The Multiscale Hybrid Method with a Localized Constraint. I. A Modified Control Volume Function for the Hybridized Mass and Momentum Equations

A new hybrid multiscaling model has been developed on the basis of the modified control volume function. Following the two-phase analogy of the same substance, the continuum and particle representations are coupled together in the framework of the mass and momentum conserva-tion laws. The new functional form of the control volume function is elaborated by using the continuum discretization principle based on the Delaunay triangulation. The derived mass and momentum equations possess the invariant form for both micro-scale particle and large-scale continuum representations.