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A Quasi-Newton Algorithm Based on a Reduced Model for Fluid-Structure Interaction Problems in Blood Flows

Jean-Frédéric Gerbeau, Marina Vidrascu (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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...

A remark on the existence of steady Navier-Stokes flows in 2D semi-infinite channel involving the general outflow condition

H. Morimoto, H. Fujita (2001)

Mathematica Bohemica

We consider the steady Navier-Stokes equations in a 2-dimensional unbounded multiply connected domain Ω under the general outflow condition. Let T be a 2-dimensional straight channel ℝ × ( - 1 , 1 ) . We suppose that Ω ∩ { x 1 < 0 } is bounded and that Ω ∩ { x 1 > - 1 } = T ∩ { x 1 > - 1 } . Let V be a Poiseuille flow in T and μ the flux of V . We look for a solution which tends to V as x 1 → ∞ . Assuming that the domain and the boundary data are symmetric with respect to the x 1 -axis, and that the axis intersects every component of the boundary, we have shown the existence...

A review on the improved regularity for the primitive equations

Francisco Guillén-González, María Ángeles Rodríguez-Bellido (2005)

Banach Center Publications

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.

A Sobolev gradient method for treating the steady-state incompressible Navier-Stokes equations

Robert Renka (2013)

Open Mathematics

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.

A splitting method using discontinuous Galerkin for the transient incompressible Navier-Stokes equations

Vivette Girault, Béatrice Rivière, Mary F. Wheeler (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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.

A splitting method using discontinuous Galerkin for the transient incompressible Navier-Stokes equations

Vivette Girault, Béatrice Rivière, Mary F. Wheeler (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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.

A stabilized finite element scheme for the Navier-Stokes equations on quadrilateral anisotropic meshes

Malte Braack (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

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...

A unified convergence analysis for local projection stabilisations applied to the Oseen problem

Gunar Matthies, Piotr Skrzypacz, Lutz Tobiska (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

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 for the solution of the stationary Navier-Stokes equations

Giovanni Prouse (1989)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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.

Currently displaying 41 – 60 of 97