Search results for "Euler"

A second strain gradient elasticity theory with second velocity gradient inertia – Part II: Dynamic behavior

2013

Abstract This paper is the sequel of a companion Part I paper devoted to the constitutive equations and to the quasi-static behavior of a second strain gradient material model with second velocity gradient inertia. In the present Part II paper, a multi-cell homogenization procedure (developed in the Part I paper) is applied to a nonhomogeneous body modelled as a simple material cell system, in conjunction with the principle of virtual work (PVW) for inertial actions (i.e. momenta and inertia forces), which at the macro-scale level takes on the typical format as for a second velocity gradient inertia material model. The latter (macro-scale) PVW is used to determine the equilibrium equations …

The Euler–Lagrange equation for the Anisotropic least gradient problem

2016

Abstract In this paper we find the Euler–Lagrange equation for the anisotropic least gradient problem inf { ∫ Ω ϕ ( x , D u ) : u ∈ B V ( Ω ) , u | ∂ Ω = f } being ϕ a metric integrand and f ∈ L 1 ( ∂ Ω ) . We also characterize the functions of ϕ -least gradient as those whose boundary of the level set is ϕ -area minimizing in Ω .

Computing oscillatory solutions of the Euler system via 𝒦-convergence

2021

We develop a method to compute effectively the Young measures associated to sequences of numerical solutions of the compressible Euler system. Our approach is based on the concept of [Formula: see text]-convergence adapted to sequences of parameterized measures. The convergence is strong in space and time (a.e. pointwise or in certain [Formula: see text] spaces) whereas the measures converge narrowly or in the Wasserstein distance to the corresponding limit.

Global Climatologies of Eulerian and Lagrangian Flow Features based on ERA-Interim

2017

Abstract This paper introduces a newly compiled set of feature-based climatologies identified from ERA-Interim (1979–2014). Two categories of flow features are considered: (i) Eulerian climatologies of jet streams, tropopause folds, surface fronts, cyclones and anticyclones, blocks, and potential vorticity streamers and cutoffs and (ii) Lagrangian climatologies, based on a large ensemble of air parcel trajectories, of stratosphere–troposphere exchange, warm conveyor belts, and tropical moisture exports. Monthly means of these feature climatologies are openly available at the ETH Zürich web page (http://eraiclim.ethz.ch) and are annually updated. Datasets at higher resolution can be obtained…

Origin and Flow History of Air Parcels in Orographic Banner Clouds

2015

Abstract Banner clouds are clouds in the lee of steep mountains or sharp ridges. Previous work suggests that the main formation mechanism is vertical uplift in the lee of the mountain. On the other hand, little is known about the Lagrangian behavior of air parcels as they pass the mountain, which motivates the current investigation. Three different diagnostics are applied in the framework of large-eddy simulations of airflow past an isolated pyramid-shaped obstacle: Eulerian tracers indicating the initial positions of the parcels, streamlines along the time-averaged wind field, and online trajectories computed from the instantaneous wind field. All three methods diagnose a plume of large ve…

Adaptive discontinuous evolution Galerkin method for dry atmospheric flow

2014

We present a new adaptive genuinely multidimensional method within the framework of the discontinuous Galerkin method. The discontinuous evolution Galerkin (DEG) method couples a discontinuous Galerkin formulation with approximate evolution operators. The latter are constructed using the bicharacteristics of multidimensional hyperbolic systems, such that all of the infinitely many directions of wave propagation are considered explicitly. In order to take into account multiscale phenomena that typically appear in atmospheric flows nonlinear fluxes are split into a linear part governing the acoustic and gravitational waves and a nonlinear part that models advection. Time integration is realiz…

Bernoullin luvut ja Euler-MacLaurinin summakaava

2007

Mechanically-based approach to non-local elasticity: Variational principles

2010

Abstract The mechanically-based approach to non-local elastic continuum, will be captured through variational calculus, based on the assumptions that non-adjacent elements of the solid may exchange central body forces, monotonically decreasing with their interdistance, depending on the relative displacement, and on the volume products. Such a mechanical model is investigated introducing primarily the dual state variables by means of the virtual work principle. The constitutive relations between dual variables are introduced defining a proper, convex, potential energy. It is proved that the solution of the elastic problem corresponds to a global minimum of the potential energy functional. Mo…

Approximate Osher–Solomon schemes for hyperbolic systems

2016

This paper is concerned with a new kind of Riemann solvers for hyperbolic systems, which can be applied both in the conservative and nonconservative cases. In particular, the proposed schemes constitute a simple version of the classical Osher-Solomon Riemann solver, and extend in some sense the schemes proposed in Dumbser and Toro (2011) 19,20. The viscosity matrix of the numerical flux is constructed as a linear combination of functional evaluations of the Jacobian of the flux at several quadrature points. Some families of functions have been proposed to this end: Chebyshev polynomials and rational-type functions. Our schemes have been tested with different initial value Riemann problems f…

A Novel Solution to Find the Dynamic Response of an Euler–Bernoulli Beam Fitted with Intraspan TMDs under Poisson Type Loading

2020

This contribution considers a virtual experiment on the vibrational response of rail and road bridges equipped with smart devices in the form of damping elements to mitigate vibrations. The internal damping of the bridge is considered a discontinuity that contain a dashpot. Exact complex eigenvalues and eigenfunctions are derived from a characteristic equation built as the determinant of a 4 x 4 matrix