Close Search Advanced
Journals
Resources
About Us
Open Access

A Unified Gas-Kinetic Scheme for Continuum and Rarefied Flows II: Multi-Dimensional Cases

A Unified Gas-Kinetic Scheme for Continuum and Rarefied Flows II: Multi-Dimensional Cases
Preview
Add to basket

Year:    2012

Communications in Computational Physics, Vol. 12 (2012), Iss. 3 : pp. 662–690

Abstract

With discretized particle velocity space, a multi-scale unified gas-kinetic scheme for entire Knudsen number flows has been constructed based on the kinetic model in one-dimensional case [J. Comput. Phys., vol. 229 (2010), pp. 7747-7764]. For the kinetic equation, to extend a one-dimensional scheme to multidimensional flow is not so straightforward. The major factor is that addition of one dimension in physical space causes the distribution function to become two-dimensional, rather than axially symmetric, in velocity space. In this paper, a unified gas-kinetic scheme based on the Shakhov model in two-dimensional space will be presented. Instead of particle-based modeling for the rarefied flow, such as the direct simulation Monte Carlo (DSMC) method, the philosophical principal underlying the current study is a partial-differential-equation (PDE)-based modeling. Since the valid scale of the kinetic equation and the scale of mesh size and time step may be significantly different, the gas evolution in a discretized space is modeled with the help of kinetic equation, instead of directly solving the partial differential equation. Due to the use of both hydrodynamic and kinetic scales flow physics in a gas evolution model at the cell interface, the unified scheme can basically present accurate solution in all flow regimes from the free molecule to the Navier-Stokes solutions. In comparison with the DSMC and Navier-Stokes flow solvers, the current method is much more efficient than DSMC in low speed transition and continuum flow regimes, and it has better capability than NS solver in capturing of non-equilibrium flow physics in the transition and rarefied flow regimes. As a result, the current method can be useful in the flow simulation where both continuum and rarefied flow physics needs to be resolved in a single computation. This paper will extensively evaluate the performance of the unified scheme from free molecule to continuum NS solutions, and from low speed micro-flow to high speed non-equilibrium aerodynamics. The test cases clearly demonstrate that the unified scheme is a reliable method for the rarefied flow computations, and the scheme provides an important tool in the study of non-equilibrium flow.

Submit Article

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.030511.220911a

Communications in Computational Physics, Vol. 12 (2012), Iss. 3 : pp. 662–690

Published online:    2012-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    29

Keywords:   

  1. Capturing the influence of intermolecular potential in rarefied gas flows by a kinetic model with velocity-dependent collision frequency

    Yuan, Ruifeng | Wu, Lei

    Journal of Fluid Mechanics, Vol. 942 (2022), Iss.

    https://doi.org/10.1017/jfm.2022.350 [Citations: 9]

  2. Modified unified kinetic scheme for all flow regimes

    Liu, Sha | Zhong, Chengwen

    Physical Review E, Vol. 85 (2012), Iss. 6

    https://doi.org/10.1103/PhysRevE.85.066705 [Citations: 13]

  3. A Unified Gas Kinetic Scheme for Transport and Collision Effects in Plasma

    Pan, Dongxin | Zhong, Chengwen | Zhuo, Congshan | Tan, Wei

    Applied Sciences, Vol. 8 (2018), Iss. 5 P.746

    https://doi.org/10.3390/app8050746 [Citations: 12]

  4. UGKS-Based Implicit Iterative Method for Multiscale Nonequilibrium Flow Simulations

    Xu, Xiaocong | Zhu, Yajun | Liu, Chang | Xu, Kun

    SIAM Journal on Scientific Computing, Vol. 44 (2022), Iss. 4 P.B996

    https://doi.org/10.1137/21M1421398 [Citations: 3]

  5. A Comparison and Unification of Ellipsoidal Statistical and Shakhov BGK Models

    Chen, Songze | Xu, Kun | Cai, Qingdong

    Advances in Applied Mathematics and Mechanics, Vol. 7 (2015), Iss. 2 P.245

    https://doi.org/10.4208/aamm.2014.m559 [Citations: 31]

  6. Unified gas-kinetic scheme with multigrid convergence for rarefied flow study

    Zhu, Yajun | Zhong, Chengwen | Xu, Kun

    Physics of Fluids, Vol. 29 (2017), Iss. 9

    https://doi.org/10.1063/1.4994020 [Citations: 61]

  7. Unified Gas Kinetic Simulations of Lid-Driven Cavity Flows: Effect of Compressibility and Rarefaction on Vortex Structures

    Venugopal, Vishnu | Iphineni, Haneesha | Praturi, Divya Sri | Girimaji, Sharath S.

    Mathematics, Vol. 12 (2024), Iss. 18 P.2807

    https://doi.org/10.3390/math12182807 [Citations: 0]

  8. Two-stage fourth-order gas-kinetic scheme for three-dimensional Euler and Navier-Stokes solutions

    Pan, Liang | Xu, Kun

    International Journal of Computational Fluid Dynamics, Vol. 32 (2018), Iss. 10 P.395

    https://doi.org/10.1080/10618562.2018.1536266 [Citations: 21]

  9. Explicit formulations of G13-based gas kinetic flux solver (G13-GKFS) for simulation of continuum and rarefied flows

    Liu, Z. J. | Yang, L. M. | Shu, C. | Chen, S. Y. | Wan, M. P. | Liu, W. | Yuan, Z. Y.

    Physics of Fluids, Vol. 33 (2021), Iss. 3

    https://doi.org/10.1063/5.0044295 [Citations: 10]

  10. A multidimensional unified gas-kinetic scheme for radiative transfer equations on unstructured mesh

    Sun, Wenjun | Jiang, Song | Xu, Kun

    Journal of Computational Physics, Vol. 351 (2017), Iss. P.455

    https://doi.org/10.1016/j.jcp.2017.09.036 [Citations: 32]

  11. A unified gas-kinetic scheme for continuum and rarefied flows IV: Full Boltzmann and model equations

    Liu, Chang | Xu, Kun | Sun, Quanhua | Cai, Qingdong

    Journal of Computational Physics, Vol. 314 (2016), Iss. P.305

    https://doi.org/10.1016/j.jcp.2016.03.014 [Citations: 66]

  12. A parallel unified gas kinetic scheme for three-dimensional multi-group neutron transport

    Shuang, Tan | Wenjun, Sun | Junxia, Wei | Guoxi, Ni

    Journal of Computational Physics, Vol. 391 (2019), Iss. P.37

    https://doi.org/10.1016/j.jcp.2019.04.041 [Citations: 16]

