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Influence of waves on Lagrangian acceleration in two-dimensional turbulent flows⋆⋆⋆⋆⋆⋆

Romain Nguyen van yen, Benjamin Kadoch, Vivek Kumar, Benjamin Ménétrier, Marie Farge, Kai Schneider, Diane Douady, Lionel Guez (2011)

ESAIM: Proceedings

The Lagrangian statistics in rotating Saint-Venant turbulence are studied by means of direct numerical simulation using a pseudo-spectral discretization fully resolving, both in time and space, all the inertio-gravity waves present in the system. To understand the influence of waves, three initial conditions are considered, one which is dominated by waves, one which is dominated by vortices, and one which is intermediate between these two extreme...

Initial boundary value problem for generalized Zakharov equations

Shujun You, Boling Guo, Xiaoqi Ning (2012)

Applications of Mathematics

This paper considers the existence and uniqueness of the solution to the initial boundary value problem for a class of generalized Zakharov equations in ( 2 + 1 ) dimensions, and proves the global existence of the solution to the problem by a priori integral estimates and the Galerkin method.

Instabilities of Diffuse Interfaces

N. Bessonov, J. Pojman, G. Viner, V. Volpert, B. Zoltowski (2008)

Mathematical Modelling of Natural Phenomena

Composition gradients in miscible liquids can create volume forces resulting in various interfacial phenomena. Experimental observations of these phenomena are related to some difficulties because they are transient, sufficiently weak and can be hidden by gravity driven flows. As a consequence, the question about their existence and about adequate mathematical models is not yet completely elucidated. In this work we present some experimental evidences of interfacial phenomena in miscible liquids...

Instability of mixed finite elements for Richards' equation

Březina, Jan (2010)

Programs and Algorithms of Numerical Mathematics

Richards' equation is a widely used model of partially saturated flow in a porous medium. In order to obtain conservative velocity field several authors proposed to use mixed or mixed-hybrid schemes to solve the equation. In this paper, we shall analyze the mixed scheme on 1D domain and we show that it violates the discrete maximum principle which leads to catastrophic oscillations in the solution.

Instability of the stationary solutions of generalized dissipative Boussinesq equation

Amin Esfahani (2014)

Applications of Mathematics

In this work we study the generalized Boussinesq equation with a dissipation term. We show that, under suitable conditions, a global solution for the initial value problem exists. In addition, we derive sufficient conditions for the blow-up of the solution to the problem. Furthermore, the instability of the stationary solutions of this equation is established.

Integrated Design of an Active Flow Control System Using a Time-Dependent Adjoint Method

E.J. Nielsen, W.T. Jones (2011)

Mathematical Modelling of Natural Phenomena

An exploratory study is performed to investigate the use of a time-dependent discrete adjoint methodology for design optimization of a high-lift wing configuration augmented with an active flow control system. The location and blowing parameters associated with a series of jet actuation orifices are used as design variables. In addition, a geometric parameterization scheme is developed to provide a compact set of design variables describing the wing...

Integration of the EPDiff equation by particle methods

Alina Chertock, Philip Du Toit, Jerrold Eldon Marsden (2012)

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

The purpose of this paper is to apply particle methods to the numerical solution of the EPDiff equation. The weak solutions of EPDiff are contact discontinuities that carry momentum so that wavefront interactions represent collisions in which momentum is exchanged. This behavior allows for the description of many rich physical applications, but also introduces difficult numerical challenges. We present a particle method for the EPDiff equation that is well-suited for this class of solutions and...

Integration of the EPDiff equation by particle methods∗∗∗∗∗∗

Alina Chertock, Philip Du Toit, Jerrold Eldon Marsden (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

The purpose of this paper is to apply particle methods to the numerical solution of the EPDiff equation. The weak solutions of EPDiff are contact discontinuities that carry momentum so that wavefront interactions represent collisions in which momentum is exchanged. This behavior allows for the description of many rich physical applications, but also introduces difficult numerical challenges. We present a particle method for the EPDiff equation that...

Interaction of compressible flow with an airfoil

Česenek, Jan, Feistauer, Miloslav (2010)

Programs and Algorithms of Numerical Mathematics

The paper is concerned with the numerical solution of interaction of compressible flow and a vibrating airfoil with two degrees of freedom, which can rotate around an elastic axis and oscillate in the vertical direction. Compressible flow is described by the Navier-Stokes equations written in the ALE form. This system is discretized by the semi-implicit discontinuous Galerkin finite element method (DGFEM) and coupled with the solution of ordinary differential equations describing the airfoil motion....

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