Un problème de Navier-Stokes avec surface libre et tension superficielle

Allain, Geneviéve

doi:10.5802/afst.614

Cited by 14 publications

(19 citation statements)

References 3 publications

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“…Gathering the Navier-Stokes equation (8), the initial and boundary conditions (9)- (12), and the velocity condition on the interface (13) leads to the following model for 2-phase flows in each subdomain Ω i , i = 1, 2:…”

Section: A Navier-stokes Model For 2-phase Flowsmentioning

confidence: 99%

An adaptive numerical scheme for solving incompressible 2-phase and free-surface flows

Frey

Kazerani

2018

Int J Numer Meth Fluids

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Summary In this paper, we present a numerical scheme for solving 2‐phase or free‐surface flows. Here, the interface/free surface is modeled using the level‐set formulation, and the underlying mesh is adapted at each iteration of the flow solver. This adaptation allows us to obtain a precise approximation for the interface/free‐surface location. In addition, it enables us to solve the time‐discretized fluid equation only in the fluid domain in the case of free‐surface problems. Fluids here are considered incompressible. Therefore, their motion is described by the incompressible Navier‐Stokes equation, which is temporally discretized using the method of characteristics and is solved at each time iteration by a first‐order Lagrange‐Galerkin method. The level‐set function representing the interface/free surface satisfies an advection equation that is also solved using the method of characteristics. The algorithm is completed by some intermediate steps like the construction of a convenient initial level‐set function (redistancing) as well as the construction of a convenient flow for the level‐set advection equation. Numerical results are presented for both bifluid and free‐surface problems.

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Section: A Navier-stokes Model For 2-phase Flowsmentioning

confidence: 99%

An adaptive numerical scheme for solving incompressible 2-phase and free-surface flows

Frey

Kazerani

2018

Int J Numer Meth Fluids

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“…Allain adapted the articles of Beale to the 2D geometry with surface tension. She proved well-posedness in [4] and [3]. In [29], Sylvester had large time existence even without surface tension.…”

Section: Introductionmentioning

confidence: 99%

Well-Posedness of Surface Wave Equations Above a Viscoelastic Fluid

Meur

2010

J. Math. Fluid Mech.

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In this article, we prove the local well-posedness, for arbitrary initial data with certain regularity assumptions, of the equations of a Viscoelastic Fluid of Johnson-Segalman type in a domain with a free surface. Managing more general constitutive laws is also briefly depicted. The 2D geometry is defined by a solid fixed bottom and an upper free boundary submitted to surface tension. The proof relies on a Lagrangian formulation. First we solve two intermediate problems through a fixed point using mainly (Allain in Appl Math Optim 16:37-50, 1987) for the Navier-Stokes part. Then we solve the whole Lagrangian problem on [0, T 0 ] for T 0 small enough through a contraction mapping. Since the Lagrangian solution is regular enough and the change of coordinates invertible, we can come back to an Eulerian one.Mathematics Subject Classification (2010). 35Q30, 35Q35, 76D03, 76D05, 76N10.

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“…For any data of some given regularity, we prove the small-time existence of a solution to the problem. The main work is the study of the linear tangent operator which is very different from [1]. In Section 2 we make explicit the linearized equations and give a weak formulation of the linear problem.…”

Section: U(x T) = V(x + U(x T) T) = U(x T) the Pressure Q(x T)mentioning

confidence: 99%

“…In 1984 [3] he studied the large-time existence and regularity of the solution with initial data near the equilibrium, with surface tension being taken into account. In [1] we were concerned with the same problem as in [2] with surface tension. We proved the small-time existence of a solution even if the initial velocity was not small, but to study the linearized problem we had to assume the initial fluid domain was near a horizontal strip.…”

Section: Introductionmentioning

confidence: 99%