Predictor and steplength selection in continuation methods for the Navier-Stokes equations

Gunzburger, Max; Peterson, Janet

doi:10.1016/0898-1221(91)90015-v

Cited by 6 publications

(3 citation statements)

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“…For example, one may use a second-order Taylor series approximation to form u 0 . Gunzburger and Peterson [24] showed that in the Navier-Stokes equations, for some cases the stepsize in Reynolds number may be chosen independently of the type of predictor used. A detailed discussion of steplength algorithms for viscoelastic flows is a topic to be analyzed in future work.…”

Section: Natural Continuationmentioning

confidence: 99%

“…The authors also formulated a method for continuation in arc length. Gunzburger and Peterson [24] investigated predictor and steplength selection for continuation in Reynolds number and concluded that for certain values of the Reynolds number, the parameter steplength can be chosen independently of the type of predictor step used. Recently, de Almeida and Derby [13] described natural and pseudo-arclength continuation algorithms adapted for large-scale simulations of driven-cavity flows and successfully computed approximations for large values of the Reynolds number.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Natural Continuationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Computation of viscoelastic fluid flows using continuation methods

Howell

2009

Journal of Computational and Applied Mathematics

View full text Add to dashboard Cite

show abstract

“…For example, continuation methods are popular choices for solving high Reynolds number flow problems; see [22,24,25] and references therein. In general, continuation methods fall into three categories: parameter continuation [1,23], mesh sequencing [29], and pseudo time stepping [8,26,27]. The advantage of continuation is that the implementation is often relatively easy and robust.…”

Section: Introductionmentioning

confidence: 99%