  13. Solving the Boltzmann equation deterministically by the fast spectral method: application to gas microflows

    Wu, Lei | Reese, Jason M. | Zhang, Yonghao

    Journal of Fluid Mechanics, Vol. 746 (2014), Iss. P.53

    https://doi.org/10.1017/jfm.2014.79 [Citations: 88]

  14. Implicit unified gas-kinetic scheme for steady state solutions in all flow regimes

    Zhu, Yajun | Zhong, Chengwen | Xu, Kun

    Journal of Computational Physics, Vol. 315 (2016), Iss. P.16

    https://doi.org/10.1016/j.jcp.2016.03.038 [Citations: 105]

  15. An asymptotic preserving unified gas kinetic scheme for frequency-dependent radiative transfer equations

    Sun, Wenjun | Jiang, Song | Xu, Kun | Li, Shu

    Journal of Computational Physics, Vol. 302 (2015), Iss. P.222

    https://doi.org/10.1016/j.jcp.2015.09.002 [Citations: 46]

  16. SPARTACUS: An open-source unified stochastic particle solver for the simulation of multiscale nonequilibrium gas flows

    Feng, Kaikai | Tian, Peng | Zhang, Jun | Fei, Fei | Wen, Dongsheng

    Computer Physics Communications, Vol. 284 (2023), Iss. P.108607

    https://doi.org/10.1016/j.cpc.2022.108607 [Citations: 11]

  17. Simulation of Fire with a Gas Kinetic Scheme on Distributed GPGPU Architectures

    Lenz, Stephan | Geier, Martin | Krafczyk, Manfred

    Computation, Vol. 8 (2020), Iss. 2 P.50

    https://doi.org/10.3390/computation8020050 [Citations: 4]

  18. A direct relaxation process for particle methods in gas-kinetic theory

    Yang, Sirui | Liu, Sha | Zhong, Chengwen | Cao, Junzhe | Zhuo, Congshan

    Physics of Fluids, Vol. 33 (2021), Iss. 7

    https://doi.org/10.1063/5.0055632 [Citations: 7]

  19. An efficient discrete velocity method with inner iteration for steady flows in all flow regimes

    Yang, L. M. | Shu, C. | Wu, J. | Liu, Y. Y. | Shen, X.

    Physics of Fluids, Vol. 34 (2022), Iss. 2

    https://doi.org/10.1063/5.0084547 [Citations: 14]

  20. Numerical simulation of flows from free molecular regime to continuum regime by a DVM with streaming and collision processes

    Yang, L.M. | Shu, C. | Wu, J. | Wang, Y.

    Journal of Computational Physics, Vol. 306 (2016), Iss. P.291

    https://doi.org/10.1016/j.jcp.2015.11.043 [Citations: 46]

  21. High order modal Discontinuous Galerkin Implicit–Explicit Runge Kutta and Linear Multistep schemes for the Boltzmann model on general polygonal meshes

    Boscheri, Walter | Dimarco, Giacomo

    Computers & Fluids, Vol. 233 (2022), Iss. P.105224

    https://doi.org/10.1016/j.compfluid.2021.105224 [Citations: 7]

  22. Simulation of three-dimensional compressible decaying isotropic turbulence using a redesigned discrete unified gas kinetic scheme

    Chen, Tao | Wen, Xin | Wang, Lian-Ping | Guo, Zhaoli | Wang, Jianchun | Chen, Shiyi

    Physics of Fluids, Vol. 32 (2020), Iss. 12

    https://doi.org/10.1063/5.0029424 [Citations: 34]

  23. A simple gas kinetic scheme for simulation of 3D incompressible thermal flows

    Yang, L. M. | Shu, C. | Yang, W. M. | Wu, J.

    Numerical Heat Transfer, Part B: Fundamentals, Vol. 72 (2017), Iss. 6 P.450

    https://doi.org/10.1080/10407790.2017.1409535 [Citations: 9]

  24. Discrete unified gas kinetic scheme for all Knudsen number flows. III. Binary gas mixtures of Maxwell molecules

    Zhang, Yue | Zhu, Lianhua | Wang, Ruijie | Guo, Zhaoli

    Physical Review E, Vol. 97 (2018), Iss. 5

    https://doi.org/10.1103/PhysRevE.97.053306 [Citations: 41]

  25. A review of rarefied gas flow in irregular micro/nanochannels

    Taassob, Arsalan | Bordbar, Alireza | Kheirandish, Sasan | Zarnaghsh, Amirreza | Kamali, Reza | Rana, Anirudh Singh

    Journal of Micromechanics and Microengineering, Vol. 31 (2021), Iss. 11 P.113002

    https://doi.org/10.1088/1361-6439/ac28a3 [Citations: 6]

  26. A novel linear stability analysis method for plane Couette flow considering rarefaction effects

    Zou, Sen | Bi, Lin | Zhong, Chengwen | Yuan, Xianxu | Tang, Zhigong

    Journal of Fluid Mechanics, Vol. 963 (2023), Iss.

    https://doi.org/10.1017/jfm.2023.230 [Citations: 5]

  27. An asymptotic preserving unified gas kinetic scheme for gray radiative transfer equations

    Sun, Wenjun | Jiang, Song | Xu, Kun

    Journal of Computational Physics, Vol. 285 (2015), Iss. P.265

    https://doi.org/10.1016/j.jcp.2015.01.008 [Citations: 69]

  28. Numerical investigation of curved channel Knudsen pump performance

    Bond, D.M. | Wheatley, V. | Goldsworthy, M.

