The linearized Boltzmann equation with Cercignani–Lampis boundary conditions: Basic flow problems in a plane channel

Abstract In preceding papers, Refs. 1,2, boundary conditions were developed for transport-relaxation equations by aid of a general reciprocity postulate for the interface. The same method is now used for the linearized Boltzmann equation. A new scheme emerges: the kinetic boundary conditions consist in a linear functional relation between interfacial "forces and fluxes" - in the sense of non-equilibrium thermodynamics - which are, broadly speaking, given by the sum and the difference of the molecular distribution function and its time-reversed, at the wall. The general properties of the kernels occurring in this atomistic boundary law are studied. The phenomenological surface coefficients of (generalized) linear thermo-hydrodynamics, as e. g. temperature jump, slip coefficients etc., can in a simple way be expressed by the kernel of the atomistic boundary law. This kernel is explicitly worked out for completely thermalizing wall collisions.

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Inlet and outlet boundary conditions for the discrete velocity direction model

Modern Physics Letters B ◽

10.1142/s0217984918500483 ◽

2018 ◽

Vol 32 (04) ◽

pp. 1850048 ◽

Cited By ~ 1

Author(s):

Zhenyu Zhang ◽

Wei Zhao ◽

Qingjun Zhao ◽

Guojing Lu ◽

Jianzhong Xu

Keyword(s):

Heat Transfer ◽

Boltzmann Equation ◽

Boundary Conditions ◽

Kinetic Method ◽

Distribution Functions ◽

Molecular Flow ◽

Discrete Velocity ◽

Flow And Heat Transfer ◽

Linearized Boltzmann Equation ◽

Direction Model

The discrete velocity direction model is an approximate method to the Boltzmann equation, which is an optional kinetic method to microgas flow and heat transfer. In this paper, the treatment of the inlet and outlet boundary conditions for the model is proposed. In the computation strategy, the microscopic molecular speed distribution functions at inlet and outlet are indirectly determined by the macroscopic gas pressure, mass flux and temperature, which are all measurable parameters in microgas flow and heat transfer. The discrete velocity direction model with the pressure correction boundary conditions was applied into the plane Poiseuille flow in microscales and the calculations cover all flow regimes. The numerical results agree well with the data of the NS equation near the continuum regime and the date of linearized Boltzmann equation and the DSMC method in the transition regime and free molecular flow. The Knudsen paradox and the nonlinear pressure distributions have been accurately captured by the discrete velocity direction model with the present boundary conditions.

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Evaluation of Various Types of Wall Boundary Conditions for the Boltzmann Equation

42nd AIAA Thermophysics Conference ◽

10.2514/6.2011-3620 ◽

2011 ◽

Author(s):

Christopher Wilson ◽

Ramesh Agarwal ◽

Felix Tcheremissine

Keyword(s):

Boltzmann Equation ◽

Boundary Conditions ◽

Wall Boundary ◽

The Boltzmann Equation ◽

Wall Boundary Conditions

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Coda

10.1093/oso/9780199592357.003.0036 ◽

2018 ◽

Author(s):

Sauro Succi

Keyword(s):

Fluid Dynamics ◽

Boltzmann Equation ◽

Broad Spectrum ◽

Lattice Boltzmann ◽

Lattice Boltzmann Equation ◽

Real Difference ◽

Complex Flow ◽

Flow Problems ◽

Subjective View

This section of the book revisits a question from the book The Lattice Boltzmann Equation (for fluid dynamics and beyond). This question is: What did we learn through lattice Boltzmann? Did LB make a real difference to our understanding of the physics of fluids and flowing matter in general? Here, the text aims to offer a subjective view, without the presumption of being right. Besides being routinely used for a broad spectrum of complex flow problems, there are, in the opinion expressed in this part of the book, a few precious instances in which LB has made a palpable difference.

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