– A previously proposed thermohydrodynamic lattice BGK scheme using nonperturbative, or non-polynomial, equilibria is found to simulate continuum equations that differ from the Euler equations of gas dynamics at leading order. Shock tube simulations with this BGK scheme coincide with solutions obtained by solving these different continuum equations with conventional methods. Both sets of soluti...

Abstract. Let G be a Banach Lie group modeled on the Banach space, possibly infinite dimensional, E. In this paper first we introduce Euler-Lagrange equations on the Lie group G with potential and right invariant metric. Euler-Lagrange equations are natural extensions of the geodesic equations on manifolds and Lie groups. In the second part, we study the geometry of the mechanical system of a r...

We are concerned with spherically symmetric solutions of the Euler equations for multidimensional compressible fluids, which are motivated by many important physical situations. Various evidences indicate that spherically symmetric solutions to the compressible Euler equations may blow up near the origin at certain time under some circumstance. The central feature is the strengthening of waves ...

In this paper we describe the classical methods used to solve the Euler equations. Special attention is devoted to the iterative method based on a contraction mapping derived from these equations in Maldonado and Moreira (2003). We test the numerical robustness of this method when it is used in models with sensitiveness to initial conditions. Finally we extend the method to the case of stochast...

We study Euler–Poincaré systems (i.e., the Lagrangian analogue of LiePoisson Hamiltonian systems) defined on semidirect product Lie algebras. We first give a derivation of the Euler–Poincaré equations for a parameter dependent Lagrangian by using a variational principle of Lagrange d’Alembert type. Then we derive an abstract Kelvin-Noether theorem for these equations. We also explore their rela...

Progresses on the dynamical system theory of 2D Euler equation are reported. An open problem is presented. The isospectral theory on Lax pairs of Euler equations is initiated.

This paper extends the derivation of the Lagrangian averaged Euler (LAEα) equations to the case of barotropic compressible flows. The aim of Lagrangian averaging is to regularize the compressible Euler equations by adding dispersion instead of artificial viscosity. Along the way, the derivation of the isotropic and anisotropic LAE-α equations is simplified and clarified. The derivation in this ...

We construct stationary solutions to the barotropic, compressible Euler and NavierStokes equations in several space dimensions with spherical or cylindrical symmetry. For given Dirichlet data on a sphere or a cylinder we first construct smooth and radially symmetric solutions to the Euler equations in the exterior domain. On the other hand, stationary smooth solutions in the interior domain nec...

The Cuachy problem for the 3D vortical flow of ideal barotropic fluid is considered. It is shown that the solution of the Cauchy problem is unique, if one considers seven dynamic equations for seven dependent variables: the density ρ, the velocity v and Lagrangian variables ξ = {ξ 1 , ξ 2 , ξ 3 }, labeling the fluid particles. If one considers only the closed (Euler) system of four equations fo...

in this paper, we present the numerical solution of ordinary dierential equations (or sdes), from each order especially second-order with time-varying and gaussian random coecients. we indicate a complete analysis for second-order equations in special case of scalar linear second-order equations (damped harmonic oscillators with additive or multi- plicative noises). making stochastic dierent...