Numerical methods for the Stokes and Navier-Stokes equations driven by threshold slip boundary conditions
نویسندگان
چکیده
In this article, we discuss the numerical solution of the Stokes and Navier-Stokes equations completed by nonlinear slip boundary conditions of friction type in two and three dimensions. To solve the Stokes system, we first reduce the related variational inequality into a saddle point-point problem for a well chosen augmented Lagrangian. To solve this saddle point problem we suggest an alternating direction method of multiplier together with finite element approximations. The solution of the Navier Stokes system combines finite element approximations, time discretization by operator splitting and augmented Lagrangian method. Numerical experiment results for two and three dimensional flow confirm the interest of these approaches.
منابع مشابه
A comparative study between two numerical solutions of the Navier-Stokes equations
The present study aimed to investigate two numerical solutions of the Navier-Stokes equations. For this purpose, the mentioned flow equations were written in two different formulations, namely (i) velocity-pressure and (ii) vorticity-stream function formulations. Solution algorithms and boundary conditions were presented for both formulations and the efficiency of each formulation was investiga...
متن کاملFinite Element Analysis for Stokes and Navier-stokes Equations Driven by Threshold Slip Boundary Conditions
This paper is devoted to the study of finite element approximations of variational inequalities with a special nonlinearity coming from boundary conditions. After re-writing the problems in the form of variational inequalities, a fixed point strategy is used to show existence of solutions. Next we prove that the finite element approximations for the Stokes and Navier Stokes equations converge r...
متن کاملOn the Time Approximation of the Stokes Equations with Nonlinear Slip Boundary Conditions
This work is concerned with the numerical approximation of the unsteady Stokes flow of a viscous incompressible fluid driven by a threshold slip boundary condition of friction type. The continuous problem is formulated as variational inequality, which is next discretize in time based on backward Euler’s scheme. We prove existence and uniqueness of the solution of the time discrete problem by me...
متن کاملSlip with friction and penetration with resistance boundary conditions for the Navier–Stokes equations—numerical tests and aspects of the implementation
We consider slip with friction and penetration with resistance boundary conditions in the steady state Navier– Stokes equations. This paper describes some aspects of the implementation of these boundary conditions for /nite element discretizations. Numerical tests on twoand three-dimensional channel 2ows across a step using the slip with friction boundary condition study the in2uence of the fri...
متن کاملOptimization with the time-dependent Navier-Stokes equations as constraints
In this paper, optimal distributed control of the time-dependent Navier-Stokes equations is considered. The control problem involves the minimization of a measure of the distance between the velocity field and a given target velocity field. A mixed numerical method involving a quasi-Newton algorithm, a novel calculation of the gradients and an inhomogeneous Navier-Stokes solver, to find the opt...
متن کامل