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Immersed boundary methods for the numerical simulation of incompressible aerodynamics and fluid-structure interactions

Nicolas James, Emmanuel Maitre, Iraj Mortazavi (2013)

Annales mathématiques Blaise Pascal

In this work three branches of Immersed Boundary Methods (IBM) are described and validated for incompressible aerodynamics and fluid-structure interactions. These three approaches are: Cut Cell method, Vortex-Penalization method and Forcing method. The first two techniques are validated for external bluff-body flow around a circular obstacle. The last one is used to predict the deformations of an elastic membrane immersed in a fluid. The paper confirms the ability of this family of numerical schemes...

Impact of the variations of the mixing length in a first order turbulent closure system

Françoise Brossier, Roger Lewandowski (2002)

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

This paper is devoted to the study of a turbulent circulation model. Equations are derived from the “Navier-Stokes turbulent kinetic energy” system. Some simplifications are performed but attention is focused on non linearities linked to turbulent eddy viscosity ν t . The mixing length ℓ acts as a parameter which controls the turbulent part in ν t . The main theoretical results that we have obtained concern the uniqueness of the solution for bounded eddy viscosities and small values of ℓ and its asymptotic...

Impact of the variations of the mixing length in a first order turbulent closure system

Françoise Brossier, Roger Lewandowski (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper is devoted to the study of a turbulent circulation model. Equations are derived from the “Navier-Stokes turbulent kinetic energy” system. Some simplifications are performed but attention is focused on non linearities linked to turbulent eddy viscosity  ν t . The mixing length ℓ acts as a parameter which controls the turbulent part in ν t . The main theoretical results that we have obtained concern the uniqueness of the solution for bounded eddy viscosities and small values of ℓ and its asymptotic...

Including eigenvalues of the plane Orr-Sommerfeld problem

Peter P. Klein (1993)

Applications of Mathematics

In an earlier paper [5] a method for eigenvalue inclussion using a Gerschgorin type theory originating from Donnelly [2] was applied to the plane Orr-Sommerfeld problem in the case of a pure Poiseuile flow. In this paper the same method will be used to deal Poiseuile and Couette flow. Potter [6] has treated this case before with an approximative method.

Inégalités de Carleman globales pour les problèmes elliptiques non homogènes

Jean-Pierre Puel (2002/2003)

Séminaire Équations aux dérivées partielles

On établit ici, suivant [5], une inégalité de Carleman globale optimale pour les solutions faibles (au sens H 1 ) d’équations elliptiques générales avec second membre dans H - 1 et trace non nulle.La motivation, qui est expliquée dans l’introduction, réside dans l’obtention d’inégalités de Carleman globale pour l’opérateur de Navier-Stokes linéarisé afin, notamment, d’étudier les questions de contrôlabilité exacte sur les trajectoires pour les équations de Navier-Stokes. Une étape majeure consiste à obtenir...

Interior regularity of weak solutions to the perturbed Navier-Stokes equations

Pigong Han (2012)

Applications of Mathematics

In this paper we establish interior regularity for weak solutions and partial regularity for suitable weak solutions of the perturbed Navier-Stokes system, which can be regarded as generalizations of the results in L. Caffarelli, R. Kohn, L. Nirenberg: Partial regularity of suitable weak solutions of the Navier-Stokes equations, Commun. Pure. Appl. Math. 35 (1982), 771–831, and S. Takahashi, On interior regularity criteria for weak solutions of the Navier-Stokes equations, Manuscr. Math. 69...

Interpolation spaces and weighted pseudo almost automorphic solutions to parabolic equations and applications to fluid dynamics

Thieu Huy Nguyen, Thi Ngoc Ha Vu, The Sac Le, Truong Xuan Pham (2022)

Czechoslovak Mathematical Journal

We investigate the existence, uniqueness and polynomial stability of the weighted pseudo almost automorphic solutions to a class of linear and semilinear parabolic evolution equations. The necessary tools here are interpolation spaces and interpolation theorems which help to prove the boundedness of solution operators in appropriate spaces for linear equations. Then for the semilinear equations the fixed point arguments are used to obtain the existence and stability of the weighted pseudo almost...

Inverse coefficient problems for variational inequalities : optimality conditions and numerical realization

Michael Hintermüller (2001)

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

We consider the identification of a distributed parameter in an elliptic variational inequality. On the basis of an optimal control problem formulation, the application of a primal-dual penalization technique enables us to prove the existence of multipliers giving a first order characterization of the optimal solution. Concerning the parameter we consider different regularity requirements. For the numerical realization we utilize a complementarity function, which allows us to rewrite the optimality...

Inverse Coefficient Problems for Variational Inequalities: Optimality Conditions and Numerical Realization

Michael Hintermüller (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider the identification of a distributed parameter in an elliptic variational inequality. On the basis of an optimal control problem formulation, the application of a primal-dual penalization technique enables us to prove the existence of multipliers giving a first order characterization of the optimal solution. Concerning the parameter we consider different regularity requirements. For the numerical realization we utilize a complementarity function, which allows us to rewrite the optimality...

Isogeometric analysis for fluid flow problems

Bastl, Bohumír, Brandner, Marek, Egermaier, Jiří, Michálková, Kristýna, Turnerová, Eva (2015)

Programs and Algorithms of Numerical Mathematics

The article is devoted to the simulation of viscous incompressible fluid flow based on solving the Navier-Stokes equations. As a numerical model we chose isogeometrical approach. Primary goal of using isogemetric analysis is to be always geometrically exact, independently of the discretization, and to avoid a time-consuming generation of meshes of computational domains. For higher Reynolds numbers, we use stabilization techniques SUPG and PSPG. All methods mentioned in the paper are demonstrated...

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