Open AccessResolution of Time-Dependent Navier-Stokes Equations with a new Boundary Condition
Publication year - 2020
Publication title -
international journal of mathematics and computers in simulation
Language(s) - English
Resource type - Journals
ISSN - 1998-0159
DOI - 10.46300/9102.2020.14.22
Subject(s) - discretization , backward euler method , mathematics , nonlinear system , finite element method , numerical analysis , generalized minimal residual method , euler equations , a priori and a posteriori , boundary value problem , adina , boundary (topology) , mathematical analysis , linear system , philosophy , physics , epistemology , quantum mechanics , thermodynamics
In this work, a numerical solution of the unsteady incompressible Navier- Stokes equations with a new boundary condition is proposed. The method suggested is based on an algorithm of discretization by finite element method in space and the Euler full-implicit scheme in time. The matrix system is solved at each iteration with a preconditioned GMRES method. Also, we proposed two types of a posteriori error indicator, with one being for the time discretization and the other for the space discretization. We prove the equivalence between the sum of the two types of error indicators and the full error. In order to evaluate the performance of the method, the numerical results of two-dimensional backward-facing step flow are compared with some previously published works or with others coming from commercial code like ADINA (Automatic Dynamic Incremental Nonlinear Analysis) system.