations. The convergence and benchmark studies performed in this paper show that the solution techniques presented are accurate, reliable, and efficient.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: International Journal for Numerical Methods in Fluids (ISSN 0271-2091); 11; 515-539
    Format: text
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  • 6
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    Solution techniques for incompressible flow problems (1989)
    In:  Other Sources
    Details
    Publication Date: 2019-07-13
    Description: A three-step Petrov-Galerkin (PG)/operator spliting scheme for the time-dependent incompressible Navier-Stokes equations is proposed. Each time step is split into two Stokes problems and one nonlinear convection-diffusion problem. Using a PG technique on the two outer Stokes problems ensures a stable scheme despite equal-order interpolation, while using a streamline upwind PG scheme on the inner convection-diffusion problem ensures a numerically stable solution at high Reynolds numbers. Numerical tests of this method have been carried out.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: International Conference on Finite Element Methods in Flow Problems; Apr 03, 1989 - Apr 07, 1989; Huntsville, AL; United States
    Format: text
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