Computing of gas flows in micro- and nanoscale channels on the base of the Boltzmann Kinetic equation

Anikin, Yu. A.; Derbakova, E. P.; Dodulad, O. I.; Kloss, Yu. Yu.; Мартынов, Д. В.; Rogozin, Oleg A.; Shuvalov, P. V.; Tcheremissine, F. G.

doi:10.1016/j.procs.2010.04.079

Cited by 6 publications

(6 citation statements)

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“…where∆ n+(ν−1)/N γ is ν ∈ N n term of sum (51), one can apply the first-order explicit Euler method in fractional steps:f…”

Section: Solution Of the Cauchy Problemmentioning

confidence: 99%

“…The described algorithm is implemented within the problem-solving environment for numerical analysis of rarefied gas flows [51,52]. The physical grid is selected under the same criteria as for the numerical solution of the KGF equations, but needs additional exponential refinement near the diffuse-reflection boundaries to ensure the numerical error is less than 10 −4 in the Knudsen layer.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…then each cubature point (term in (51)) ensures the conservation of mass, momentum and kinetic energy for the found projective velocities ζ λν +sa and projection weights r λν a . Second, to satisfy…”

Section: Projection-interpolation Techniquementioning

confidence: 99%

“…Let f n γ denotes an approximate solution of (47) for velocity ζ γ (γ ∈ Γ) at time t n (n ∈ N). Rewriting (51) as…”

Section: Solution Of the Cauchy Problemmentioning

confidence: 99%

“…The Korobov lattice rule [47,48] is used as an equal-weight cubature rule in (51). The integration lattice is randomly shifted every time step to obtain a sequence of sets of cubature points (N n ) n∈N .…”

Section: Solution Of the Cauchy Problemmentioning

confidence: 99%

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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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“…where∆ n+(ν−1)/N γ is ν ∈ N n term of sum (51), one can apply the first-order explicit Euler method in fractional steps:f…”

Section: Solution Of the Cauchy Problemmentioning

confidence: 99%

Section: Numerical Examplesmentioning

confidence: 99%

Section: Projection-interpolation Techniquementioning

confidence: 99%

“…Let f n γ denotes an approximate solution of (47) for velocity ζ γ (γ ∈ Γ) at time t n (n ∈ N). Rewriting (51) as…”

Section: Solution Of the Cauchy Problemmentioning

confidence: 99%

Section: Solution Of the Cauchy Problemmentioning