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Articles

An Investigation of Uncertainty Propagation in Non-equilibrium Flows

Pages 294-318 | Received 23 Nov 2021, Accepted 11 Jul 2022, Published online: 02 Aug 2022

References

  • Bourgat, Jean-François, Patrick Le Tallec, and Moulay D. Tidriri. 1995. “Coupling Boltzmann and Navier–Stokes Equations by Friction.” Journal of Computational Physics 127 (2): 227–245.
  • Cacuci, Dan G. 2003. Sensitivity and Uncertainty Analysis, Volume I: Theory. Boca Raton: Chapman & Hall/CRC.
  • Chapman, Sydney, and Thomas George Cowling. 1970. 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.
  • Degond, Pierre, Giacomo Dimarco, and Luc Mieussens. 2007. “A Moving Interface Method for Dynamic Kinetic–Fluid Coupling.” Journal of Computational Physics 227 (2): 1176–1208.
  • Dimarco, Giacomo, and Lorenzo Pareschi. 2019. “Multi-scale Control Variate Methods for Uncertainty Quantification in Kinetic Equations.” Journal of Computational Physics 388: 63–89.
  • 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.
  • Grad, Harold. 1949. “On the Kinetic Theory of Rarefied Gases.” Communications on Pure and Applied Mathematics 2 (4): 331–407.
  • Hilbert, David. 1902. “Mathematical Problems.” Bulletin of the American Mathematical Society 8 (10): 437–479.
  • Hu, Jingwei, and Shi Jin. 2017. “Uncertainty Quantification for Kinetic Equations.” In Uncertainty Quantification for Hyperbolic and Kinetic Equations, 193–229. Cham: Springer.
  • Lee Rodgers, Joseph, and W. Alan Nicewander. 1988. “Thirteen Ways to Look at the Correlation Coefficient.” The American Statistician 42 (1): 59–66.
  • Lemou, Mohammed, and Luc Mieussens. 2008. “A New Asymptotic Preserving Scheme Based on Micro–Macro Formulation for Linear Kinetic Equations in the Diffusion Limit.” SIAM Journal on Scientific Computing 31 (1): 334–368.
  • Lennard-Jones, John Edward. 1924. “On the Determination of Molecular Fields. II. From the Equation of State of Gas.” Proceedings of the Royal Society of London. Series A 106: 463–477.
  • Najm, Habib N. 2009. “Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics.” Annual Review of Fluid Mechanics 41: 35–52.
  • Saltelli, Andrea, Stefano Tarantola, and K. P.-S. Chan. 1999. “A Quantitative Model-Independent Method for Global Sensitivity Analysis of Model Output.” Technometrics 41 (1): 39–56.
  • Sun, Quanhua, Iain D. Boyd, and Graham V. Candler. 2004. “A Hybrid Continuum/Particle Approach for Modeling Subsonic, Rarefied Gas Flows.” Journal of Computational Physics 194 (1): 256–277.
  • Walters, Robert W., and Luc Huyse. 2002. “Uncertainty Analysis for Fluid Mechanics with Applications.” Technical Report. National Aeronautics and Space Administration Hampton VA Langley Research Center.
  • Wijesinghe, H. S., R. D. Hornung, A. L. Garcia, and N. G. Hadjiconstantinou. 2004. “Three-dimensional Hybrid Continuum-Atomistic Simulations for Multiscale Hydrodynamics.” Journal of Fluids Engineering 126 (5): 768–777.
  • Xiao, Tianbai. 2021a. “A Flux Reconstruction Kinetic Scheme for the Boltzmann Equation.” Journal of Computational Physics 447: 110689.
  • Xiao, Tianbai. 2021b. “Kinetic.jl: A Portable Finite Volume Toolbox for Scientific and Neural Computing.” Journal of Open Source Software 6 (62): 3060.
  • Xiao, Tianbai, Qingdong Cai, and Kun Xu. 2017. “A Well-Balanced Unified Gas-Kinetic Scheme for Multiscale Flow Transport Under Gravitational Field.” Journal of Computational Physics 332: 475–491.
  • Xiao, Tianbai, and Martin Frank. 2021a. “A Stochastic Kinetic Scheme for Multi-scale Flow Transport with Uncertainty Quantification.” Journal of Computational Physics 437: 110337.
  • Xiao, Tianbai, and Martin Frank. 2021b. “A Stochastic Kinetic Scheme for Multi-scale Plasma Transport with Uncertainty Quantification.” Journal of Computational Physics 432: 110139.
  • Xiao, Tianbai, Chang Liu, Kun Xu, and Qingdong Cai. 2020. “A Velocity-Space Adaptive Unified Gas Kinetic Scheme for Continuum and Rarefied Flows.” Journal of Computational Physics 415: 109535.
  • Xiao, Tianbai, Kun Xu, Qingdong Cai, and Tiezheng Qian. 2018. “An Investigation of Non-equilibrium Heat Transport in a Gas System Under External Force Field.” International Journal of Heat and Mass Transfer 126: 362–379.
  • Xiu, Dongbin, and George Em Karniadakis. 2003. “Modeling Uncertainty in Flow Simulations Via Generalized Polynomial Chaos.” Journal of Computational Physics 187 (1): 137–167.
  • 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.
  • 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.

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