    International Journal of Heat and Mass Transfer, Vol. 76 (2014), Iss. P.1

    https://doi.org/10.1016/j.ijheatmasstransfer.2014.04.021 [Citations: 25]

  29. A unified gas kinetic scheme with moving mesh and velocity space adaptation

    Chen, Songze | Xu, Kun | Lee, Cunbiao | Cai, Qingdong

    Journal of Computational Physics, Vol. 231 (2012), Iss. 20 P.6643

    https://doi.org/10.1016/j.jcp.2012.05.019 [Citations: 118]

  30. Unified stochastic particle simulation of polyatomic gas flows using SPARTACUS

    Tian, Peng | Feng, Kaikai | Ma, Qihan | Li, Zhihui | Zhang, Jun

    Computers & Fluids, Vol. 265 (2023), Iss. P.105987

    https://doi.org/10.1016/j.compfluid.2023.105987 [Citations: 2]

  31. Finite Element Algorithm for Dynamic Thermoelasticity Coupling Problems and Application to Transient Response of Structure with Strong Aerothermodynamic Environment

    Li, Zhihui | Ma, Qiang | Cui, Junzhi

    Communications in Computational Physics, Vol. 20 (2016), Iss. 3 P.773

    https://doi.org/10.4208/cicp.270515.010216a [Citations: 25]

  32. Approximation of the Boltzmann collision operator based on hermite spectral method

    Wang, Yanli | Cai, Zhenning

    Journal of Computational Physics, Vol. 397 (2019), Iss. P.108815

    https://doi.org/10.1016/j.jcp.2019.07.014 [Citations: 19]

  33. Third-order discrete unified gas kinetic scheme for continuum and rarefied flows: Low-speed isothermal case

    Wu, Chen | Shi, Baochang | Shu, Chang | Chen, Zhen

    Physical Review E, Vol. 97 (2018), Iss. 2

    https://doi.org/10.1103/PhysRevE.97.023306 [Citations: 18]

  34. An Implicit Unified Gas Kinetic Scheme for Radiative Transfer with Equilibrium and Non-Equilibrium Diffusive Limits

    Sun, Wenjun | Jiang, Song | Xu, Kun

    Communications in Computational Physics, Vol. 22 (2017), Iss. 4 P.889

    https://doi.org/10.4208/cicp.OA-2016-0261 [Citations: 27]

  35. Numerical investigation into the performance of alternative Knudsen pump designs

    Bond, D.M. | Wheatley, V. | Goldsworthy, M.

    International Journal of Heat and Mass Transfer, Vol. 93 (2016), Iss. P.1038

    https://doi.org/10.1016/j.ijheatmasstransfer.2015.10.069 [Citations: 31]

  36. On the asymptotic preserving property of the unified gas kinetic scheme for the diffusion limit of linear kinetic models

    Mieussens, Luc

    Journal of Computational Physics, Vol. 253 (2013), Iss. P.138

    https://doi.org/10.1016/j.jcp.2013.07.002 [Citations: 73]

  38. High order central WENO-Implicit-Explicit Runge Kutta schemes for the BGK model on general polygonal meshes

    Boscheri, Walter | Dimarco, Giacomo

    Journal of Computational Physics, Vol. 422 (2020), Iss. P.109766

    https://doi.org/10.1016/j.jcp.2020.109766 [Citations: 18]

  39. A fast iterative scheme for the linearized Boltzmann equation

    Wu, Lei | Zhang, Jun | Liu, Haihu | Zhang, Yonghao | Reese, Jason M.

    Journal of Computational Physics, Vol. 338 (2017), Iss. P.431

    https://doi.org/10.1016/j.jcp.2017.03.002 [Citations: 36]

  40. Grad's distribution function for 13 moments-based moment gas kinetic solver for steady and unsteady rarefied flows: Discrete and explicit forms

    Liu, W. | Liu, Z.J. | Zhang, Z.L. | Teo, C.J. | Shu, C.

    Computers & Mathematics with Applications, Vol. 137 (2023), Iss. P.112

    https://doi.org/10.1016/j.camwa.2023.02.006 [Citations: 2]

  41. Unified X-space parallelization algorithm for conserved discrete unified gas kinetic scheme

    Zhang, Qi | Wang, Yunlan | Pan, Dongxin | Chen, Jianfeng | Liu, Sha | Zhuo, Congshan | Zhong, Chengwen

    Computer Physics Communications, Vol. 278 (2022), Iss. P.108410

    https://doi.org/10.1016/j.cpc.2022.108410 [Citations: 10]

  42. Arbitrary Lagrangian-Eulerian-type conserved discrete unified gas kinetic scheme for the simulations of transonic continuum and rarefied gas flows with moving boundaries

    Wang, Yong | Liu, Sha | Zhuo, Congshan | Zhong, Chengwen

    Applied Mathematical Modelling, Vol. 113 (2023), Iss. P.545

    https://doi.org/10.1016/j.apm.2022.08.028 [Citations: 7]

  43. Discrete unified gas kinetic scheme for all Knudsen number flows: Low-speed isothermal case

    Guo, Zhaoli | Xu, Kun | Wang, Ruijie

    Physical Review E, Vol. 88 (2013), Iss. 3

    https://doi.org/10.1103/PhysRevE.88.033305 [Citations: 319]

  44. Multiscale Radiative Transfer in Cylindrical Coordinates

    Sun, Wenjun | Jiang, Song | Xu, Kun

    Communications on Applied Mathematics and Computation, Vol. 1 (2019), Iss. 1 P.117

    https://doi.org/10.1007/s42967-019-0007-x [Citations: 2]

  45. Onsager's cross coupling effects in gas flows confined to micro-channels

    Wang, Ruijie | Xu, Xinpeng | Xu, Kun | Qian, Tiezheng

    Physical Review Fluids, Vol. 1 (2016), Iss. 4

    https://doi.org/10.1103/PhysRevFluids.1.044102 [Citations: 10]

  46. The study of sound wave propagation in rarefied gases using unified gas-kinetic scheme

    Wang, Rui-Jie | Xu, Kun

    Acta Mechanica Sinica, Vol. 28 (2012), Iss. 4 P.1022

    https://doi.org/10.1007/s10409-012-0116-5 [Citations: 16]

  47. A Unified Gas-Kinetic Scheme for Continuum and Rarefied Flows III: Microflow Simulations

    Huang, Juan-Chen | Xu, Kun | Yu, Pubing

    Communications in Computational Physics, Vol. 14 (2013), Iss. 5 P.1147

    https://doi.org/10.4208/cicp.190912.080213a [Citations: 77]

  48. GPU acceleration of an iterative scheme for gas-kinetic model equations with memory reduction techniques

    Zhu, Lianhua | Wang, Peng | Chen, Songze | Guo, Zhaoli | Zhang, Yonghao

    Computer Physics Communications, Vol. 245 (2019), Iss. P.106861

    https://doi.org/10.1016/j.cpc.2019.106861 [Citations: 9]

  49. A unified gas-kinetic scheme for axisymmetric flow in all Knudsen number regimes

    Li, Shiyi | Li, Qibing | Fu, Song | Xu, Kun

    Journal of Computational Physics, Vol. 366 (2018), Iss. P.144

    https://doi.org/10.1016/j.jcp.2018.04.004 [Citations: 7]

