Solving the Boltzmann equation in the case of passing to the hydrodynamic flow regime

Cheremisin, F. G.

doi:10.1134/1.1310733

Cited by 24 publications

(11 citation statements)

References 4 publications

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“…Despite this, developing methods that can span a wide range of temporal scales is equally important and challenging. In the context of kinetic problems, algebraic decomposition (4.1) can be exploited for this purpose: Cheremisin [67] developed a deterministic method for solving the Boltzmann equation which uses such a decomposition to remove the stiffness associated with integrating the Boltzmann equation in the limit Kn → 0. For particle methods, time-relaxed [43] integration schemes, briefly described in §4, provide a promising new direction.…”

Section: Discussionmentioning

confidence: 99%

On efficient simulations of multiscale kinetic transport

Radtke

Péraud

Hadjiconstantinou

2013

Phil. Trans. R. Soc. A.

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We discuss a new class of approaches for simulating multiscale kinetic problems, with particular emphasis on applications related to small-scale transport. These approaches are based on a decomposition of the kinetic description into an equilibrium part, which is described deterministically (analytically or numerically), and the remainder, which is described using a particle simulation method. We show that it is possible to derive evolution equations for the two parts from the governing kinetic equation, leading to a decomposition that is dynamically and automatically adaptive, and a multiscale method that seamlessly bridges the two descriptions without introducing any approximation . Our discussion pays particular attention to stochastic particle simulation methods that are typically used to simulate kinetic phenomena; in this context, these decomposition approaches can be thought of as control-variate variance-reduction formulations, with the nearby equilibrium serving as the control. Such formulations can provide substantial computational benefits in a broad spectrum of applications because a number of transport processes and phenomena of practical interest correspond to perturbations from nearby equilibrium distributions. In many cases, the computational cost reduction is sufficiently large to enable otherwise intractable simulations.

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Section: Discussionmentioning

confidence: 99%

On efficient simulations of multiscale kinetic transport

Radtke

Péraud

Hadjiconstantinou

2013

Phil. Trans. R. Soc. A.

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“…The collision integral is evaluated by a special projection technique proposed in Tcheremissine (1997) that guarantees exact fulfillment of conservation law of mass, impulse, and energy. Important improvement of the method that secured exact computation of the collision integral from the Maxwellian function was made in Tcheremissine (2000). It sharply increased the accuracy of calculations in near equilibrium area of the flow, in particular for low perturbed, low-speed flows.…”

Section: Introductionmentioning

confidence: 99%

Solution of the Boltzmann Kinetic Equation for Low Speed Flows

Tcheremissine

2008

Transport Theory and Statistical Physics

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“…It can be satisfied, when the grid has a large volume, but refines for small molecular velocities. The extension of the Tcheremissine's projection-interpolation discrete-velocity method [28,29,30,31] for nonuniform grids [32] based on the methodology of multi-point projection [33] can effectively solve the considered class of problems.Asymptotic analysis of the Boltzmann equation for slow nonisothermal flows shows that the steady-state heat-conduction equation does not correctly describe a rarefied gas in the continuum limit (Kn → 0) [34]. This fact is also confirmed by numerical analysis [9].…”

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confidence: 99%

Slow nonisothermal flows: Numerical and asymptotic analysis of the Boltzmann equation

Rogozin

2017

Comput. Math. and Math. Phys.

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In memory of Oscár Gavriilovich Friedlánder (1939 Slow flows of a slightly rarefied gas under high thermal stresses are considered. The correct fluiddynamic description of this class of flows is based on the Kogan-Galkin-Friedlander equations, containing some non-Navier-Stokes terms in the momentum equation. Appropriate boundary conditions are determined from the asymptotic analysis of the Knudsen layer on the basis of the Boltzmann equation. Boundary conditions up to the second order of the Knudsen number are studied. Some two-dimensional examples are examined for their comparative analysis. The fluid-dynamic results are supported by numerical solution of the Boltzmann equation obtained by the Tcheremissine's projection-interpolation discrete-velocity method extended for nonuniform grids. The competition pattern between the first-and the second-order nonlinear thermal-stress flows has been obtained for the first time.

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Solving the Boltzmann equation in the case of passing to the hydrodynamic flow regime

Cited by 24 publications

References 4 publications

On efficient simulations of multiscale kinetic transport

On efficient simulations of multiscale kinetic transport

Solution of the Boltzmann Kinetic Equation for Low Speed Flows

Slow nonisothermal flows: Numerical and asymptotic analysis of the Boltzmann equation

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