Conservative evaluation of Boltzmann collision integral in discrete ordinates approximation

Tcheremissine, F. G.

doi:10.1016/s0898-1221(97)00269-1

Cited by 60 publications

(34 citation statements)

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“…The procedure of [5] is employed in the present work. It should be noted that interpolation with similar properties was earlier proposed by Tcheremissine [4], where the corresponding method of calculating the collision integral was called a conservative projection-interpolation method. Figure 1 shows the quadrature nodes on the sphere (marked by crosses) for one pair of nodes of a rectangular computational grid.…”

Section: Conservative Interpolation Schemes Of Calculating the Collismentioning

confidence: 99%

“…Direct deterministic methods of solving the Boltzmann equation include discrete velocity methods (DVM) [2][3][4][5][6][7][8][9][10][11] and spectral methods (see, e.g., [12]). Application of deterministic methods in practice is not very popular because such a solution is computationally expensive, especially for strongly non-equilibrium flows, such as flows with strong shock waves.…”

Section: Introductionmentioning

confidence: 99%

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High-accuracy deterministic solution of the Boltzmann equation for the shock wave structure

et al. 2015

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A new deterministic method of solving the Boltzmann equation has been proposed. The method has been employed in numerical studies of the plane shock wave structure in a hard sphere gas. Results for Mach numbers M = 4 and M = 8 have been compared with predictions of the direct simulation Monte Carlo (DSMC) method, which has been used to obtain the reference solution. Particular attention in estimating the solution accuracy has been paid to a fine structural effect: the presence of a total temperature peak exceeding the temperature value further downstream. The results of solving the Boltzmann equation for the shock wave structure are in excellent agreement with the DSMC predictions.

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Section: Conservative Interpolation Schemes Of Calculating the Collismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

High-accuracy deterministic solution of the Boltzmann equation for the shock wave structure

et al. 2015

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“…In deterministic methods of solving the Boltzmann equation, the calculation is based on grids in velocity space; but particles found at the grid points before a collision do not wind up at grid points after the collision, which leads to an energy and momentum deficit in the system. To ensure that the conservation laws are obeyed during collisions of the particles, artificial methods are used which distribute the particle over nearest-lying grid points [7,8].…”

Section: Introductionmentioning

confidence: 99%

Successive Scaling of Quasiparticle Velocities on a Time Step in the Kinetic Force Method with a Two-Particle Distribution Function

Saveliev

Filko

2015

Russ Phys J

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As is well known, the algorithm of the kinetic force method, based on the kinetic equation for the two-particle distribution function, guarantees conservation of energy and momentum during a "quasicollision" of each separate pair of quasiparticles. But in the modeling of relaxation of the entire gas an energy deficit nevertheless appears at the step of reconstructing the one-particle distribution function. A new variant of the algorithm of the kinetic force method is proposed in which the energy of the system of molecules is conserved at any step of the modeling of relaxation without additional corrections. By virtue of this, the advantages of modeling on the basis of the two-particle distribution function of pairs of quasiparticles are used more efficiently.

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“…[20][21][22][23][24], is still hard task even nowadays when power computers are available. At the same time, the model equations like BGK [16] and S-model [17] are effective tools and widely used for practical calculations, see e.g., Refs.…”

Section: Introductionmentioning

confidence: 99%

Numerical modelling of rarefied gas flow through a slit at arbitrary pressure ratio based on the kinetic equation

Graur

Polikarpov

Sharipov

2011

Z. Angew. Math. Phys.

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A rarefied gas flow through a thin slit at an arbitrary gas pressure ratio is calculated on the basis of the kinetic model equations (BGK and S-model) applying the discrete velocity method. The calculations are carried out for the whole range of the gas rarefaction from the free-molecular regime to the hydrodynamic one. Numerical data on the flow rate and distributions of density, bulk velocity and temperature are reported. Comparisons of the present results with those based on the direct simulation Monte Carlo method and on the linearized BGK kinetic equation are performed. The conditions of applicability of the linearized theory are discussed. (2010). 82B40 kinetic theory of gases. Mathematics Subject Classification

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Conservative evaluation of Boltzmann collision integral in discrete ordinates approximation

Cited by 60 publications

References 1 publication

High-accuracy deterministic solution of the Boltzmann equation for the shock wave structure

High-accuracy deterministic solution of the Boltzmann equation for the shock wave structure

Successive Scaling of Quasiparticle Velocities on a Time Step in the Kinetic Force Method with a Two-Particle Distribution Function

Numerical modelling of rarefied gas flow through a slit at arbitrary pressure ratio based on the kinetic equation

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