In this note, we develop a theory of Euler-Poincaré reduction for discrete Lagrangian field theories. We introduce the concept of Euler-Poincaré equations for discrete field theories, as well as a natural extension of the Moser-Veselov scheme, and show that both are equivalent. The resulting discrete field equations are interpreted in terms of discrete differential geometry. An application to t...

The author proposes a two-dimensional generalization of Constantin-Lax-Majda model. Some results about singular solutions are given. This model might be the first step toward Euler equations. Along same line (vorticity formulation), presents some further He possibly models various aspects difficulties related with and Navier-Stokes discussions on possible connection between turbulence equations...

We examine numerically the issue of convergence for initial-value solutions and similarity solutions of the compressible Euler equations in two dimensions in the presence of vortex sheets ~slip lines!. We consider the problem of a normal shock wave impacting an inclined density discontinuity in the presence of a solid boundary. Two solution techniques are examined: the first solves the Euler eq...

In this paper we present a unigrid multi–model formulation for transonic flow calculations based on solving, in sequence, the full potential equation and the the Euler equations. The goal is to minimize the overall computation time to simulate steady flows by using a more computational efficient physical model in the early iteration steps. The proposed method is based on two steps. In the first...

We consider the convergence in the L norm, uniformly in time, of the Navier-Stokes equations with Dirichlet boundary conditions to the Euler equations with slip boundary conditions. We prove that if the Oleinik conditions of no back-flow in the trace of the Euler flow, and of a lower bound for the Navier-Stokes vorticity is assumed in a Kato-like boundary layer, then the inviscid limit holds. M...

the complex-step derivative approximation is applied to compute numerical derivatives. in this study, we propose a new formula of fractional complex-step method utilizing jumarie definition. based on this method, we illustrated an approximate analytic solution for the fractional cauchy-euler equations. application in image denoising is imposed by introducing a new fractional mask depending on s...

We consider solutions of the Boltzmann equation, in a d-dimensional torus, d = 2,3, for macroscopic times T = t / e N , e a: 1, t 2 0, when the space variations are on a macroscopic scale x = eN-’r , N 2 2, x in the unit torus. Let u ( x , r ) be, for t to, a smooth solution of the incompressible Navier Stokes equations (INS) for N = 2 and of the Incompressible Euler equation (IE) for N > 2. We...

In this paper, we define and study Hyers–Ulam stability of order 1 for Euler’s equation m−1 the Euler–Poisson in calculus variations two special cases, when these equations have form y″(x)=f(x) y(m)(x)=f(x), respectively. We prove some estimations Jyx−Jy0x, where y is an approximate solution y0 exact corresponding Euler Euler-Poisson equations, also give examples.