scholarly journals Finite Element Discretization in Shape Optimization Problems for the Stationary Navier-Stokes Equation

2013 ◽  
pp. 437-444
Author(s):  
Dan Tiba
Keyword(s):  
Finite Element ◽  
Shape Optimization ◽  
Stokes Equation ◽  
Optimization Problems ◽  
Navier Stokes ◽  
Finite Element Discretization ◽  
Navier Stokes Equation ◽  
Element Discretization

scholarly journals Shape Optimization by Pursuing Diffeomorphisms

2015 ◽  
Vol 15 (3) ◽  
pp. 291-305 ◽  
Author(s):  
Ralf Hiptmair ◽  
Alberto Paganini
Keyword(s):  
Finite Element ◽  
Shape Optimization ◽  
Optimization Problems ◽  
Approximation Properties ◽  
The Finite Element Method ◽  
Finite Element Discretization ◽  
Element Discretization ◽  
B Spline ◽  
Ill Posed ◽  
Well Posed

AbstractWe consider PDE constrained shape optimization in the framework of finite element discretization of the underlying boundary value problem. We present an algorithm tailored to preserve and exploit the approximation properties of the finite element method, and that allows for arbitrarily high resolution of shapes. It employs (i) B-spline based representations of the deformation diffeomorphism, and (ii) superconvergent domain integral expressions for the shape gradient. We provide numerical evidence of the performance of this method both on prototypical well-posed and ill-posed shape optimization problems.

scholarly journals AUTOMATIC INSERTION OF A TURBULENCE MODEL IN THE FINITE ELEMENT DISCRETIZATION OF THE NAVIER–STOKES EQUATIONS

2009 ◽  
Vol 19 (07) ◽  
pp. 1139-1183 ◽  
Author(s):  
CHRISTINE BERNARDI ◽  
TOMÁS CHACÓN REBOLLO ◽  
FRÉDÉRIC HECHT ◽  
ROGER LEWANDOWSKI
Keyword(s):  
Finite Element ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Stokes Equations ◽  
A Posteriori Error Estimates ◽  
Navier Stokes ◽  
Mesh Adaptivity ◽  
Finite Element Discretization ◽  
Navier Stokes Equations ◽  
Element Discretization

We consider the finite element discretization of the Navier–Stokes equations locally coupled with the equation for the turbulent kinetic energy through an eddy viscosity. We prove a posteriori error estimates which allow to automatically determine the zone where the turbulent kinetic energy must be inserted in the Navier–Stokes equations and also to perform mesh adaptivity in order to optimize the discretization of these equations. Numerical results confirm the interest of such an approach.

scholarly journals Numerical solution of Navier stokes equation using control volume and finite element method

2016 ◽  
Vol 5 (1) ◽  
pp. 63
Author(s):  
Musa Adam Aigo
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Solution ◽  
Stokes Equation ◽  
Control Volume ◽  
Navier Stokes ◽  
Weak Formulation ◽  
Navier Stokes Equation ◽  
Fast Solution ◽  
Element Method

<p>The aim of this paper is twofold first we will  provide a numerical solution of the Navier Stokes equation using the Projection technique and finite element method. The problem will be introduced in weak formulation and a Finite Element method will be developed, then solve in a fast way the sparse system derived. Second, the projection method with Control volume approach will be applied to get a fast solution, in iterations count.</p>

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