Tresca Boundary Conditions Research Articles

Stokes flow with Tresca boundary condition: a posteriori error analysis

Stokes flow with Tresca boundary condition: a posteriori error analysis

A coupled model of the fluid flow with nonlinear slip Tresca boundary condition

In this article, we consider the finite element discretization of the time-dependent Stokes equations written under the Boussinesq approximation, coupled with the convection-diffusion equation and provided with Tresca's Friction Law. Existence and uniqueness of a solution are established. To solve Stokes variational inequality, we suggest an alternating direction method of multiplier. We derive some a priori estimates and validate the obtained theoretical results by numerical simulations.

STUDY OF THE VISCOELASTIC PROBLEMS WITH SHORT MEMORY IN A THIN DOMAIN WITH TRESCA BOUNDARY CONDITIONS

In this paper, we are interested in the study of the asymptotic behavior of non linear problem in a quasistatic regime in a thin domain with Tresca boundary conditions. In the first step, we derive a variational formulation of the mechanical problem and prove the existence and uniqueness of the weak solution. We study the limit when the ε tends to zero, we prove the convergence of the unknowns which are the displacement and the velocity and we obtain the limit problem and the specific Reynolds equation.

Unsteady flow of Bingham fluid in a thin layer with mixed boundary conditions

"In this paper we consider the dynamic system for Bingham fluid in a three-dimensional thin domain with Fourier and Tresca boundary condition. We study the existence and uniqueness results for the weak solution, then we establish its asymptotic behavior, when the depth of the thin domain tends to zero. This study yields a mechanical laws that give a new description of the behavior this system."

Existence of contacts for the motion of a rigid body into a viscous incompressible fluid with the Tresca boundary conditions

We consider a fluid-structure interaction system composed by a rigid ball immersed into a viscous in-compressible fluid. The motion of the structure satisfies the Newton laws and the fluid equations are the standard Navier-Stokes system. At the boundary of the fluid domain, we use the Tresca boundary conditions, that permit the fluid to slip tangentially on the boundary under some conditions on the stress tensor. More precisely, there is a threshold determining if the fluid can slip or not and there is a friction force acting on the part where the fluid can slip. Our main result is the existence of contact in finite time between the ball and the exterior boundary of the fluid for this system in the bidimensional case and in presence of gravity.

Asymptotic Behavior of Solutions to Free Boundary Problem with Tresca Boundary Conditions

In this paper, we study the asymptotic behavior of an incompressible Herschel-Bulkley fluid in a thin domain with Tresca boundary conditions. We study the limit when the ε tends to zero, we prove the convergence of the unknowns which are the velocity and the pressure of the fluid, and we obtain the limit problem and the specific Reynolds equation.

Asymptotic Convergence of a Generalized Non-Newtonian Fluid with Tresca Boundary Conditions

The goal of this article is to study the asymptotic analysis of an incompressible Herschel-Bulkley fluid in a thin domain with Tresca boundary conditions. The yield stress and the constant viscosity are assumed to vary with respect to the thin layer parameter e. Firstly, the problem statement and variational formulation are formulated. We then obtained the existence and the uniqueness result of a weak solution and the estimates for the velocity field and the pressure independently of the parameter e. Finally, we give a specific Reynolds equation associated with variational inequalities and prove the uniqueness.

Study of Stokes dynamical system in a thin domain with Fourier and Tresca boundary conditions

Asymptotic analysis of an incompressible Stokes fluid in a dynamic regime in a three-dimensional thin domain [Formula: see text] with mixed boundary conditions and Tresca friction law is studied in this paper. The problem statement and variational formulation of the problem are reformulated in a fixed domain. In which case, the estimates on velocity and pressure are proved. These estimates will be useful in order to give a specific Reynolds equation associated with variational inequalities and prove the uniqueness.