  50. A conserved discrete unified gas kinetic scheme for microchannel gas flows in all flow regimes

    Liu, Hongtao | Cao, Yong | Chen, Qing | Kong, Mingchi | Zheng, Liang

    Computers & Fluids, Vol. 167 (2018), Iss. P.313

    https://doi.org/10.1016/j.compfluid.2018.03.023 [Citations: 41]

  51. A Unified Gas Kinetic Scheme for Continuum and Rarefied Flows V: Multiscale and Multi-Component Plasma Transport

    Liu, Chang | Xu, Kun

    Communications in Computational Physics, Vol. 22 (2017), Iss. 5 P.1175

    https://doi.org/10.4208/cicp.OA-2017-0102 [Citations: 63]

  52. Implicit unified gas-kinetic scheme for steady state solution of hypersonic thermodynamic non-equilibrium flows

    Zhang, Rui | Liu, Sha | Chen, Jianfeng | Jin, Hao | Zhuo, Congshan | Zhong, Chengwen

    Communications in Nonlinear Science and Numerical Simulation, Vol. 140 (2025), Iss. P.108367

    https://doi.org/10.1016/j.cnsns.2024.108367 [Citations: 0]

  53. A unified stochastic particle Bhatnagar-Gross-Krook method for multiscale gas flows

    Fei, Fei | Zhang, Jun | Li, Jing | Liu, ZhaoHui

    Journal of Computational Physics, Vol. 400 (2020), Iss. P.108972

    https://doi.org/10.1016/j.jcp.2019.108972 [Citations: 53]

  54. An implicit parallel UGKS solver for flows covering various regimes

    Jiang, Dingwu | Mao, Meiliang | Li, Jin | Deng, Xiaogang

    Advances in Aerodynamics, Vol. 1 (2019), Iss. 1

    https://doi.org/10.1186/s42774-019-0008-5 [Citations: 39]

  55. Can we find steady-state solutions to multiscale rarefied gas flows within dozens of iterations?

    Su, Wei | Zhu, Lianhua | Wang, Peng | Zhang, Yonghao | Wu, Lei

    Journal of Computational Physics, Vol. 407 (2020), Iss. P.109245

    https://doi.org/10.1016/j.jcp.2020.109245 [Citations: 62]

  56. Discrete unified gas kinetic scheme for all Knudsen number flows. II. Thermal compressible case

    Guo, Zhaoli | Wang, Ruijie | Xu, Kun

    Physical Review E, Vol. 91 (2015), Iss. 3

    https://doi.org/10.1103/PhysRevE.91.033313 [Citations: 202]

  57. A multiscale stochastic particle method based on the Fokker-Planck model for nonequilibrium gas flows

    Cui, Ziqi | Feng, Kaikai | Ma, Qihan | Zhang, Jun

    Journal of Computational Physics, Vol. 520 (2025), Iss. P.113458

    https://doi.org/10.1016/j.jcp.2024.113458 [Citations: 0]

  58. Thermal lattice Boltzmann flux solver and its application for simulation of incompressible thermal flows

    Wang, Y. | Shu, C. | Teo, C.J.

    Computers & Fluids, Vol. 94 (2014), Iss. P.98

    https://doi.org/10.1016/j.compfluid.2014.02.006 [Citations: 84]

  59. An implicit lattice Boltzmann method for simulations of compressible plasma kinetics

    Huang, Haoyu | Jin, Ke | Li, Kai | Li, Heng | Zheng, Xiaojing

    Physics of Fluids, Vol. 36 (2024), Iss. 8

    https://doi.org/10.1063/5.0221986 [Citations: 0]

  60. Simplification of the unified gas kinetic scheme

    Chen, Songze | Guo, Zhaoli | Xu, Kun

    Physical Review E, Vol. 94 (2016), Iss. 2

    https://doi.org/10.1103/PhysRevE.94.023313 [Citations: 24]

  61. Locally refined discrete velocity grids for stationary rarefied flow simulations

    Baranger, C. | Claudel, J. | Hérouard, N. | Mieussens, L.

    Journal of Computational Physics, Vol. 257 (2014), Iss. P.572

    https://doi.org/10.1016/j.jcp.2013.10.014 [Citations: 62]

  62. Direct modeling for computational fluid dynamics

    Xu, Kun

    Acta Mechanica Sinica, Vol. 31 (2015), Iss. 3 P.303

    https://doi.org/10.1007/s10409-015-0453-2 [Citations: 7]

  63. Unified gas-kinetic wave-particle methods. II. Multiscale simulation on unstructured mesh

    Zhu, Yajun | Liu, Chang | Zhong, Chengwen | Xu, Kun

    Physics of Fluids, Vol. 31 (2019), Iss. 6

    https://doi.org/10.1063/1.5097645 [Citations: 51]

  64. A discrete unified gas-kinetic scheme for multi-species rarefied flows

    Xin, Ziyang | Zhang, Yue | Guo, Zhaoli

    Advances in Aerodynamics, Vol. 5 (2023), Iss. 1

    https://doi.org/10.1186/s42774-022-00135-9 [Citations: 0]

  65. Progress of the unified wave-particle methods for non-equilibrium flows from continuum to rarefied regimes

    Liu, Sha | Xu, Kun | Zhong, Chengwen

    Acta Mechanica Sinica, Vol. 38 (2022), Iss. 6

    https://doi.org/10.1007/s10409-022-22123-x [Citations: 5]

  66. Numerical investigation of the heat and mass transfer analogy in rarefied gas flows

    Bond, D. | Goldsworthy, M.J. | Wheatley, V.

    International Journal of Heat and Mass Transfer, Vol. 85 (2015), Iss. P.971

    https://doi.org/10.1016/j.ijheatmasstransfer.2015.02.051 [Citations: 11]

  67. Thermal rarefied gas flow simulations with moving boundaries based on discrete unified gas kinetic scheme and immersed boundary method

    He, Qing | Tao, Shi | Liu, Gaojie | Wang, Liang | Ge, Ya | Chen, Jiechao | Yang, Xiaoping

    International Journal of Heat and Mass Transfer, Vol. 226 (2024), Iss. P.125508

    https://doi.org/10.1016/j.ijheatmasstransfer.2024.125508 [Citations: 0]

  68. Numerical simulations of micro-channel devices with Lattice Boltzmann method

    Timokhin, Maksim | Tikhonov, Mikhail

    31ST INTERNATIONAL SYMPOSIUM ON RAREFIED GAS DYNAMICS: RGD31, (2019), P.160006

    https://doi.org/10.1063/1.5119653 [Citations: 2]

