Existence of weak solutions for a Bingham fluid-rigid body system

Obando, Benjamin; Takahashi, Takéo

doi:10.1016/j.anihpc.2018.12.001

Cited by 5 publications

(7 citation statements)

References 51 publications

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“…We combine (35) with ( 34) and (32) to deduce (31). We conclude that u ∈ V is a solution to the inequality (31).…”

Section: Proof Of Theoremmentioning

confidence: 88%

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A Class of Variational–Hemivariational Inequalities for Bingham Type Fluids

Migórski

Dudek²

2022

Appl Math Optim

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In this paper we investigate a new class of elliptic variational–hemivariational inequalities without the relaxed monotonicity condition of the generalized subgradient. The inequality describes the mathematical model of the steady state flow of incompressible fluid of Bingham type in a bounded domain. The boundary condition represents a generalization of the no leak condition, and a multivalued and nonmonotone version of a nonlinear Navier–Fujita frictional slip condition. The analysis provides results on existence of solution to a variational–hemivariational inequality, continuous dependence of the solution on the data, existence of solutions to optimal control problems, and the dependence of the solution on the yield limit. The proofs profit from results of nonsmooth analysis and the theory of multivalued pseudomontone operators.

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“…We combine (35) with ( 34) and (32) to deduce (31). We conclude that u ∈ V is a solution to the inequality (31).…”

Section: Proof Of Theoremmentioning

confidence: 88%

“…for all v ∈ V . In order to show existence of solution to (31), we consider the auxiliary inclusion problem.…”

Section: Proof Of Theoremmentioning

confidence: 99%

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A Class of Variational–Hemivariational Inequalities for Bingham Type Fluids

Migórski

Dudek²

2022

Appl Math Optim

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“…Much research has been dedicated to the theoretical and practical aspects of the channel flow using Bingham fluids. For the system overriding the motion, the weak solutions have been addressed in [16], and in pipes and plane channel Poiseuille flow, nonlinear stability has been investigated in [17]. For the problem of incoming flow in a pipe, spatial decay estimations have been studied in [18], and slip conditions are used to study Couette-Poiseuille flow in a porous channel in [19].…”

Section: Introductionmentioning

confidence: 99%

Computational Analysis of Fluid Forces on an Obstacle in a Channel Driven Cavity: Viscoplastic Material Based Characteristics

et al. 2022

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In the current work, an investigation has been carried out for the Bingham fluid flow in a channel-driven cavity with a square obstacle installed near the inlet. A square cavity is placed in a channel to accomplish the desired results. The flow has been induced using a fully developed parabolic velocity at the inlet and Neumann condition at the outlet, with zero no-slip conditions given to the other boundaries. Three computational grids, C1, C2, and C3, are created by altering the position of an obstacle of square shape in the channel. Fundamental conservation and rheological law for viscoplastic Bingham fluids are enforced in mathematical modeling. Due to the complexity of the representative equations, an effective computing strategy based on the finite element approach is used. At an extra-fine level, a hybrid computational grid is created; a very refined level is used to obtain results with higher accuracy. The solution has been approximated using P2 − P1 elements based on the shape functions of the second and first-order polynomial polynomials. The parametric variables are ornamented against graphical trends. In addition, velocity, pressure plots, and line graphs have been provided for a better physical understanding of the situation Furthermore, the hydrodynamic benchmark quantities such as pressure drop, drag, and lift coefficients are assessed in a tabular manner around the external surface of the obstacle. The research predicts the effects of Bingham number (Bn) on the drag and lift coefficients on all three grids C1, C2, and C3, showing that the drag has lower values on the obstacle in the C2 grid compared with C1 and C3 for all values of Bn. Plug zone dominates in the channel downstream of the obstacle with augmentation in Bn, limiting the shear zone in the vicinity of the obstacle.

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“…Many papers are devoted to the study of Bingham fluids both from a theoretical and a practical point of view. Existence of weak solutions for the system governing the motion is investigated in [3], studies nonlinear stability of Poiseuille flow in pipes and plane channels in [4], spatial decay estimates are obtained for the problem of entry flow in a pipe in [5], and Couette-Poiseuille flow in a porous channel is studied with slip conditions in [6]. Some papers deal with the convective flow of a Bingham fluid in a vertical channel: the natural convection is studied in [7] for the Couette-Poiseuille flow and in [8,9] for the Poiseuille flow, the effect of internal and external heating on the free convective flow in a porous channel is investigated using Pascal's piecewise-linear law in [10], and the mixed convection is analyzed in [11].…”

Section: Introductionmentioning

confidence: 99%

Magnetohydrodynamic Flow of a Bingham Fluid in a Vertical Channel: Mixed Convection

Borrelli

Giantesio

Patria

2021

Fluids

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In this paper, we describe our study of the mixed convection of a Boussinesquian Bingham fluid in a vertical channel in the absence and presence of an external uniform magnetic field normal to the walls. The velocity, the induced magnetic field, and the temperature are analytically obtained. A detailed analysis is conducted to determine the plug regions in relation to the values of the Bingham number, the buoyancy parameter, and the Hartmann number. In particular, the velocity decreases as the Bingham number increases. Detailed considerations are drawn for the occurrence of the reverse flow phenomenon. Moreover, a selected set of diagrams illustrating the influence of various parameters involved in the problem is presented and discussed.

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Existence of weak solutions for a Bingham fluid-rigid body system

Cited by 5 publications

References 51 publications

A Class of Variational–Hemivariational Inequalities for Bingham Type Fluids

A Class of Variational–Hemivariational Inequalities for Bingham Type Fluids

Computational Analysis of Fluid Forces on an Obstacle in a Channel Driven Cavity: Viscoplastic Material Based Characteristics

Magnetohydrodynamic Flow of a Bingham Fluid in a Vertical Channel: Mixed Convection

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