Euler Equations Of Hydrodynamics Research Articles

96/04197 Trajectories of burning coal particles in highly swirling reactive flows

Results are described of computations of 3-D compressible Rayleigh-Taylor instability. The instability is an important mixing mechanism in a variety of flows such as supernovae and inertial confinement fusion. The code uses Flux Corrected Transport to solve the Euler equations of hydrodynamics. Results of the simulations have been characterized by considering differing resolutions and in terms of growth-rates, Mach number evolution, pattern formation, and (weakly) turbulent structures.

96/04181 Scaling in bouyancy driven turbulent premixed flames

Results are described of computations of 3-D compressible Rayleigh-Taylor instability. The instability is an important mixing mechanism in a variety of flows such as supernovae and inertial confinement fusion. The code uses Flux Corrected Transport to solve the Euler equations of hydrodynamics. Results of the simulations have been characterized by considering differing resolutions and in terms of growth-rates, Mach number evolution, pattern formation, and (weakly) turbulent structures.

96/04190 Study of carbon deposition in coke ovens

Results are described of computations of 3-D compressible Rayleigh-Taylor instability. The instability is an important mixing mechanism in a variety of flows such as supernovae and inertial confinement fusion. The code uses Flux Corrected Transport to solve the Euler equations of hydrodynamics. Results of the simulations have been characterized by considering differing resolutions and in terms of growth-rates, Mach number evolution, pattern formation, and (weakly) turbulent structures.

Integrals of the Euler equations of multidimensional hydrodynamics and superconductivity

Integrals of motion of a multidimensional ideal fluid and multidimensional superconductivity connected with invariants of the coadjoint representation of the corresponding infinite dimensional Lie algebras are constructed. An ergodic interpretation of the integrals of motion of magnetohydrodynamics is suggested.

Intense evaporation from a three-dimensional periodic surface

By means of the Boltzmann equation the problem of the intense evaporation of a substance from a three-dimensional periodic surface having inhomogeneities of characteristic dimension of the order of the molecular mean free path is solved by direct statistical modeling. Slip flow boundary conditions are obtained for the Euler equations of hydrodynamics describing the flow outside the Knudsen layer in terms of the controlling parameters. The problem has been solved on a two-processor computer in the parallel processing regime. Certain aspects of the parallelization of problems of the kinetic theory of gases solvable by direct statistical modeling on multiprocessor computers are discussed.

A Concise Presentation of the Euler Equations of Hydrodynamics

(1984). A Concise Presentation of the Euler Equations of Hydrodynamics. Communications in Partial Differential Equations: Vol. 9, No. 6, pp. 539-559.

Invariant forms and some structural properties of the hydrodynamic Euler equations (in Russian)

A new invariant form of hydrodynamics Euler equations is introduced and certain qualitative properties of solutions are established.

Kinetic theory of dense fluids. II. The generalized Chapman-Enskog solution

In the second paper of this series we solve the kinetic equation proposed in the previous paper by a method following the spirit of Chapman and Enskog (generalized Chapman-Enskog method). The zeroth-order solution to the kinetic equation leads to the Euler equations in hydrodynamics for real fluids, and the first-order solution to the Navier-Stokes equations for real fluids. General formulas for transport coefficients such as viscosity and heat-conductivity coefficients are obtained for dense fluids, which are given in terms of time-correlation functions of fluxes conjugate to the thermodynamic forces. The results have the same formal structures as the time-correlation functions in linear response theory except for the collision operator appearing in place of the Liouville operator in the evolution operator for the system.

A Unifying Principle in Statistical Mechanics

A fundamental problem of statistical mechanics is to obtain simplified descriptions of complex systems. A general principle is presented for obtaining equations of motion for such descriptions. The principle involves maximizing an appropriate entropy functional. It also involves the particle dynamics through the Liouville equation. Various special cases are presented in which the principle yields the Vlasov equation, the Boltzmann equation, Euler's hydrodynamic equations, a generalization of Grad's ten-moment approximation, the Gibbs distribution (i.e., equilibrium statistical mechanics), and Onsager's equations of irreversible thermodynamics. The principle also yields, trivially, the Liouville equation and Hamilton's equations of classical mechanics. Some of these results have been derived elsewhere by very similar procedures, but apparently the generality of the principle has been unrecognized. In terms of the general principle, the origin of irreversibility in the various equations of motion is easily seen, and the relation between the numerous definitions of entropy is clarified. No a priori justification of the principle itself is given.

Equations of Motion for Continuous Matter of Special Relativity in the Lagrange Variables

THE equations of motion for continuous matter of special relativity are usually1 deduced by equating to zero the divergence of the material energy (the ‘Minkowski’) tensor: where ρ is the rest density and p is the pressure supposed given as a function of the x µ. v µ means dx µ/ds. In this way we get the equation of continuity: dp/ds is considered small and is usually ignored; in fact, it represents the action of the pressure in creating matter2. We further get for the equations of motion (ignoring dp/ds): These equations may be called the Euler equations, since the first three equations in (3) are the Euler equations of classical hydrodynamics.

Simulation of fluid–particles flows: heavy particles, flowing regime, and asymptotic-preserving schemes

We are interested in an Eulerian-Lagrangian model describing particulate flows. The model under study consists of the Euler system and a Vlasov-Fokker-Planck equation coupled through momentum and energy exchanges. This problem contains asymptotic regimes that make the coupling terms stiff, and lead to a limiting model of purely hydrodynamic type. We design a numerical scheme which is able to capture this asymptotic behavior without requiring prohibitive stability conditions. The construction of this Asymptotic Preserving scheme relies on an implicit discretization of the stiff terms which can be treated by efficient inversion methods. This method is a natural coupling of a kinetic solver for the particles with a kinetic scheme for the hydrodynamic Euler equations. Numerical experiments are conducted to study the performance of this scheme in various asymptotic regimes.