11,229 research outputs found
Reduced formulation of a steady fluid-structure interaction problem with parametric coupling
We propose a two-fold approach to model reduction of fluid-structure
interaction. The state equations for the fluid are solved with reduced basis
methods. These are model reduction methods for parametric partial differential
equations using well-chosen snapshot solutions in order to build a set of
global basis functions. The other reduction is in terms of the geometric
complexity of the moving fluid-structure interface. We use free-form
deformations to parameterize the perturbation of the flow channel at rest
configuration. As a computational example we consider a steady fluid-structure
interaction problem: an incmpressible Stokes flow in a channel that has a
flexible wall.Comment: 10 pages, 3 figure
On the stability of bubble functions and a stabilized mixed finite element formulation for the Stokes problem
In this paper we investigate the relationship between stabilized and enriched
finite element formulations for the Stokes problem. We also present a new
stabilized mixed formulation for which the stability parameter is derived
purely by the method of weighted residuals. This new formulation allows equal
order interpolation for the velocity and pressure fields. Finally, we show by
counterexample that a direct equivalence between subgrid-based stabilized
finite element methods and Galerkin methods enriched by bubble functions cannot
be constructed for quadrilateral and hexahedral elements using standard bubble
functions.Comment: 25 pages, 13 figures (The previous version was compiled by mistake
with the wrong style file, the current one uses amsart, and there is no
difference in the text or the figures
Continuation-conjugate gradient methods for the least squares solution of nonlinear boundary value problems
We discuss in this paper a new combination of methods for solving nonlinear boundary value problems containing a parameter. Methods of the continuation type are combined with least squares formulations, preconditioned conjugate gradient algorithms and finite element approximations.
We can compute branches of solutions with limit points, bifurcation points, etc.
Several numerical tests illustrate the possibilities of the methods discussed in the present paper; these include the Bratu problem in one and two dimensions, one-dimensional bifurcation and perturbed bifurcation problems, the driven cavity problem for the Navier–Stokes equations
Vector potential methods
Vector potential and related methods, for the simulation of both inviscid and viscous flows over aerodynamic configurations, are briefly reviewed. The advantages and disadvantages of several formulations are discussed and alternate strategies are recommended. Scalar potential, modified potential, alternate formulations of Euler equations, least-squares formulation, variational principles, iterative techniques and related methods, and viscous flow simulation are discussed
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