Comparison of the Shakhov kinetic equation and DSMC method as applied to space vehicle aerothermodynamics

Титарев, В. А.; Фролова, А. А.; Рыков, В. А.; Vashchenkov, P. V.; Shevyrin, A. A.; Bondar, Ye. A.

doi:10.1016/j.cam.2019.112354

Cited by 22 publications

(5 citation statements)

References 40 publications

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“…Comparisons with calculations using the exact Boltzmann equation, the direct simulation Monte Carlo method, and with experimental data have confirmed good accuracy of the S-model, see e.g. [5,6,7,8,9] and references therein.…”

Section: Introductionmentioning

confidence: 61%

Numerical solution of the Boltzmann equation with S-model collision integral using tensor decompositions

Chikitkin,

Kornev,

Titarev

2019

Preprint

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Paper presents a new solver for numerical solution of the Boltzmann kinetic equation with Shakhov model collision integral (S-model) for arbitrary spatial domains. Numerical method utilizes Tensor-Train decomposition, which allows to reduce required computer memory for up to 30 times even on a moderate velocity mesh. This improvement is achieved by representing values of distribution function on the structured velocity mesh as a 3D tensor in Tensor-Train format. The resulting numerical method makes it possible to solve complex 3D problems on modern desktop computers.Our implementation may serve as a prototype code for researchers concerned with numerical solution of the kinetic equations in 3D domains by the discrete velocity method.

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Section: Introductionmentioning

confidence: 61%

Numerical solution of the Boltzmann equation with S-model collision integral using tensor decompositions

Chikitkin,

Kornev,

Titarev

2019

Preprint

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“…The flow characteristics are analyzed on the basis of the Shakhov kinetic model [29]. The Shakhov kinetic model is considered one of the most widely used kinetic models in the study of isothermal (e.g., [8,23,24,[30][31][32][33]) and non-isothermal (e.g., [34][35][36][37][38][39][40][41]) gas flows in the whole range of the gas rarefaction, and its reliability has been demonstrated by performing comparisons with available experimental measurements [42][43][44][45] and DSMC data [46][47][48][49]. The Shakhov model, in its applied form, recovers both shear viscosity and thermal conductivity simultaneously and it fulfills all the collision invariants.…”

Section: Complete 4d Kinetic Solutionmentioning

confidence: 99%

Numerical Study of Rarefied Gas Flow in Diverging Channels of Finite Length at Various Pressure Ratios

Tantos,

Litovoli,

Teichmann

et al. 2024

Fluids

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In the present work, the gas flows through diverging channels driven by small, moderate, and large pressure drops are studied, considering a wide range of the gas rarefaction from free molecular limit through transition flow regime up to early slip regime. The analysis is performed using the Shakhov kinetic model, and applying the deterministic DVM method. The complete 4D flow problem is considered by including the upstream and downstream reservoirs. A strong effect of the channel geometry on the flow pattern is shown, with the distributions of the macroscopic quantities differing qualitatively and quantitatively from the straight channel flows. The mass flow rate data set from the complete solution is compared with the corresponding set obtained from the approximate kinetic methodology, which is based on the fully developed mass flow rate data available in the literature. In addition, the use of the end-effect approach significantly improves the applicability range of the approximate kinetic methodology. The influence of the wall temperature on the flow characteristics is also studied and is found to be strong in less-rarefied cases, with the mass flow rate in these cases being a decreasing function of the temperature wall. Overall, the present analysis is expected to be useful in the development and optimization of technological devices in vacuum and aerospace technologies.

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“…In fact, regardless of the amount of computation, most rarefied gas dynamics methods, such as DSMC [ 10 ] and the Boltzmann model equation solvers [ 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 ], can recover the NS solution in the continuum regime. Based on these methods, a viscous interaction model can be established for all flow regimes.…”

Section: Introductionmentioning

confidence: 99%

“…A total of 727 billion cells in a six-dimensional mesh and 23,800 cores on almost the largest computer systems available in China in 2015 were used in the last case [ 20 ]. Titarev [ 11 , 12 , 13 , 14 , 15 , 16 ] has developed an implicit parallel code, Nesvetay, in recent years. A breakthrough in Nesvetay is the adaptive velocity mesh which is almost linearly dependent on the free-stream Mach number [ 14 ].…”

Section: Introductionmentioning

confidence: 99%

“…For a M = 25 flow around the TsaGI reentry space vehicle, 18 billion six-dimensional mesh cells and only 5000 core-hours of computer time are consumed, which is state of the art. By comparison with DSMC results, Titarev also evaluated the BGK and Shakhov model equations as applied to hypersonic flows for both aerodynamics and heat transfer in [ 14 , 15 , 16 ]. Apart from the unstructured mesh technique used in Nesvetay, another efficient approach based on an adaptive octree velocity mesh is proposed by Baranger [ 17 ].…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear Modeling Study of Aerodynamic Characteristics of an X38-like Vehicle at Strong Viscous Interaction Regions

Jiang

Wang

et al. 2022

Entropy

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Strong viscous interaction and multiple flow regimes exist when vehicles fly at high altitude and high Mach number conditions. The Navier–Stokes(NS) solver is no longer applicable in the above situation. Instead, the direct simulation Monte Carlo (DSMC) method or Boltzmann model equation solvers are usually needed. However, they are computationally more expensive than the NS solver. Therefore, it is of great engineering value to establish the aerodynamic prediction model of vehicles at high altitude and high Mach number conditions. In this paper, the hypersonic aerodynamic characteristics of an X38-like vehicle in typical conditions from 70 km to 110 km are simulated using the unified gas kinetic scheme (UGKS), which is applicable for all flow regimes. The contributions of pressure and viscous stress on the force coefficients are analyzed. The viscous interaction parameters, Mach number, and angle of attack are used as independent variables, and the difference between the force coefficients calculated by UGKS and the Euler solver is used as a dependent variable to establish a nonlinear viscous interaction model between them in the range of 70–110 km. The evaluation of the model is completed using the correlation coefficient and the relative orthogonal distance. The conventional viscous interaction effect and rarefied effect are both taken into account in the model. The model can be used to quickly obtain the hypersonic aerodynamic characteristics of X38-like vehicle in a wide range, which is meaningful for engineering design.

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Comparison of the Shakhov kinetic equation and DSMC method as applied to space vehicle aerothermodynamics

Cited by 22 publications

References 40 publications

Numerical solution of the Boltzmann equation with S-model collision integral using tensor decompositions

Numerical solution of the Boltzmann equation with S-model collision integral using tensor decompositions

Numerical Study of Rarefied Gas Flow in Diverging Channels of Finite Length at Various Pressure Ratios

Nonlinear Modeling Study of Aerodynamic Characteristics of an X38-like Vehicle at Strong Viscous Interaction Regions

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