Non-Local Scattering Kernel and the Hydrodynamic Limit |
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Authors: | Maria Carmela Lombardo Russel E Caflisch Marco Sammartino |
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Institution: | (1) Dipartimento di Matematica, Università di Palermo, Via Archirafi 34, 90123 Palermo, Italy;(2) Department of Mathematics, UCLA, 520 Portola Plaza, Los Angeles, CA 90095, USA |
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Abstract: | In this paper we study the interaction of a fluid with a wall in the framework of the kinetic theory. We consider the possibility
that the fluid molecules can penetrate the wall to be reflected by the inner layers of the wall. This results in a scattering
kernel which is a non-local generalization of the classical Maxwell scattering kernel. The proposed scattering kernel satisfies
a global mass conservation law and a generalized reciprocity relation. We study the hydrodynamic limit performing a Knudsen
layer analysis, and derive a new class of (weakly) nonlocal boundary conditions to be imposed to the Navier–Stokes equations. |
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Keywords: | Boltzmann equation Hydrodynamic limit Navier– Stokes flow Nonlocal boundary conditions |
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