Numerical Transport Process of Splitting Kinetic Schemes in the Navier–Stokes–Fourier Limit

References

• Aristov, V. V. 2001. Direct Methods for Solving the Boltzmann Equation and Study of Nonequilibrium Flows. Vol. 60. Dordrecht: Springer Science & Business Media.
   Google Scholar
• Bhatnagar, Prabhu Lal, Eugene P. Gross, and Max Krook. 1954. “A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-component Systems.” Physical Review 94 (3): 511–525.
   Web of Science ®Google Scholar
• Bird, Graeme A., and J. M. Brady. 1994. Molecular Gas Dynamics and the Direct Simulation of Gas Flows. Oxford: Clarendon Press.
   Google Scholar
• Chapman, Sydney, and Thomas George Cowling. 1990. The Mathematical Theory of Non-uniform Gases: An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases. New York: Cambridge University Press.
   Google Scholar
• Chen, Shiyi, and Gary D. Doolen. 1998. “Lattice Boltzmann Method for Fluid Flows.” Annual Review of Fluid Mechanics 30 (1): 329–364.
   Web of Science ®Google Scholar
• Dimarco, Giacomo, and Lorenzo Pareschi. 2013. “Asymptotic Preserving Implicit-explicit Runge–Kutta Methods for Nonlinear Kinetic Equations.” SIAM Journal on Numerical Analysis 51 (2): 1064–1087.
   Web of Science ®Google Scholar
• Filbet, Francis, and Shi Jin. 2010. “A Class of Asymptotic-preserving Schemes for Kinetic Equations and Related Problems with Stiff Sources.” Journal of Computational Physics 229 (20): 7625–7648.
   Web of Science ®Google Scholar
• Goshayeshi, Bijan, Ehsan Roohi, and Stefan Stefanov. 2015. “A Novel Simplified Bernoulli Trials Collision Scheme in the Direct Simulation Monte Carlo with Intelligence Over Particle Distances.” Physics of Fluids 27 (10): 107104.
   Google Scholar
• Guo, Zhaoli, and Chang Shu. 2013. Lattice Boltzmann Method and Its Application in Engineering. Vol. 3. Singapore: World Scientific.
   Google Scholar
• Guo, Zhaoli, Kun Xu, and Ruijie Wang. 2013. “Discrete Unified Gas Kinetic Scheme for All Knudsen Number Flows: Low-speed Isothermal Case.” Physical Review E 88 (3): 033305.
   Google Scholar
• Guo, Zhaoli, Ruijie Wang, and Kun Xu. 2015. “Discrete Unified Gas Kinetic Scheme for All Knudsen Number Flows. II. Thermal Compressible Case.” Physical Review E 91 (3): 033313.
   Google Scholar
• Guo, Zhaoli, Jiequan Li, and Kun Xu. 2019. “On Unified Preserving Properties of Kinetic Schemes.” arXiv preprint arXiv:1909.04923.
   Google Scholar
• Lallemand, Pierre, Li-shi Luo, Manfred Krafczyk, and Wen-An Yong. 2021. “The Lattice Boltzmann Method for Nearly Incompressible Flows.” Journal of Computational Physics 431 (9): 109713.
   Google Scholar
• Li, Zhi-Hui, and Han-Xin Zhang. 2004. “Study on Gas Kinetic Unified Algorithm for Flows From Rarefied Transition to Continuum.” Journal of Computational Physics 193 (2): 708–738.
   Web of Science ®Google Scholar
• Liu, Chang, Yajun Zhu, and Kun Xu. 2020. “Unified Gas-Kinetic Wave-particle Methods I: Continuum and Rarefied Gas Flow.” Journal of Computational Physics 401 (10): 108977.
   Google Scholar
• Lotfian, Ali, and Ehsan Roohi. 2019. “Radiometric Flow in Periodically Patterned Channels: Fluid Physics and Improved Configurations.” Journal of Fluid Mechanics 860: 544–576.
