All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 32 Next

Displaying 621 – 640 of 819

Showing per page

Spectral discretization of Darcy equations coupled with Navier-Stokes equations by vorticity-velocity-pressure formulation

Yassine Mabrouki, Jamil Satouri (2022)

Applications of Mathematics

We consider a model coupling the Darcy equations in a porous medium with the Navier-Stokes equations in the cracks, for which the coupling is provided by the pressure's continuity on the interface. We discretize the coupled problem by the spectral element method combined with a nonoverlapping domain decomposition method. We prove the existence of solution for the discrete problem and establish an error estimation. We conclude with some numerical tests confirming the results of our analysis.

Spectral element discretization of the vorticity, velocity and pressure formulation of the Stokes problem

Karima Amoura, Christine Bernardi, Nejmeddine Chorfi (2006)

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

We consider the Stokes problem provided with non standard boundary conditions which involve the normal component of the velocity and the tangential components of the vorticity. We write a variational formulation of this problem with three independent unknowns: the vorticity, the velocity and the pressure. Next we propose a discretization by spectral element methods which relies on this formulation. A detailed numerical analysis leads to optimal error estimates for the three unknowns and numerical...

Spectral element discretization of the vorticity, velocity and pressure formulation of the Stokes problem

Karima Amoura, Christine Bernardi, Nejmeddine Chorfi (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider the Stokes problem provided with non standard boundary conditions which involve the normal component of the velocity and the tangential components of the vorticity. We write a variational formulation of this problem with three independent unknowns: the vorticity, the velocity and the pressure. Next we propose a discretization by spectral element methods which relies on this formulation. A detailed numerical analysis leads to optimal error estimates for the three unknowns and numerical...

Stabilité et asymptotique en temps grand de solutions globales des équations de Navier-Stokes

Isabelle Gallagher, Dragoş Iftimie, Fabrice Planchon (2002)

Journées équations aux dérivées partielles

We study a priori global strong solutions of the incompressible Navier-Stokes equations in three space dimensions. We prove that they behave for large times like small solutions, and in particular they decay to zero as time goes to infinity. Using that result, we prove a stability theorem showing that the set of initial data generating global solutions is open.

Stability for a certain class of numerical methods – abstract approach and application to the stationary Navier-Stokes equations

Elżbieta Motyl (2012)

Annales de la faculté des sciences de Toulouse Mathématiques

We consider some abstract nonlinear equations in a separable Hilbert space H and some class of approximate equations on closed linear subspaces of H . The main result concerns stability with respect to the approximation of the space H . We prove that, generically, the set of all solutions of the exact equation is the limit in the sense of the Hausdorff metric over H of the sets of approximate solutions, over some filterbase on the family of all closed linear subspaces of H . The abstract results are...

Stability of a finite element method for 3D exterior stationary Navier-Stokes flows

Paul Deuring (2007)

Applications of Mathematics

We consider numerical approximations of stationary incompressible Navier-Stokes flows in 3D exterior domains, with nonzero velocity at infinity. It is shown that a P1-P1 stabilized finite element method proposed by C. Rebollo: A term by term stabilization algorithm for finite element solution of incompressible flow problems, Numer. Math. 79 (1998), 283–319, is stable when applied to a Navier-Stokes flow in a truncated exterior domain with a pointwise boundary condition on the artificial boundary....

Stability of Constant Solutions to the Navier-Stokes System in ℝ³

Piotr Bogusław Mucha (2001)

Applicationes Mathematicae

The paper examines the initial value problem for the Navier-Stokes system of viscous incompressible fluids in the three-dimensional space. We prove stability of regular solutions which tend to constant flows sufficiently fast. We show that a perturbation of a regular solution is bounded in W r 2 , 1 ( ℝ ³ × [ k , k + 1 ] ) for k ∈ ℕ. The result is obtained under the assumption of smallness of the L₂-norm of the perturbing initial data. We do not assume smallness of the W r 2 - 2 / r ( ℝ ³ ) -norm of the perturbing initial data or smallness of the...

Stability of oscillating boundary layers in rotating fluids

Nader Masmoudi, Frédéric Rousset (2008)

Annales scientifiques de l'École Normale Supérieure

We prove the linear and non-linear stability of oscillating Ekman boundary layers for rotating fluids in the so-called ill-prepared case under a spectral hypothesis. Here, we deal with the case where the viscosity and the Rossby number are both equal to ε . This study generalizes the study of [23] where a smallness condition was imposed and the study of [26] where the well-prepared case was treated.

Stability with respect to domain of the low Mach number limit of compressible heat-conducting viscous fluid

Aneta Wróblewska-Kamińska (2023)

Archivum Mathematicum

We investigate the asymptotic limit of solutions to the Navier-Stokes-Fourier system with the Mach number proportional to a small parameter ε → 0 , the Froude number proportional to ε and when the fluid occupies large domain with spatial obstacle of rough surface varying when ε → 0 . The limit velocity field is solenoidal and satisfies the incompressible Oberbeck–Boussinesq approximation. Our studies are based on weak solutions approach and in order to pass to the limit in a convective term we apply the spectral...

Stationary states and moving planes

Gerhard Ströhmer (2008)

Banach Center Publications

Most of the paper deals with the application of the moving plane method to different questions concerning stationary accumulations of isentropic gases. The first part compares the concepts of stationarity arising from the points of view of dynamics and the calculus of variations. Then certain stationary solutions are shown to be unstable. Finally, using the moving plane method, a short proof of the existence of energy-minimizing gas balls is given.

Steady compressible Navier-Stokes-Fourier system in two space dimensions

Petra Pecharová, Milan Pokorný (2010)

Commentationes Mathematicae Universitatis Carolinae

We study steady flow of a compressible heat conducting viscous fluid in a bounded two-dimensional domain, described by the Navier-Stokes-Fourier system. We assume that the pressure is given by the constitutive equation p ( ρ , θ ) ∼ ρ γ + ρ θ , where ρ is the density and θ is the temperature. For γ > 2 , we prove existence of a weak solution to these equations without any assumption on the smallness of the data. The proof uses special approximation of the original problem, which guarantees the pointwise boundedness of the...

Steady compressible Oseen flow with slip boundary conditions

Tomasz Piasecki (2009)

Banach Center Publications

We prove the existence of solution in the class H²(Ω) × H¹(Ω) to the steady compressible Oseen system with slip boundary conditions in a two dimensional, convex domain with boundary of class H 5 / 2 . The method is to regularize a weak solution obtained via the Galerkin method. The problem of regularization is reduced to the problem of solvability of a certain transport equation by application of the Helmholtz decomposition. The method works under an additional assumption on the geometry of the boundary....

Currently displaying 621 – 640 of 819