Half-Space Problem for the Discrete Boltzmann Equation : Condensing Vapor Flow in the Presence of a Non-condensable Gas

• We consider a non-linear half-space problem related to the condensation problem for the discrete Boltzmann equation and extend some known results for a single-component gas to the case when a non-condensable gas is present. The vapor is assumed to tend to an assigned Maxwellian at infinity, as the non-condensable gas tends to zero at infinity. We assume that the vapor is completely absorbed and that the non-condensable gas is diffusively reflected at the condensed phase and that the vapor molecules leaving the condensed phase are distributed according to a given distribution. The conditions, on the given distribution, needed for the existence of a unique solution of the problem are investigated. We also find exact solvability conditions and solutions for a simplified six+four-velocity model, as the given distribution is a Maxwellian at rest, and study a simplified twelve+six-velocitymodel.

Subject headings

NATURVETENSKAP  -- Matematik -- Algebra och logik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Algebra and Logic (hsv//eng)

Keyword

Boltzmann equation

boundary layers

discrete velocity models

half-space problem

non-condensable gas

Matematik

Mathematics

Publication and Content Type

ref (subject category)

art (subject category)