  69. A well-balanced unified gas-kinetic scheme for multiscale flow transport under gravitational field

    Xiao, Tianbai | Cai, Qingdong | Xu, Kun

    Journal of Computational Physics, Vol. 332 (2017), Iss. P.475

    https://doi.org/10.1016/j.jcp.2016.12.022 [Citations: 21]

  70. A conservative implicit scheme for three-dimensional steady flows of diatomic gases in all flow regimes using unstructured meshes in the physical and velocity spaces

    Zhang, Rui | Liu, Sha | Chen, Jianfeng | Zhuo, Congshan | Zhong, Chengwen

    Physics of Fluids, Vol. 36 (2024), Iss. 1

    https://doi.org/10.1063/5.0186520 [Citations: 4]

  71. An implicit unified gas-kinetic scheme for unsteady flow in all Knudsen regimes

    Zhu, Yajun | Zhong, Chengwen | Xu, Kun

    Journal of Computational Physics, Vol. 386 (2019), Iss. P.190

    https://doi.org/10.1016/j.jcp.2019.01.033 [Citations: 47]

  72. On the total enthalpy behavior inside a shock wave

    Shoev, Georgy V. | Timokhin, Maksim Yu. | Bondar, Yevgeniy A.

    Physics of Fluids, Vol. 32 (2020), Iss. 4

    https://doi.org/10.1063/5.0005741 [Citations: 17]

  73. Numerical modeling of the heat and mass transfer of rarefied gas flows in a double-sided oscillatory lid-driven cavity

    He, Qing | Tao, Shi | Wang, Liang | Chen, Jiechao | Yang, Xiaoping

    International Journal of Heat and Mass Transfer, Vol. 230 (2024), Iss. P.125788

    https://doi.org/10.1016/j.ijheatmasstransfer.2024.125788 [Citations: 1]

  74. Comparison of Discrete Velocity Method and Gas-Kinetic Method for Binary Gas Mixtures

    Todorova, B. N. | Steijl, R.

    Journal of Thermophysics and Heat Transfer, Vol. 34 (2020), Iss. 1 P.45

    https://doi.org/10.2514/1.T5741 [Citations: 3]

  75. Knudsen pumps: a review

    Wang, Xiaowei | Su, Tianyi | Zhang, Wenqing | Zhang, Zhijun | Zhang, Shiwei

    Microsystems & Nanoengineering, Vol. 6 (2020), Iss. 1

    https://doi.org/10.1038/s41378-020-0135-5 [Citations: 39]

  76. Employing Per-Component Time Step in DSMC Simulations of Disparate Mass and Cross-Section Gas Mixtures

    Maltsev, Roman V.

    Communications in Computational Physics, Vol. 14 (2013), Iss. 3 P.703

    https://doi.org/10.4208/cicp.220612.071112a [Citations: 0]

  77. Coupled discrete unified gas kinetic scheme for the thermal compressible flows in all Knudsen number regimes

    Liu, Hongtao | Kong, Mingchi | Chen, Qing | Zheng, Liang | Cao, Yong

    Physical Review E, Vol. 98 (2018), Iss. 5

    https://doi.org/10.1103/PhysRevE.98.053310 [Citations: 19]

  78. A variant of improved discrete velocity method for efficient simulation of flows in entire Knudsen number regimes

    Yuan, Z. Y. | Yang, L. M. | Shu, C. | Jiang, K. | Zhang, L. Q.

    Physics of Fluids, Vol. 36 (2024), Iss. 2

    https://doi.org/10.1063/5.0188013 [Citations: 1]

  79. Influence of Knudsen and Mach numbers on Kelvin-Helmholtz instability

    Mohan, Vishnu | Sameen, A | Srinivasan, Balaji | Girimaji, Sharath S.

    Physical Review E, Vol. 103 (2021), Iss. 5

    https://doi.org/10.1103/PhysRevE.103.053104 [Citations: 8]

  80. Numerical investigation on performance of three solution reconstructions at cell interface in DVM simulation of flows in all Knudsen number regimes

    Yang, L.M. | Shu, C. | Yang, W.M. | Wu, J. | Zhang, M.Q.

    International Journal for Numerical Methods in Fluids, Vol. 90 (2019), Iss. 11 P.545

    https://doi.org/10.1002/fld.4734 [Citations: 6]

  81. Unified gas kinetic scheme combined with Cartesian grid method for intermediate Mach numbers

    Ragta, Lokesh Kumar | Srinivasan, Balaji | Sinha, Sawan S.

    International Journal for Numerical Methods in Fluids, Vol. 85 (2017), Iss. 9 P.507

    https://doi.org/10.1002/fld.4393 [Citations: 8]

  82. A piecewise-hierarchical particle count method suitable for the implementation of the unified gas-kinetic wave–particle method on graphics processing unit devices

    Yu, Hang | Xie, Wenjia | Ren, Weijie | Tian, Zhengyu

    Physics of Fluids, Vol. 36 (2024), Iss. 10

    https://doi.org/10.1063/5.0227425 [Citations: 0]

  83. Continuum breakdown in compressible mixing layers

    Mohan, Vishnu | Sameen, A. | Srinivasan, Balaji | Girimaji, Sharath S.

    Physical Review E, Vol. 105 (2022), Iss. 6

    https://doi.org/10.1103/PhysRevE.105.065102 [Citations: 3]

  84. A robust numerical method for the R13 equations of rarefied gas dynamics: Application to lid driven cavity

    Rana, Anirudh | Torrilhon, Manuel | Struchtrup, Henning

    Journal of Computational Physics, Vol. 236 (2013), Iss. P.169

    https://doi.org/10.1016/j.jcp.2012.11.023 [Citations: 84]

  85. On the vortical characteristics and cold-to-hot transfer of rarefied gas flow in a lid driven isosceles orthogonal triangular cavity with isothermal walls

    Roohi, Ehsan | Shahabi, Vahid | Bagherzadeh, Amir

    International Journal of Thermal Sciences, Vol. 125 (2018), Iss. P.381

    https://doi.org/10.1016/j.ijthermalsci.2017.12.005 [Citations: 23]

  86. Unlocking the Key to Accelerating Convergence in the Discrete Velocity Method for Flows in the Near Continuous/Continuous Flow Regimes

    Han, Linchang | Yang, Liming | Li, Zhihui | Wu, Jie | Du, Yinjie | Shen, Xiang

    Entropy, Vol. 25 (2023), Iss. 12 P.1609

    https://doi.org/10.3390/e25121609 [Citations: 0]
  87. A Unified Computational Fluid Dynamics Framework from Rarefied to Continuum Regimes

