Anhp adaptive strategy for finite element approximations of the Navier-Stokes equations

1995 ◽  
Vol 20 (8-9) ◽  
pp. 831-851 ◽  
Author(s):  
J. Tinsley Oden ◽  
Weihan Wu ◽  
Vincent Legat
Keyword(s):  
Finite Element ◽  
Stokes Equations ◽  
Adaptive Strategy ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Finite Element Approximations

FINITE ELEMENT ERROR ANALYSIS OF SPACE AVERAGED FLOW FIELDS DEFINED BY A DIFFERENTIAL FILTER

2004 ◽  
Vol 14 (04) ◽  
pp. 603-618 ◽  
Author(s):  
ADRIAN DUNCA ◽  
VOLKER JOHN
Keyword(s):  
Finite Element ◽  
Stokes Equations ◽  
Finite Element Approximation ◽  
Flow Fields ◽  
Navier Stokes ◽  
Element Approximation ◽  
Navier Stokes Equations ◽  
Finite Element Approximations ◽  
Three Space ◽  
Element Error

This paper analyzes finite element approximations of space averaged flow fields which are given by filtering, i.e. averaging in space, the solution of the steady state Stokes and Navier–Stokes equations with a differential filter. It is shown that [Formula: see text], the error of the filtered velocity [Formula: see text] and the filtered finite element approximation of the velocity [Formula: see text], converges under certain conditions of higher order than [Formula: see text], the error of the velocity and its finite element approximation. It is also proved that this statement stays true if the L2-error of finite element approximations of [Formula: see text] and [Formula: see text] is considered. Numerical tests in two and three space dimensions support the analytical results.

scholarly journals On mathematical modelling of aeroelastic problems with finite element method

2018 ◽  
Vol 180 ◽  
pp. 02104
Author(s):  
Petr Sváček
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Small Displacement ◽  
Structure Model ◽  
Navier Stokes Equations ◽  
Aeroelastic Response ◽  
Finite Element Approximations ◽  
Element Method

This paper is interested in solution of two-dimensional aeroelastic problems. Two mathematical models are compared for a benchmark problem. First, the classical approach of linearized aerodynamical forces is described to determine the aeroelastic instability and the aeroelastic response in terms of frequency and damping coefficient. This approach is compared to the coupled fluid-structure model solved with the aid of finite element method used for approximation of the incompressible Navier-Stokes equations. The finite element approximations are coupled to the non-linear motion equations of a flexibly supported airfoil. Both methods are first compared for the case of small displacement, where the linearized approach can be well adopted. The influence of nonlinearities for the case of post-critical regime is discussed.

Finite element analyses of flow in a cavity with internal blockages

2002 ◽  
Vol 216 (5) ◽  
pp. 517-530 ◽  
Author(s):  
O B Fawehinmi ◽  
P H Gaskell ◽  
H M Thompson
Keyword(s):  
Finite Element ◽  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Finite Element Approximations ◽  
Stagnation Points ◽  
Advantages And Disadvantages ◽  
The Rich ◽  
Reported Data

Although studies of flows in cavities without internal blockages are extremely common, those in which blockages arise are correspondingly rare. The present work describes a numerical study of one such flow using two complementary finite element approximations to the governing Navier-Stokes equations. Two formulations are adopted: the first employs a streamfunction-vorticity representation that has proven effective in elucidating fine flow detail in related cavity flows while the second is expressed in terms of primitive variables. The advantages and disadvantages of each formulation in relation to ease of application of boundary conditions and efficiency of numerical solution are compared and contrasted. In both cases, results for the chosen test problem are found to be in excellent agreement and reveal that previously reported data for this problem are in error. Moreover, results are presented that demonstrate the rich variety of flow patterns, recirculation regions and stagnation points that can arise as the cavity geometry and external wall speeds are varied.

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