Full Numerical Approach Research Articles

Full size, model and numerical evaluations of the smoke ventilator aerodynamic efficiency:development and qualification

Natural smoke and heat exhaust ventilators have to be tested: ability of opening and combustion products extraction. This paper describes the various test installations devoted to smoke ventilator aerodynamic efficiency evaluation at CSTB (Full size, scaled down and numerical approaches). Results of these three approaches are compared and analysed. Finally, a critical analysis of the European standard project is achieved. New proposals are given in order to improve the test procedure and avoid discrepancies between test installations.

Plunge waveforms from inspiralling binary black holes.

We study the coalescence of nonspinning binary black holes from near the innermost stable circular orbit down to the final single rotating black hole. We use a technique that combines the full numerical approach to solve the Einstein equations, applied in the truly nonlinear regime, and linearized perturbation theory around the final distorted single black hole at later times. We compute the plunge waveforms, which present a non-negligible signal lasting for t approximately 100M showing early nonlinear ringing, and we obtain estimates for the total gravitational energy and angular momentum radiated.

Second order gauge invariant gravitational perturbations of a Kerr black hole

We investigate higher than the first order gravitational perturbations in the Newman-Penrose formalism. Equations for the Weyl scalar $\psi_4,$ representing outgoing gravitational radiation, can be uncoupled into a single wave equation to any perturbative order. For second order perturbations about a Kerr black hole, we prove the existence of a first and second order gauge (coordinates) and tetrad invariant waveform, $\psi_I$, by explicit construction. This waveform is formed by the second order piece of $\psi_4$ plus a term, quadratic in first order perturbations, chosen to make $\psi_I$ totally invariant and to have the appropriate behavior in an asymptotically flat gauge. $\psi_I$ fulfills a single wave equation of the form ${\cal T}\psi_I=S,$ where ${\cal T}$ is the same wave operator as for first order perturbations and $S$ is a source term build up out of (known to this level) first order perturbations. We discuss the issues of imposition of initial data to this equation, computation of the energy and momentum radiated and wave extraction for direct comparison with full numerical approaches to solve Einstein equations.

An efficient and accurate calculation of traction in elastohydrodynamic contacts

Traction calculation is an important step in the design and lubrication optimization of machine components with elastohydrodynamic (EHD) contacts. The availability of an accurate and robust method of calculation can be a valuable tool for the machine designer. This paper presents a method of traction calculation that combines the key features of the full numerical approach and previously reported approximation methods. Specifically, the contact pressure and the film thickness are approximated by closed-form expressions while the temperature distribution is numerically calculated using a finite difference method. This scheme of calculation largely eliminates the numerical instability problem that frequently occurs in the full numerical approach while yielding results much more accurate than those obtained by previous approximation methods. The method is robust and allows the use of any rheological models for the lubricant. It is relatively easy to implement on a computer to efficiently calculate traction in both line and point EHD contacts.

Vortex-shedding phenomena in solid rocket motors

In the past 20 years, periodic vortex shedding as a source of acoustic energy inside solid propellant rocket motors has been continuously studied, in connection with several motors that exhibited oscillatory behaviors although they were predicted stable by means of conventional linear stability methods. On that subject, correlations through Strouhal numbers are commonly used. In this article, the meanings of various Strouhal number definitions are discussed. The basic mechanisms for sound production in ducts or chambers are then discussed through simple tools, such as the linear hydrodynamic stability analysis, Flandro's method and the acoustic balance technique, which provide good insights into the physics of the phenomenon. Necessary conditions for vortex-shedding-driven motors are then arrived at and illustrated by actual firing results. Finally, the full numerical approaches are shown to provide unprecedented insight into the mechanisms behind the vortexshedding phenomenon and are believed to open the way to quantitative predictions of frequencies and oscillatory levels.

Single-Particle Scattering Approximation for the Pair Function of an Electron Liquid: Full Numerical Approach

Abstract The static pair correlation function of the three-dimensional homogeneous electron gas at given temperature and density is estimated by the scattering of non-interacting particles in an effective potential. The full numerical treatment of the self-consistency problem yields results that are in excellent agreement with those obtained within a generalized Thomas–Fermi approximation.