    Xu, Kun

    2021

    https://doi.org/10.1017/9781108877534 [Citations: 16]

  88. A Variance-Reduced Direct Monte Carlo Simulation Method for Solving the Boltzmann Equation Over a Wide Range of Rarefaction

    Sadr, Mohsen | Hadjiconstantinou, Nicolas

    SSRN Electronic Journal, Vol. (2022), Iss.

    https://doi.org/10.2139/ssrn.4148310 [Citations: 0]

  89. Dimension-Reduced Hyperbolic Moment Method for the Boltzmann Equation with BGK-Type Collision

    Cai, Zhenning | Fan, Yuwei | Li, Ruo | Qiao, Zhonghua

    Communications in Computational Physics, Vol. 15 (2014), Iss. 5 P.1368

    https://doi.org/10.4208/cicp.220313.281013a [Citations: 16]

  90. Addressing the gas kinetics Boltzmann equation with branching-path statistics

    Terrée, Guillaume | El Hafi, Mouna | Blanco, Stéphane | Fournier, Richard | Dauchet, Jérémi | Gautrais, Jacques

    Physical Review E, Vol. 105 (2022), Iss. 2

    https://doi.org/10.1103/PhysRevE.105.025305 [Citations: 7]

  91. Reduced order modeling-based discrete unified gas kinetic scheme for rarefied gas flows

    Zhao, Xiang | Wu, Chen | Chen, Zhen | Yang, Liming | Shu, Chang

    Physics of Fluids, Vol. 32 (2020), Iss. 6

    https://doi.org/10.1063/5.0009614 [Citations: 22]

  92. Unified gas-kinetic wave-particle methods V: Diatomic molecular flow

    Xu, Xiaocong | Chen, Yipei | Liu, Chang | Li, Zhihui | Xu, Kun

    Journal of Computational Physics, Vol. 442 (2021), Iss. P.110496

    https://doi.org/10.1016/j.jcp.2021.110496 [Citations: 16]

  93. Multiple solutions of nonlinear coupled constitutive relation model and its rectification in non-equilibrium flow computation

    Cao, Junzhe | Liu, Sha | Zhong, Chengwen | Zhuo, Congshan | Xu, Kun

    Computers & Mathematics with Applications, Vol. 174 (2024), Iss. P.1

    https://doi.org/10.1016/j.camwa.2024.08.017 [Citations: 0]

  94. Application of event-driven molecular dynamics approach to rarefied gas dynamics problems

    Yakunchikov, Artem | Kosyanchuk, Vasily

    Computers & Fluids, Vol. 170 (2018), Iss. P.121

    https://doi.org/10.1016/j.compfluid.2018.05.002 [Citations: 21]

  95. On the validity of the Boltzmann-BGK model through relaxation evaluation

    Sun, Quan-Hua | Cai, Chun-Pei | Gao, Wei

    Acta Mechanica Sinica, Vol. 30 (2014), Iss. 2 P.133

    https://doi.org/10.1007/s10409-014-0017-x [Citations: 5]

  96. Unified gas-kinetic wave-particle methods I: Continuum and rarefied gas flow

    Liu, Chang | Zhu, Yajun | Xu, Kun

    Journal of Computational Physics, Vol. 401 (2020), Iss. P.108977

    https://doi.org/10.1016/j.jcp.2019.108977 [Citations: 62]

  97. Numerical modeling of submicron particles for acoustic concentration in gaseous flow

    Liu, Jizhou | Li, Xiaodong | Hu, Fang Q.

    The Journal of the Acoustical Society of America, Vol. 147 (2020), Iss. 1 P.152

    https://doi.org/10.1121/10.0000568 [Citations: 1]

  98. Discrete Boltzmann model for implosion- and explosionrelated compressible flow with spherical symmetry

    Xu, Ai-Guo | Zhang, Guang-Cai | Zhang, Yu-Dong | Wang, Pei | Ying, Yang-Jun

    Frontiers of Physics, Vol. 13 (2018), Iss. 5

    https://doi.org/10.1007/s11467-018-0777-z [Citations: 15]

  99. Modeling of nonequilibrium effects in a compressible plasma based on the lattice Boltzmann method

    Huang, Haoyu | Jin, Ke | Li, Kai | Zheng, Xiaojing

    Physics of Plasmas, Vol. 31 (2024), Iss. 9

    https://doi.org/10.1063/5.0211465 [Citations: 0]

  100. A comparative study of an asymptotic preserving scheme and unified gas-kinetic scheme in continuum flow limit

    Chen, Songze | Xu, Kun

    Journal of Computational Physics, Vol. 288 (2015), Iss. P.52

    https://doi.org/10.1016/j.jcp.2015.02.014 [Citations: 51]

  101. Solving the discrete S-model kinetic equations with arbitrary order polynomial approximations

    Bond, D.M. | Wheatley, V. | Macrossan, M.N. | Goldsworthy, M.

    Journal of Computational Physics, Vol. 259 (2014), Iss. P.175

    https://doi.org/10.1016/j.jcp.2013.11.026 [Citations: 4]

  102. Boosting the convergence of low-variance DSMC by GSIS

    Luo, Liyan | Li, Qi | Wu, Lei

    Advances in Aerodynamics, Vol. 5 (2023), Iss. 1

    https://doi.org/10.1186/s42774-023-00138-0 [Citations: 2]

  103. Unified gas-kinetic particle method for dilute granular flow and its application in a solid jet

    Wang, Zhao | Yan, Hong

    Acta Mechanica Sinica, Vol. 36 (2020), Iss. 1 P.22

    https://doi.org/10.1007/s10409-019-00908-4 [Citations: 5]

  104. Comparison of Fifth-Order WENO Scheme and Finite Volume WENO-Gas-Kinetic Scheme for Inviscid and Viscous Flow Simulation

    Luo, Jun | Xuan, Lijun | Xu, Kun

    Communications in Computational Physics, Vol. 14 (2013), Iss. 3 P.599

    https://doi.org/10.4208/cicp.110212.021112a [Citations: 18]

  105. Heat and mass transfer of oscillatory lid-driven cavity flow in the continuum, transition and free molecular flow regimes

    Wang, Peng | Su, Wei | Zhu, Lianhua | Zhang, Yonghao

    International Journal of Heat and Mass Transfer, Vol. 131 (2019), Iss. P.291

    https://doi.org/10.1016/j.ijheatmasstransfer.2018.11.060 [Citations: 19]

  106. Unified gas-kinetic scheme for microchannel and nanochannel flows

    Liu, Sha | Zhong, Chengwen | Bai, Jie

    Computers & Mathematics with Applications, Vol. 69 (2015), Iss. 1 P.41

    https://doi.org/10.1016/j.camwa.2014.11.009 [Citations: 10]

  107. Instability of mixing layers: Momentum and thermal transport in the continuum breakdown regime

    Mohan, Vishnu | Sameen, A. | Srinivasan, Balaji | Girimaji, Sharath S.

