Finite element solution of the unsteady Navier-Stokes equations by a fractional step method

Donéa, J.; Giuliani, S.; Laval, H.; Quartapelle, L.

doi:10.1016/0045-7825(82)90054-8

Cited by 211 publications

(79 citation statements)

References 17 publications

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“…Alternatively, within finite elements, Donea et al (1982) introduced a pressure-correction fractional-step method, designed to significantly reduce computational overheads in transient incompressible viscous flow situations. Similarly, Zienkiewicz et al (1995) have introduced the characteristic-based-split procedure (CBS).…”

Section: Background Theorymentioning

confidence: 99%

Computation of weakly‐compressible highly‐viscous liquid flows

Webster

Keshtiban²,

Belblidia³

2004

Engineering Computations

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Section: Background Theorymentioning

confidence: 99%

Computation of weakly‐compressible highly‐viscous liquid flows

Webster

Keshtiban²,

Belblidia³

2004

Engineering Computations

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“…In practice, the projection method is combined with any kind of spatial discretization technique, viz., finite differences (see e.g. Bell et al [4]), finite elements (Donea et al [13], Gresho and Chan [15]), or spectral approximations (Ku et al [22]). The aim of the present paper to provide a framework and an error analysis for such fully discretized schemes.…”

mentioning

confidence: 99%

On the approximation of the unsteady Navier-Stokes equations by finite element projection methods

Guermond

Quartapelle

1998

Numerische Mathematik

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161

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Summary. This paper provides an analysis of a fractional-step projection method to compute incompressible viscous flows by means of finite element approximations. The analysis is based on the idea that the appropriate functional setting for projection methods must accommodate two different spaces for representing the velocity fields calculated respectively in the viscous and the incompressible half steps of the method. Such a theoretical distinction leads to a finite element projection method with a Poisson equation for the incremental pressure unknown and to a very practical implementation of the method with only the intermediate velocity appearing in the numerical algorithm. Error estimates in finite time are given. An extension of the method to a problem with unconventional boundary conditions is also considered to illustrate the flexibility of the proposed method. Mathematics Subject Classification (1991): 35Q30, 65M12, 65M60

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“…The total numbers of elements and nodes were 64120 and 65762, respectively. The velocity correction method 18,19) was adopted for equal-order interpolation functions. The pressure is obtained implicitly from the In time integration, it is known that the forward Euler method generates negative diffusivity due to its second order truncation error.…”

Section: Governing Equationsmentioning

confidence: 99%

Numerical Simulations to Determine the Most Appropriate Welding and Ventilation Conditions in Small Enclosed Workspace.

et al. 2000

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In order to improve arc welding work in a small enclosed workspace, numerical simulations were conducted to find the most appropriate welding and ventilation conditions, such as welding currents, hood position and flow rates with no blowhole formation. In the simulations, distributions of airflow vectors and fume concentrations were calculated for two hood opening positions: one faced a welder's breathing zone, the other a contaminant source. As a result it was predicted that a hood opening facing a breathing zone remarkably lowered the fume concentration in the breathing zone compared with that facing a contaminant source. The reliability was confirmed in CO 2 arc welding experiments in the enclosed workspace by using a welding robot. In addition, the number of blowholes in welds, examined with x-ray, decreased with the increase in the welding current and with the decrease in the exhaust flow rate. These results showed that the fume concentration near welder's breathing zone and the number of blowholes could be reduced effectively by appropriate selection of the welding current and hood position, and it was confirmed that the numerical simulations were sufficiently useful to predict these appropriate welding conditions.

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Finite element solution of the unsteady Navier-Stokes equations by a fractional step method

Cited by 211 publications

References 17 publications

Computation of weakly‐compressible highly‐viscous liquid flows

Computation of weakly‐compressible highly‐viscous liquid flows

On the approximation of the unsteady Navier-Stokes equations by finite element projection methods

Numerical Simulations to Determine the Most Appropriate Welding and Ventilation Conditions in Small Enclosed Workspace.

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