An iterative solver for the Oseen problem and numerical solution of incompressible Navier-Stokes equations

Olshanskii, Maxim A.

doi:10.1002/(sici)1099-1506(199907/08)6:5<353::aid-nla169>3.0.co;2-j

Numer. Linear Algebra Appl.

1999

DOI: 10.1002/(sici)1099-1506(199907/08)6:5<353::aid-nla169>3.0.co;2-j

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An iterative solver for the Oseen problem and numerical solution of incompressible Navier-Stokes equations

Maxim A. Olshanskii

¹

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Cited by 42 publications

(32 citation statements)

References 34 publications

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“…The results in [12], [10], and in the present paper show that for the application of coupled (pressure-velocity) solvers and implicit schemes the rotation form of the Navier-Stokes equations has interesting advantages compared to the convection form. Some numerical experiments with a low order finite element method for rotation form of the incompressible Navier-Stokes equations and comparision with the convection form can be found in [13].…”

mentioning

confidence: 60%

Navier--Stokes Equations in Rotation Form: A Robust Multigrid Solver for the Velocity Problem

Olshanskii

¹

,

Reusken²

2002

SIAM J. Sci. Comput.

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Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.

“…The results in [12], [10], and in the present paper show that for the application of coupled (pressure-velocity) solvers and implicit schemes the rotation form of the Navier-Stokes equations has interesting advantages compared to the convection form. Some numerical experiments with a low order finite element method for rotation form of the incompressible Navier-Stokes equations and comparision with the convection form can be found in [13].…”

mentioning

confidence: 60%

Navier--Stokes Equations in Rotation Form: A Robust Multigrid Solver for the Velocity Problem

Olshanskii

¹

,

Reusken²

2002

SIAM J. Sci. Comput.

Self Cite

Get access via publisher Add to collection Cite

Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.

“…in Turek (1999) for the convection form, can be extended to its rotation form. Moreover, preconditioners to the pressureregularized Oseen problem being well-tuned to the case of large Reynolds numbers are at hand (Olshanskii, 1999). Numerical results are in preparation and will be reported elsewhere.…”

Section: Discussionmentioning

confidence: 99%

Stable finite-element calculation of incompressible flows using the rotation form of convection

Lube¹

2002

IMA Journal of Numerical Analysis

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Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.

“…To our knowledge, the only other solver explicitly developed for the rotation form of the Navier-Stokes equations is Olshanskii's block triangular preconditioner; see, e.g., [21] or the brief discussion in section 4.2. This preconditioner is very effective for the solution of unsteady Oseen-type problems.…”

Section: Comparison With Other Methodsmentioning

confidence: 99%

An Efficient Solver for the Incompressible Navier–Stokes Equations in Rotation Form

Benzi¹,

Liu²

2007

SIAM J. Sci. Comput.

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Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.

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