First-order quasilinear canonical representation of the characteristic formulation of the Einstein equations

We prescribe a choice of 18 variables in all that casts the equations of the fully nonlinear characteristic formulation of general relativity in first--order quasi-linear canonical form. At the analytical level, a formulation of this type allows us to make concrete statements about existence of solutions. In addition, it offers concrete advantages for numerical applications as it now becomes possible to incorporate advanced numerical techniques for first order systems, which had thus far not been applicable to the characteristic problem of the Einstein equations, as well as in providing a framework for a unified treatment of the vacuum and matter problems. This is of relevance to the accurate simulation of gravitational waves emitted in astrophysical scenarios such as stellar core collapse.Comment: revtex4, 7 pages, text and references added, typos corrected, to appear in Phys. Rev.

Gravity effect on the locally heated liquid film driven by gas flow in an inclined minichannel

Thin nonisothermal liquid film flowing under action of gravity force and co-current gas flow, which create the tangential force on the gas-liquid interface, in an inclined minichannel is considered. 3D time dependant mathematical model has been developed. Effects of surface tension, temperature dependent viscosity and thermocapillarity are taken into account. The effect of gravity as well as the effect of gas speed has been studied to define main features of the film dynamics. In calculations vector of gravitational acceleration is oriented along the flow and is equal to the normal Earth gravity and Lunar gravity. Our investigations have shown that gravity has a significant effect on the film deformations. At the lower gravity conditions 3D liquid film pattern changes noticeably in spanwise direction and a middle stream between two main lateral waves appears. Also speed of film deformation is higher and stabilization time is longer. Variation of gas Reynolds number from 543 to 2000 does not change noticeably film pattern at normal gravity. At lower gravity conditions increasing of gas Reynolds number decreases significantly the width of the thermocapillary deformations and leads to a film stabilization.En ligne: http://www.springerlink.com/content/q281764097634023/info:eu-repo/semantics/publishe