Hydrodynamic Limit with Geometric Correction of Stationary Boltzmann Equation

2014/09/13 by Lei Wu, Wu, Lei
Mathematics · Engineering · #Gas Dynamics and Kinetic Theory #Lattice Boltzmann Simulation Studies #Fluid Dynamics and Turbulent Flows

paper · pdf · doi:10.48550/arxiv.1409.3945

Abstract

We consider the hydrodynamic limit of a stationary Boltzmann equation in a unit plate with in-flow boundary. We prove the solution can be approximated in L^∞ by the sum of interior solution which satisfies steady incompressible Navier-Stokes-Fourier system, and boundary layer with geometric correction. Also, we construct a counterexample to the classical theory which states the behavior of solution near boundary can be described by the Knudsen layer derived from the Milne problem.

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