Navier-Stokes/Darcy coupling: modeling, analysis, and numerical approximation.
New wall laws for the unsteady incompressible Navier-Stokes equations on rough domains
Different effective boundary conditions or wall laws for unsteady incompressible Navier-Stokes equations over rough domains are derived in the laminar setting. First and second order unsteady wall laws are proposed using two scale asymptotic expansion techniques. The roughness elements are supposed to be periodic and the influence of the rough boundary is incorporated through constitutive constants. These constants are obtained by solving steady Stokes problems and so they are calculated only once....
New Wall Laws for the Unsteady Incompressible Navier-Stokes Equations on Rough Domains
Different effective boundary conditions or wall laws for unsteady incompressible Navier-Stokes equations over rough domains are derived in the laminar setting. First and second order unsteady wall laws are proposed using two scale asymptotic expansion techniques. The roughness elements are supposed to be periodic and the influence of the rough boundary is incorporated through constitutive constants. These constants are obtained by solving steady Stokes problems and so they are calculated only...
Non-matching mortar discretization analysis for the coupling Stokes-Darcy equations.
Numerical algorithm for the stationary, nonhomogeneous Navier-Stokes equations.
Numerical analysis of Euler-SUPG modified method for transient viscoelastic flow.
Numerical analysis of the Navier-Stokes equations
This paper discusses some conceptional questions of the numerical simulation of viscous incompressible flow which are related to the presence of boundaries.
Numerical approximation of nematic liquid crystal flows governed by the Ericksen-Leslie equations
Numerical approximation of the flow of liquid crystals governed by the Ericksen-Leslie equations is considered. Care is taken to develop numerical schemes which inherit the Hamiltonian structure of these equations and associated stability properties. For a large class of material parameters compactness of the discrete solutions is established which guarantees convergence.
Numerical approximation of nematic liquid crystal flows governed by the Ericksen-Leslie equations*
Numerical approximation of the flow of liquid crystals governed by the Ericksen-Leslie equations is considered. Care is taken to develop numerical schemes which inherit the Hamiltonian structure of these equations and associated stability properties. For a large class of material parameters compactness of the discrete solutions is established which guarantees convergence.
Numerical approximations of the relative rearrangement : the piecewise linear case. Application to some nonlocal problems
Numerical Approximations of the Relative Rearrangement: The piecewise linear case. Application to some Nonlocal Problems
We first prove an abstract result for a class of nonlocal problems using fixed point method. We apply this result to equations revelant from plasma physic problems. These equations contain terms like monotone or relative rearrangement of functions. So, we start the approximation study by using finite element to discretize this nonstandard quantities. We end the paper by giving a numerical resolution of a model containing those terms.
Numerical homogenization of well singularities in the flow transport through heterogeneous porous media: fully discrete scheme
Motivated by well-driven flow transport in porous media, Chen and Yue proposed a numerical homogenization method for Green function [Multiscale Model. Simul.1 (2003) 260–303]. In that paper, the authors focused on the well pore pressure, so the local error analysis in maximum norm was presented. As a continuation, we will consider a fully discrete scheme and its multiscale error analysis on the velocity field.
Numerical methods for fourth order nonlinear degenerate diffusion problems
Numerical schemes are presented for a class of fourth order diffusion problems. These problems arise in lubrication theory for thin films of viscous fluids on surfaces. The equations being in general fourth order degenerate parabolic, additional singular terms of second order may occur to model effects of gravity, molecular interactions or thermocapillarity. Furthermore, we incorporate nonlinear surface tension terms. Finally, in the case of a thin film flow driven by a surface active agent (surfactant),...
Numerical simulation of a pulsatile flow through a flexible channel
An algorithm for approximation of an unsteady fluid-structure interaction problem is proposed. The fluid is governed by the Navier-Stokes equations with boundary conditions on pressure, while for the structure a particular plate model is used. The algorithm is based on the modal decomposition and the Newmark Method for the structure and on the Arbitrary lagrangian Eulerian coordinates and the Finite Element Method for the fluid. In this paper, the continuity of the stresses at the interface was...
Numerical simulation of a pulsatile flow through a flexible channel
An algorithm for approximation of an unsteady fluid-structure interaction problem is proposed. The fluid is governed by the Navier-Stokes equations with boundary conditions on pressure, while for the structure a particular plate model is used. The algorithm is based on the modal decomposition and the Newmark Method for the structure and on the Arbitrary Lagrangian Eulerian coordinates and the Finite Element Method for the fluid. In this paper, the continuity of the stresses at the interface...
Numerical simulation of a viscoelastic fluid with a preconditioned Schwarz method
In this paper we apply a domain decomposition method to approach the solution of a non-Newtonian viscoelastic Oldroyd-B model. The numerical scheme is based on a fixed-point argument applied to the original non-linear system of partial differential equations decoupled into a Navier-Stokes system and a tensorial transport equation. Using a modified Schwarz algorithm, involving block preconditioners for the Navier-Stokes equations, the decoupled problems are solved iteratively. Numerical simulations...
Numerical simulation of suspension induced rheology
Flow of particles suspended in a fluid can be found in numerous industrial processes utilizing sedimentation, fluidization and lubricated transport such as food processing, catalytic processing, slurries, coating, paper manufacturing, particle injection molding and filter operation. The ability to understand rheology effects of particulate flows is elementary for the design, operation and efficiency of the underlying processes. Despite the fact that particle technology is widely used, it is still...
Numerical simulation of the motion of a three-dimensional glacier
The motion of a three-dimensional glacier is considered. Ice is modeled as an incompressible non-Newtonian fluid. At each time step, given the shape of the glacier, a nonlinear elliptic system has to be solved in order to obtain the two components of the horizontal velocity field. Then, the shape of the glacier is updated by solving a transport equation. Finite element techniques are used to compute the velocity field and to solve the transport equation. Numerical results are compared to experiments...
Numerical solution of compressible flow
Numerical study of a descending sphere in a low Reynolds number strongly stratified fluid.