    Physical Review E, Vol. 108 (2023), Iss. 5

    https://doi.org/10.1103/PhysRevE.108.L053101 [Citations: 0]

  108. A multiscale discrete velocity method for diatomic molecular gas

    Zhang, Qingdian | Zhuo, Congshan | Mu, Junlei | Zhong, Chengwen | Liu, Sha

    Physics of Fluids, Vol. 35 (2023), Iss. 7

    https://doi.org/10.1063/5.0153834 [Citations: 5]

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

    Jiang, Dingwu | Wang, Pei | Li, Jin | Mao, Meiliang

    Entropy, Vol. 24 (2022), Iss. 6 P.836

    https://doi.org/10.3390/e24060836 [Citations: 4]

  110. A discrete unified gas kinetic scheme with sparse velocity grid for rarefied gas flows

    Zhang, Shuyang | Li, Weidong | Fang, Ming | Guo, Zhaoli

    Computers & Fluids, Vol. 283 (2024), Iss. P.106391

    https://doi.org/10.1016/j.compfluid.2024.106391 [Citations: 0]

  111. A simple hydrodynamic-particle method for supersonic rarefied flows

    Liu, W. | Shu, C. | Teo, C. J. | Yuan, Z. Y. | Liu, Y. Y. | Zhang, Z. L.

    Physics of Fluids, Vol. 34 (2022), Iss. 5

    https://doi.org/10.1063/5.0088946 [Citations: 7]

  112. A Comparative Study of a Discrete Velocity Method and a Gas-Kinetic Method for a Binary Gas Mixture

    Todorova, Blaga | Steijl, Rene

    AIAA Scitech 2019 Forum, (2019),

    https://doi.org/10.2514/6.2019-1052 [Citations: 0]

  113. WENO-enhanced gas-kinetic scheme for direct simulations of compressible transition and turbulence

    Kumar, G. | Girimaji, S.S. | Kerimo, J.

    Journal of Computational Physics, Vol. 234 (2013), Iss. P.499

    https://doi.org/10.1016/j.jcp.2012.10.005 [Citations: 74]

  114. Burnett Spectral Method for High-Speed Rarefied Gas Flows

    Hu, Zhicheng | Cai, Zhenning

    SIAM Journal on Scientific Computing, Vol. 42 (2020), Iss. 5 P.B1193

    https://doi.org/10.1137/19M1294010 [Citations: 10]

  115. dugksFoam: An open source OpenFOAM solver for the Boltzmann model equation

    Zhu, Lianhua | Chen, Songze | Guo, Zhaoli

    Computer Physics Communications, Vol. 213 (2017), Iss. P.155

    https://doi.org/10.1016/j.cpc.2016.11.010 [Citations: 45]

  116. Discrete unified gas kinetic scheme for flows of binary gas mixture based on the McCormack model

    Zhang, Yue | Zhu, Lianhua | Wang, Peng | Guo, Zhaoli

    Physics of Fluids, Vol. 31 (2019), Iss. 1

    https://doi.org/10.1063/1.5063846 [Citations: 36]

  117. The dynamic mechanism of a moving Crookes radiometer

    Chen, Songze | Xu, Kun | Lee, Cunbiao

    Physics of Fluids, Vol. 24 (2012), Iss. 11

    https://doi.org/10.1063/1.4765353 [Citations: 15]

  118. Flow of a monatomic rarefied gas over a circular cylinder: Calculations based on the ab initio potential method

    Volkov, Alexey N. | Sharipov, Felix

    International Journal of Heat and Mass Transfer, Vol. 114 (2017), Iss. P.47

    https://doi.org/10.1016/j.ijheatmasstransfer.2017.05.127 [Citations: 12]

  119. Non-equilibrium thermal transport and entropy analyses in rarefied cavity flows

    Venugopal, Vishnu | Praturi, Divya Sri | Girimaji, Sharath S.

    Journal of Fluid Mechanics, Vol. 864 (2019), Iss. P.995

    https://doi.org/10.1017/jfm.2018.1028 [Citations: 17]

  120. Improved fully implicit discrete-velocity method for efficient simulation of flows in all flow regimes

    Yang, L. M. | Chen, Z. | Shu, C. | Yang, W. M. | Wu, J. | Zhang, L. Q.

    Physical Review E, Vol. 98 (2018), Iss. 6

    https://doi.org/10.1103/PhysRevE.98.063313 [Citations: 30]

  121. Discrete unified gas kinetic scheme on unstructured meshes

    Zhu, Lianhua | Guo, Zhaoli | Xu, Kun

    Computers & Fluids, Vol. 127 (2016), Iss. P.211

    https://doi.org/10.1016/j.compfluid.2016.01.006 [Citations: 89]

  122. Particle simulation of nonequilibrium gas flows based on ellipsoidal statistical Fokker–Planck model

    Jiang, Yazhong | Gao, Zhenxun | Lee, Chun-Hian

    Computers & Fluids, Vol. 170 (2018), Iss. P.106

    https://doi.org/10.1016/j.compfluid.2018.04.034 [Citations: 15]

  123. Development of explicit formulations of G45-based gas kinetic scheme for simulation of continuum and rarefied flows

    Liu, Z. J. | Shu, C. | Chen, S. Y. | Liu, W. | Yuan, Z. Y. | Yang, L. M.

    Physical Review E, Vol. 105 (2022), Iss. 4

    https://doi.org/10.1103/PhysRevE.105.045302 [Citations: 6]

  124. Kinetic comparative study on aerodynamic characteristics of hypersonic reentry vehicle from near-continuous flow to free molecular flow

    Li, Jin | Jiang, Dingwu | Geng, Xiangren | Chen, Jianqiang

    Advances in Aerodynamics, Vol. 3 (2021), Iss. 1

    https://doi.org/10.1186/s42774-021-00063-0 [Citations: 11]

  125. Development of a discrete gas-kinetic scheme for simulation of two-dimensional viscous incompressible and compressible flows

    Yang, L. M. | Shu, C. | Wang, Y.

