Defect correction method for viscoelastic fluid flows at high Weissenberg number

Ervin, Vincent J.; Lee, Hyesuk

doi:10.1002/num.20090

Cited by 28 publications

(26 citation statements)

References 18 publications

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“…In the late 1970's Hemker (Bohmer et al) discovered that DCM, properly interpreted, is good also for nearly singular problems. Examples for which this has been successful include equilibrium Euler equations (Lallemand and Koren [13]), high Reynolds number problems (Layton et al [5]), and viscoelastic problems (Ervin and Lee [10]). …”

Section: A Previous Resultsmentioning

confidence: 98%

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A defect correction method for the time‐dependent Navier‐Stokes equations

Labovschii

2008

Numerical Methods Partial

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A method for solving the time dependent Navier-Stokes equations, aiming at higher Reynolds' number, is presented. The direct numerical simulation of flows with high Reynolds' number is computationally expensive. The method presented is unconditionally stable, computationally cheap, and gives an accurate approximation to the quantities sought. In the defect step, the artificial viscosity parameter is added to the inverse Reynolds number as a stability factor, and the system is antidiffused in the correction step. Stability of the method is proven, and the error estimations for velocity and pressure are derived for the one-and two-step defect-correction methods. The spacial error is O(h) for the one-step defect-correction method, and O(h 2 ) for the two-step method, where h is the diameter of the mesh. The method is compared to an alternative approach, and both methods are applied to a singularly perturbed convection-diffusion problem. The numerical results are given, which demonstrate the advantage (stability, no oscillations) of the method presented.

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Section: A Previous Resultsmentioning

confidence: 98%

“…Hemker [7], Koren [8], Heinrichs [9], Layton et al [5], Ervin and Lee [10], and Section IA for a review of this work.…”

Section: Introductionmentioning

confidence: 99%

A defect correction method for the time‐dependent Navier‐Stokes equations

Labovschii

2008

Numerical Methods Partial

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“…The SUPG method was investigated in [19], where the existence of a solution to the discrete problem was shown by a fixed point theory and an finite element error estimate was derived. The model equations (1.5)-(1.7) were studied in [6] and [8]. In [8] the SUPG method was examined for a continuous weak problem as well as for a discrete problem of the Oseen viscoelastic equations (1.5)-(1.7).…”

Section: )mentioning

confidence: 99%

Analysis and finite element approximation of an optimal control problem for the Oseen viscoelastic fluid flow

Lee

2007

Journal of Mathematical Analysis and Applications

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“…The defect-correction method has been applied to steady-state viscoelastic flows [17,16,32] for high Weissenberg number. In their approach, the defect step consisted of a nonlinear iteration in which the Weissenberg number was replaced with an artificially reduced value, and the correction step sought to improve on the approximation found in the defect step.…”

Section: Continuation In Weissenberg Numbermentioning

confidence: 99%

Computation of viscoelastic fluid flows using continuation methods

Howell

2009

Journal of Computational and Applied Mathematics

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a b s t r a c tThe numerical simulation of viscoelastic fluid flow becomes more difficult as a physical parameter, the Weissenberg number, increases. Specifically, at a Weissenberg number larger than a critical value, the iterative nonlinear solver fails to converge, a phenomenon known as the high Weissenberg number problem. In this work we describe the application and implementation of continuation methods to the nonlinear Johnson-Segalman model for steady-state viscoelastic flows. Simple, natural, and pseudo-arclength continuation approaches in Weissenberg number are investigated for a discontinuous Galerkin finite element discretization of the equations. Computations are performed for a benchmark contraction flow and, several aspects of the performance of the continuation methods including high Weissenberg number limits, are discussed.

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Defect correction method for viscoelastic fluid flows at high Weissenberg number

Cited by 28 publications

References 18 publications

A defect correction method for the time‐dependent Navier‐Stokes equations

A defect correction method for the time‐dependent Navier‐Stokes equations

Analysis and finite element approximation of an optimal control problem for the Oseen viscoelastic fluid flow

Computation of viscoelastic fluid flows using continuation methods

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