Artificial boundary conditions for the exterior spatial Navier–Stokes problem

Назаров, С. А.; Specovius–Neugebauer, Maria

doi:10.1016/s1620-7742(00)01288-5

Cited by 13 publications

(27 citation statements)

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“…In the particular framework of fluid mechanics, the case of Oseen equations were considered for instance in [14] while the case of stationnary homogeneous Navier-Stokes equations is treated e.g. in [12,17,18] (see also the references therein). In each of these works the original physical domain is supposed to have a particular shape (typically an exterior domain or an half space).…”

mentioning

confidence: 99%

Outflow boundary conditions for the incompressible non-homogeneous Navier-Stokes equations

Boyer¹,

Fabrie²

2007

Discrete &Amp; Continuous Dynamical Systems - B

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Abstract. In this paper we propose the analysis of the incompressible nonhomogeneous Navier-Stokes equations with nonlinear outflow boundary condition. This kind of boundary condition appears to be, in some situations, a useful way to perform numerical computations of the solution to the unsteady Navier-Stokes equations when the Dirichlet data are not given explicitly by the physical context on a part of the boundary of the computational domain.The boundary condition we propose, following previous works in the homogeneous case, is a relationship between the normal component of the stress and the outflow momentum flux taking into account inertial effects. We prove the global existence of a weak solution to this model both in 2D and 3D. In particular, we show that the nonlinear boundary condition under study holds for such a solution in a weak sense, even though the normal component of the stress and the density may not have traces in the usual sense.

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mentioning

confidence: 99%

Outflow boundary conditions for the incompressible non-homogeneous Navier-Stokes equations

Boyer¹,

Fabrie²

2007

Discrete &Amp; Continuous Dynamical Systems - B

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“…We begin by indicating some theoretical results concerning pointwise artificial boundary conditions for elliptic equations. Such results may be found in [40] (Laplace equations), [41] (Stokes system), [15] (Oseen system) and [42] (Navier-Stokes system with zero velocity at infinity).…”

Section: Introductionmentioning

confidence: 75%

Stability of a finite element method for 3D exterior stationary Navier-Stokes flows

Deuring

2007

Appl Math

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“…can be proved using exactly the same modification of the abstract scheme above as in [26], thus we repeat only the main ideas. The error fulfils the system…”

Section: Strong Solutions To the Navier-stokes Problem And Their Asymmentioning

confidence: 99%

Artificial Boundary Conditions for the Stokes and Navier–Stokes Equations in Domains that are Layer-Like at Infinity

Назаров¹,

Specovius–Neugebauer²

2008

Z. Anal. Anwend.

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Artificial boundary conditions are presented to approximate solutions to Stokes-and Navier-Stokes problems in domains that are layer-like at infinity. Based on results about existence and asymptotics of the solutions v ∞ , p ∞ to the problems in the unbounded domainare the approximating solutions on the truncated domain Ω R , the parameter R controls the exhausting of Ω. The artificial boundary conditions involve the Steklov-Poincaré operator on a circle together with its inverse and thus turn out to be a combination of local and nonlocal boundary operators. Depending on the asymptotic decay of the data of the problems, in the linear case the error vanishes of order O(R −N ), where N can be arbitrarily large.

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Artificial boundary conditions for the exterior spatial Navier–Stokes problem

Cited by 13 publications

References 0 publications

Outflow boundary conditions for the incompressible non-homogeneous Navier-Stokes equations

Outflow boundary conditions for the incompressible non-homogeneous Navier-Stokes equations

Stability of a finite element method for 3D exterior stationary Navier-Stokes flows

Artificial Boundary Conditions for the Stokes and Navier–Stokes Equations in Domains that are Layer-Like at Infinity

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