Abstract
in this work, we introduce the unsteady incompressible Navier-Stokes equations with a new boundary condition, generalizes the Dirichlet and the Neumann conditions. Then we derive an adequate variational formulation of time-dependent Navier- Stokes equations. We then prove the existence theorem and a uniqueness result. A Mixed finite-element discretization is used to generate the nonlinear system corresponding to the Navier-Stokes equations. The solution of the linearized system is carried out using the GMRES method. In order to evaluate the performance of the method, the numerical results are compared with others coming from commercial code like Adina system.
Highlights
We offer a choice of twodimensional domains on which the problem can be posed, along with boundary conditions and other aspects of the problem, and a choice of finite element discretizations on a quadrilateral element mesh, whereas the discrete NavierStokes equations require a method such as the generalized minimum residual method (GMRES), which is designed for non symmetric systems [9, 19]
Mixed finite element discretization of the weak formulation of the Navier- Stokes equations gives rise to a nonlinear system of algebraic equations
These features clearly demonstrate the high accuracy achieved by the proposed mixed finite element method for solving the unsteady Navier-Stokes equations in the lid-driven squared cavity
Summary
This paper presents the unsteady Navier-Stocks equations with a new boundary condition noted by. This condition generalizes the known conditions, especially the conditions of Dirichlet, Neumann. We prove that the weak formulation of the proposed modeling has a unique solution. To calculate this latter, we use the discretization by mixed finite element method.
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