   Web of Science ®Google Scholar
• Mieussens, Luc. 2000. “Discrete Velocity Model and Implicit Scheme for the BGK Equation of Rarefied Gas Dynamics.” Mathematical Models and Methods in Applied Sciences 10 (08): 1121–1149.
   Google Scholar
• Pareschi, Lorenzo, and Giovanni Russo. 2000. “Asymptotic Preserving Monte Carlo Methods for the Boltzmann Equation.” Transport Theory and Statistical Physics 29 (3–5): 415–430.
   Web of Science ®Google Scholar
• Pareschi, Lorenzo, and Giovanni Russo. 2001. “Time Relaxed Monte Carlo Methods for the Boltzmann Equation.” SIAM Journal on Scientific Computing 23 (4): 1253–1273.
   Web of Science ®Google Scholar
• Rafieenasab, Sepehr, Ehsan Roohi, and Alireza Teymourtash. 2020. “Numerical Analysis of Nonlinear Thermal Stress Flow Between Concentric Elliptical Cylinders.” Physics of Fluids 32 (10): 102007.
   Google Scholar
• Roohi, Ehsan, and Stefan Stefanov. 2016. “Collision Partner Selection Schemes in DSMC: From Micro/nano Flows to Hypersonic Flows.” Physics Reports 656 (5): 1–38.
   Google Scholar
• Shen, Ching. 2006. Rarefied Gas Dynamics: Fundamentals, Simulations and Micro Flows. Berlin: Springer Science & Business Media.
   Google Scholar
• Xu, Kun. 2001. “A Gas-kinetic BGK Scheme for the Navier–Stokes Equations and Its Connection with Artificial Dissipation and Godunov Method.” Journal of Computational Physics 171 (1): 289–335.
   Web of Science ®Google Scholar
• Xu, Kun. 2015. Direct Modeling for Computational Fluid Dynamics: Construction and Application of Unified Gas-kinetic Schemes. Singapore: World Scientific.
   Google Scholar
• Xu, Kun. 2021. A Unified Computational Fluid Dynamics Framework From Rarefied to Continuum Regimes. Cambridge: Cambridge University Press.
   Google Scholar
• Xu, Kun, and Juan-Chen Huang. 2010. “A Unified Gas-Kinetic Scheme for Continuum and Rarefied Flows.” Journal of Computational Physics 229 (20): 7747–7764.
   Web of Science ®Google Scholar
• Yang, J. Y., and J. C. Huang. 1995. “Rarefied Flow Computations Using Nonlinear Model Boltzmann Equations.” Journal of Computational Physics 120 (2): 323–339.
   Web of Science ®Google Scholar
• Zhu, Yajun, and Kun Xu. 2021. “The First Decade of Unified Gas Kinetic Scheme.” arXiv preprint arXiv:2102.01261.
   Google Scholar
• Zhu, Yajun, Chengwen Zhong, and Kun Xu. 2016. “Implicit Unified Gas-Kinetic Scheme for Steady State Solutions in All Flow Regimes.” Journal of Computational Physics 315 (3): 16–38.
   Google Scholar
• Zhu, Yajun, Chengwen Zhong, and Kun Xu. 2017. “Unified Gas-Kinetic Scheme with Multigrid Convergence for Rarefied Flow Study.” Physics of Fluids 29 (9): 096102.
   Google Scholar
• Zhu, Yajun, Chengwen Zhong, and Kun Xu. 2019. “An Implicit Unified Gas-Kinetic Scheme for Unsteady Flow in All Knudsen Regimes.” Journal of Computational Physics 386 (9): 190–217.
   Google Scholar
• Zhu, Yajun, Chang Liu, Chengwen Zhong, and Kun Xu. 2019. “Unified Gas-Kinetic Wave-Particle Methods. II. Multiscale Simulation on Unstructured Mesh.” Physics of Fluids 31 (6): 067105.
   Google Scholar
• Zhu, Yajun, Chengwen Zhong, and Kun Xu. 2020. “Ray Effect in Rarefied Flow Simulation.” Journal of Computational Physics 422 (3): 109751.
   Google Scholar