Abstract
Abstract In order to have, a kinetic equation suited to liquid dynamics and phase transitions, the intermolecular potential is split into a repulsive hard-core and an attractive tail. The hard-core is treated as in the revised Enskog equation, whereas the tail enters the equation only linearly, in a mean-field term. Such an equation is called the Enskog-Vlasov equation. The goal of the paper is to present a construction of a class of models of the Enskog-Vlasov equation, based on the idea of discretization of the velocity space. A proposal of solution of two problems is given: discrete velocity models of the Enskog collisional operator; discrete velocity models of kinetic equations with self-consistent forces. The conservation equations which follow from the proposed models have the structure of the capillarity equations with a vander Waals-like pressure formula, if the Kac limit is imposed on the attractive tail.
Published Version
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