Stokes Problem with Slip Boundary Conditions of Friction Type: Error Analysis of a Four-Field Mixed Variational Formulation

In this work, a finite element approximation of the Stokes problem under a slip boundary condition of friction type, known as the Tresca boundary condition, is considered. We treat the approximate problem of a four field mixed formulation using the $${\mathbb {P}}^{1}$$ -bubble element for the velocity field, $${\mathbb {P}}^{1}$$ element for the pressure field and the $${\mathbb {P}}^{1}$$ element for the Lagrange multipliers $$\lambda _{n}$$ and $$\lambda _{t}$$ defined on the slip boundary. The multiplier $$\lambda _{t}$$ is introduced to regularize the non-differentiable problem, whereas $$\lambda _{n}$$ treats the impermeability condition. Existence and uniqueness results for both continuous and discrete problems are proven and an a priori error estimate is established. Numerical realization of such problem is discussed and some numerical tests are provided.

About new models of slip/no-slip boundary condition in thin film flows

The behaviour of a thin fluid film with a new slip/no slip model (The double parameter slip DPS) on a part of the boundary is studied. From the Stokes equations, the convergence of the velocity, pressure and wall-stress is established. The limit problem is described in terms of a new Reynolds equation involving shear stress and associated with a variational equation. Existence and uniqueness are proved. Relation with the previously known thin film problem with Tresca boundary condition is highlighted. A numerical algorithm is proposed and numerical examples are given.

Asymptotic behavior of solutions to a boundary value problem with mixed boundary conditions and friction law

In this paper, we consider a non-linear problem in a stationary regime in a three-dimensional thin domain Omega^{varepsilon} with Fourier and Tresca boundary conditions. In the first step, we derive a variational formulation of the mechanical problem. We then study the asymptotic behavior in the one dimension case when the domain parameter tends to zero. In the latter case, a specific Reynolds equation associated with variational inequalities is obtained and the uniqueness of the limit velocity and pressure are proved.

Asymptotic Analysis of a Bingham Fluid in a Thin Domain with Fourier and Tresca Boundary Conditions

In this paper we prove first the existence and uniqueness results for the weak solution, to the stationary equations for Bingham fluid in a three dimensional bounded domain with Fourier and Tresca boundary condition; then we study the asymptotic analysis when one dimension of the fluid domain tend to zero. The strong convergence of the velocity is proved, a specific Reynolds limit equation and the limit of Tresca free boundary conditions are obtained.

Asymptotic Analysis of a Bingham Fluid in a Thin Domain with Fourier and Tresca Boundary Conditions

AbstractIn this paper we prove first the existence and uniqueness results for the weak solution, to the stationary equations for Bingham fluid in a three dimensional bounded domain with Fourier and Tresca boundary condition; then we study the asymptotic analysis when one dimension of the fluid domain tend to zero. The strong convergence of the velocity is proved, a specific Reynolds limit equation and the limit of Tresca free boundary conditions are obtained.

Experimental and FEM-supported investigation of wet ceramic clay extrusion for the determination of stress distributions on the applied tools’ surfaces

Aiming at assessing the stress distribution on the surface of a die mandrel during the extrusion of ceramic products, the flow of wet ground clay was simulated both in a ram extrusion device and by a FEM-based model, considering the von Mises criterion for the flow stress, the associative flow rule and the rigid–viscoplastic constitutive equation. The friction between clay and die is approached by the Tresca boundary condition, which proves a more realistic approach than the Coulomb friction law for the contact conditions between a plastically deforming material and a rigid surface. The Tresca friction factor and the material parameters of the constitutive model are determined through comparison of experimental and theoretical results. The distributions of clay sliding velocity and normal and frictional stress on the mandrel surface are then assessed through the numerical simulation model. It is found that no sticking areas appear on the mandrel surface.

ON A LUBRICATION PROBLEM WITH FOURIER AND TRESCA BOUNDARY CONDITIONS

The asymptotic behavior of a Stokes flow with Fourier boundary condition on one part on the boundary and Tresca free boundary friction condition on the other, when one dimension of the fluid domain tends to zero is studied. The strong convergence of the velocity is proved, a specific Reynolds equation is obtained, and the uniqueness of the limit velocity and pressure distributions is established.

On a free boundary problem for the Reynolds equation derived from the Stokes system with Tresca boundary conditions

The asymptotic behaviour of a Stokes flow with Tresca free boundary friction conditions when one dimension of the fluid domain tends to zero is studied. A specific Reynolds equation associated with variational inequalities is obtained and uniqueness is proved.