    Physical Review E, Vol. 93 (2016), Iss. 3

    https://doi.org/10.1103/PhysRevE.93.033311 [Citations: 27]

  126. Computation of 1-D shock structure using nonlinear coupled constitutive relations and generalized hydrodynamic equations

    Zhao, Wenwen | Jiang, Zhongzheng | Chen, Weifang

    (2016) P.140007

    https://doi.org/10.1063/1.4967638 [Citations: 3]

  127. Development of convolutional neural network-based surrogate model for three-dimensional vacuum plume prediction via direct simulation Monte Carlo method

    Zhang, Baiyi | Cai, Guobiao | Gao, Da | Weng, Huiyan | Wang, Weizong | He, Bijiao

    Physics of Fluids, Vol. 36 (2024), Iss. 7

    https://doi.org/10.1063/5.0216768 [Citations: 0]

  128. A semi-implicit gas-kinetic scheme for smooth flows

    Wang, Peng | Guo, Zhaoli

    Computer Physics Communications, Vol. 205 (2016), Iss. P.22

    https://doi.org/10.1016/j.cpc.2016.04.005 [Citations: 5]

  129. Unified gas-kinetic scheme for diatomic molecular simulations in all flow regimes

    Liu, Sha | Yu, Pubing | Xu, Kun | Zhong, Chengwen

    Journal of Computational Physics, Vol. 259 (2014), Iss. P.96

    https://doi.org/10.1016/j.jcp.2013.11.030 [Citations: 79]

  130. Unified gas-kinetic simulation of slider air bearing

    Wang, Ruijie | Xu, Kun

    Theoretical and Applied Mechanics Letters, Vol. 4 (2014), Iss. 2 P.022001

    https://doi.org/10.1063/2.1402201 [Citations: 3]

  131. A variance-reduced direct Monte Carlo simulation method for solving the Boltzmann equation over a wide range of rarefaction

    Sadr, Mohsen | Hadjiconstantinou, Nicolas G.

    Journal of Computational Physics, Vol. 472 (2023), Iss. P.111677

    https://doi.org/10.1016/j.jcp.2022.111677 [Citations: 13]

  132. Conserved discrete unified gas-kinetic scheme with unstructured discrete velocity space

    Chen, Jianfeng | Liu, Sha | Wang, Yong | Zhong, Chengwen

    Physical Review E, Vol. 100 (2019), Iss. 4

    https://doi.org/10.1103/PhysRevE.100.043305 [Citations: 46]

  133. The high performance parallel algorithm for Unified Gas-Kinetic Scheme

    Li, Shiyi | Li, Qibing | Fu, Song | Xu, Jinxiu

    (2016) P.180007

    https://doi.org/10.1063/1.4967676 [Citations: 4]

  134. A unified stochastic particle method with spatiotemporal adaptation for simulating multiscale gas flows

    Feng, Kaikai | Cui, Ziqi | Tian, Peng | Zhang, Jun

    Journal of Computational Physics, Vol. 505 (2024), Iss. P.112915

    https://doi.org/10.1016/j.jcp.2024.112915 [Citations: 1]

  135. Application of unified gas-kinetic scheme for hypersonic non-equilibrium flow

    Wang, Zhao | Yan, Hong | Li, Qibing | Xu, Kun

    21st AIAA International Space Planes and Hypersonics Technologies Conference, (2017),

    https://doi.org/10.2514/6.2017-2245 [Citations: 0]

  136. Coupling improved discrete velocity method and G13-based gas kinetic flux solver: A hybrid method and its application for non-equilibrium flows

    Liu, W. | Liu, Y. Y. | Yang, L. M. | Liu, Z. J. | Yuan, Z. Y. | Shu, C. | Teo, C. J.

    Physics of Fluids, Vol. 33 (2021), Iss. 9

    https://doi.org/10.1063/5.0062107 [Citations: 9]

  137. A novel solver for simulation of flows from continuum regime to rarefied regime at moderate Knudsen number

    Liu, Z.J. | Shu, C. | Chen, S.Y. | Yang, L.M. | Wan, M.P. | Liu, W.

    Journal of Computational Physics, Vol. 415 (2020), Iss. P.109548

    https://doi.org/10.1016/j.jcp.2020.109548 [Citations: 14]

  138. A unified gas-kinetic scheme for continuum and rarefied flows VI: Dilute disperse gas-particle multiphase system

    Liu, Chang | Wang, Zhao | Xu, Kun

    Journal of Computational Physics, Vol. 386 (2019), Iss. P.264

    https://doi.org/10.1016/j.jcp.2018.12.040 [Citations: 33]

  139. A Moving Mesh Method for Kinetic/Hydrodynamic Coupling

    Hu, Zhicheng | Wang, Heyu

    Advances in Applied Mathematics and Mechanics, Vol. 4 (2012), Iss. 06 P.685

    https://doi.org/10.4208/aamm.12-12S01 [Citations: 2]

  140. DSMC investigation of rarefied gas flow in a four-sided lid driven cavity: Effect of rarefaction and lid velocities

    Nabapure, Deepak | Murthy K, Ram Chandra

    Journal of Computational Science, Vol. 49 (2021), Iss. P.101276

    https://doi.org/10.1016/j.jocs.2020.101276 [Citations: 6]

  141. A comparative study of the DSBGK and DVM methods for low-speed rarefied gas flows

    Ho, Minh Tuan | Li, Jun | Wu, Lei | Reese, Jason M. | Zhang, Yonghao

    Computers & Fluids, Vol. 181 (2019), Iss. P.143

    https://doi.org/10.1016/j.compfluid.2019.01.019 [Citations: 18]

  142. Efficient simulation of multidimensional continuum and non-continuum flows by a parallelised unified gas kinetic scheme solver

    Ragta, Lokesh Kumar | Srinivasan, Balaji | Sinha, Sawan Suman

    International Journal of Computational Fluid Dynamics, Vol. 31 (2017), Iss. 6-8 P.292

    https://doi.org/10.1080/10618562.2017.1350265 [Citations: 5]

  143. Unified gas-kinetic scheme for diatomic molecular flow with translational, rotational, and vibrational modes

    Wang, Zhao | Yan, Hong | Li, Qibing | Xu, Kun

    Journal of Computational Physics, Vol. 350 (2017), Iss. P.237

    https://doi.org/10.1016/j.jcp.2017.08.045 [Citations: 35]