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We propose a quasi-Newton algorithm for solving
fluid-structure interaction problems. The basic idea of the method is
to build an approximate tangent operator which is cost effective and
which takes into account the so-called added mass effect.
Various test cases show that the method allows a significant reduction
of the computational effort compared to relaxed fixed point
algorithms. We present 2D and 3D fluid-structure simulations performed
either with a simple 1D structure model or with...
We prove a regularity criterion for micropolar fluid flows in terms of one partial derivative of the velocity in a Morrey-Campanato space.
The incompressible three-dimensional Navier-Stokes equations are considered. A new regularity criterion for weak solutions is established in terms of the pressure gradient.
We consider the steady Navier-Stokes equations in a 2-dimensional unbounded multiply connected domain under the general outflow condition. Let be a 2-dimensional straight channel . We suppose that is bounded and that . Let be a Poiseuille flow in and the flux of . We look for a solution which tends to as . Assuming that the domain and the boundary data are symmetric with respect to the -axis, and that the axis intersects every component of the boundary, we have shown the existence...
In this work we will study some types of regularity properties of solutions for the geophysical model of hydrostatic Navier-Stokes equations, the so-called Primitive Equations (PE). Also, we will present some results about uniqueness and asymptotic behavior in time.
We review several regularity criteria for the Navier-Stokes equations and prove some new ones, containing different components of the velocity gradient.
The velocity-vorticity-pressure formulation of the steady-state incompressible Navier-Stokes equations in two dimensions is cast as a nonlinear least squares problem in which the functional is a weighted sum of squared residuals. A finite element discretization of the functional is minimized by a trust-region method in which the trustregion radius is defined by a Sobolev norm and the trust-region subproblems are solved by a dogleg method. Numerical test results show the method to be effective.
In this paper we solve the time-dependent incompressible Navier-Stokes equations by splitting the non-linearity and incompressibility, and using discontinuous or continuous finite element methods in space. We prove optimal error estimates for the velocity and suboptimal estimates for the pressure. We present some numerical experiments.
In this paper we solve the time-dependent incompressible Navier-Stokes
equations by splitting the non-linearity and incompressibility, and
using discontinuous or continuous finite element methods in space. We
prove optimal error estimates for the velocity and suboptimal
estimates for the pressure. We present some numerical experiments.
In this paper, a stability theorem of the Navier-Stokes flow past a rotating body is reported. Concerning the linearized problem, the proofs of the generation of a C₀ semigroup and its decay properties are sketched.
It is well known that the classical local projection
method as well as residual-based stabilization techniques, as for instance
streamline upwind Petrov-Galerkin (SUPG), are optimal on isotropic
meshes. Here we extend the local projection stabilization for the Navier-Stokes
system to anisotropic quadrilateral meshes in two spatial dimensions. We
describe the new method
and prove an a priori error estimate.
This method leads on anisotropic meshes to qualitatively better
convergence behavior...
The discretisation of the Oseen problem by finite element methods may suffer
in general from two shortcomings. First, the discrete inf-sup
(Babuška-Brezzi)
condition can be violated. Second, spurious oscillations
occur due to the dominating convection. One way to overcome both
difficulties is the use of local projection techniques. Studying
the local projection method in an abstract setting, we show that
the fulfilment of a local inf-sup condition between approximation and
projection spaces...
A uniqueness criterion is given for the weak solution of the Navier-Stokes equations in the stationary case. Precisely, it is proved that, for a generic known term, there exists one and only one solution such that the mechanical power of the corresponding flow is maximum and that this maximum is "stable" in an appropriate sense.
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