Search results for "Euler"

Existence and uniqueness for the Prandtl equations

2001

International audience; Under the hypothesis of analyticity of the data with respect to the tangential variable we prove the existence and uniqueness of the mild solution of Prandtl boundary layer equation. This can be considered an improvement of the results of [8] as we do not require analyticity with respect to the normal variable. (C) 2001 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.

Removability of a Level Set for Solutions of Quasilinear Equations

2005

In this paper, we study the removability of a level set for the solutions of quasilinear elliptic and parabolic equations of the second order. We show, under rather general assumptions on the coeff...

Eulerian models of the rotating flexible wheelset for high frequency railway dynamics

2019

Abstract In this paper three formulations based on an Eulerian approach are presented to obtain the dynamic response of an elastic solid of revolution, which rotates around its main axis at constant angular velocity. The formulations are especially suitable for the study of the interaction of a solid with a non-rotating structure, such as occurs in the coupled dynamics of a railway wheelset with the track. With respect to previous publications that may adopt similar hypotheses, this paper proposes more compact formulations and eliminates certain numerical problems associated with the presence of second-order derivatives with respect to the spatial coordinates. Three different models are dev…

Solutions via double wave ansatz to the 1-D non-homogeneous gas-dynamics equations

2020

Abstract In this paper classes of double wave solutions of the 1D Euler system describing a ideal fluid in the non-homogeneous case have been determined. In order that the analytical procedure under interest to hold, suitable model laws for the source term involved in the governing model were characterized. Finally such a class of exact double wave solutions has been used for solving some problems of interest in nonlinear wave propagation.

Integral and differential approaches to Eringen's nonlocal elasticity models accounting for boundary effects with applications to beams in bending

2021

Stochastic Response Of Fractionally Damped Beams

2014

Abstract This paper aims at introducing the governing equation of motion of a continuous fractionally damped system under generic input loads, no matter the order of the fractional derivative. Moreover, particularizing the excitation as a random noise, the evaluation of the power spectral density performed in frequency domain highlights relevant features of such a system. Numerical results have been carried out considering a cantilever beam under stochastic loads. The influence of the fractional derivative order on the power spectral density response has been investigated, underscoring the damping effect in reducing the power spectral density amplitude for higher values of the fractional de…

Galaxy cluster mergers

2009

We present the results of an Eulerian adaptive mesh refinement (AMR) hydrodynamical and N-body simulation in a $\Lambda$CDM cosmology. The simulation incorporates common cooling and heating processes for primordial gas. A specific halo finder has been designed and applied in order to extract a sample of galaxy clusters directly obtained from the simulation without considering any resimulating scheme. We have studied the evolutionary history of the cluster halos, and classified them into three categories depending on the merger events they have undergone: major mergers, minor mergers, and relaxed clusters. The main properties of each one of these classes and the differences among them are di…

Mechanically Based Nonlocal Euler-Bernoulli Beam Model

2014

AbstractThis paper presents a nonlocal Euler-Bernoulli beam model. It is assumed that the equilibrium of a beam segment is attained because of the classical local stress resultants, along with long-range volume forces and moments exchanged by the beam segment with all the nonadjacent beam segments. Elastic long-range volume forces/moments are considered, built as linearly depending on the product of the volumes of the interacting beam segments and on generalized measures of their relative motion, based on the pure deformation modes of the beam. Attenuation functions governing the space decay of the nonlocal effects are introduced. The motion equations are derived in an integro-differential …

On the Measurements of Numerical Viscosity and Resistivity in Eulerian MHD Codes

2016

We propose a simple ansatz for estimating the value of the numerical resistivity and the numerical viscosity of any Eulerian MHD code. We test this ansatz with the help of simulations of the propagation of (magneto)sonic waves, Alfven waves, and the tearing mode instability using the MHD code Aenus. By comparing the simu- lation results with analytical solutions of the resistive-viscous MHD equations and an empirical ansatz for the growth rate of tearing modes we measure the numerical viscosity and resistivity of Aenus. The comparison shows that the fast-magnetosonic speed and wavelength are the characteristic velocity and length, respectively, of the aforementioned (relatively simple) syst…

Regularized Euler-alpha motion of an infinite array of vortex sheets

2016

We consider the Euler- $$\alpha $$ regularization of the Birkhoff–Rott equation and compare its solutions with the dynamics of the non regularized vortex-sheet. For a flow induced by an infinite array of planar vortex-sheets we analyze the complex singularities of the solutions.Through the singularity tracking method we show that the regularized solution has several complex singularities that approach the real axis. We relate their presence to the formation of two high-curvature points in the vortex sheet during the roll-up phenomenon.