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Transport Theory and Statistical Physics Volume 29, 2000 - Issue 3-5: Proceedings of the Fifth International Workshop on Mathematical Aspects of Fluid and Plasma Dynamics
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Original Articles

Asymptotic preserving Monte Carlo methods for the Boltzmann equation

L. Pareschi Mathematics Department, University of Ferrara, E-mail: [email protected]
&
G. Russo Mathematics Department, University of L'Aquila, E-mail: [email protected]
Pages 415-430 | Received 08 Dec 1998, Accepted 28 Aug 1999, Published online: 02 Sep 2006

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Yajun Zhu, Chengwen Zhong & Kun Xu. (2021) Numerical Transport Process of Splitting Kinetic Schemes in the Navier–Stokes–Fourier Limit. International Journal of Computational Fluid Dynamics 35:8, pages 653-665.
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S.S. Nourazar, P. Jahangiri, A. Aboutalebi, A.A. Ganjaei, M. Nourazar & J. Khadem. (2011) On a modified Monte-Carlo method and variable soft sphere model for rarefied binary gas mixture flow simulation. International Journal of Computational Fluid Dynamics 25:5, pages 271-285.
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Articles from other publishers (31)

Yufeng Wei, Yajun Zhu & Kun Xu. (2024) Unified gas-kinetic wave-particle methods VII: Diatomic gas with rotational and vibrational nonequilibrium. Journal of Computational Physics 497, pages 112610.
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Yufeng Wei, Junzhe Cao, Xing Ji & Kun Xu. (2023) Adaptive wave-particle decomposition in UGKWP method for high-speed flow simulations. Advances in Aerodynamics 5:1.
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Musfequs Salehin & A. B. M. Toufique Hasan. (2023) Transitional rarefied flows over NACA 0012 airfoil in supersonic conditions: A DSMC investigation. Journal of Mechanical Science and Technology.
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Fei Fei. (2023) A time-relaxed Monte Carlo method preserving the Navier-Stokes asymptotics. Journal of Computational Physics 486, pages 112128.
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Liyan Luo, Qi Li & Lei Wu. (2023) Boosting the convergence of low-variance DSMC by GSIS. Advances in Aerodynamics 5:1.
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Kun Xu. 2021. A Unified Computational Fluid Dynamics Framework from Rarefied to Continuum Regimes. A Unified Computational Fluid Dynamics Framework from Rarefied to Continuum Regimes.
Chang Liu, Yajun Zhu & Kun Xu. (2020) Unified gas-kinetic wave-particle methods I: Continuum and rarefied gas flow. Journal of Computational Physics 401, pages 108977.
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. (2019) Unified gas-kinetic wave-particle methods. II. Multiscale simulation on unstructured mesh. Physics of Fluids 31:6, pages 067105.
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Abdelghani Bellouquid & Jacques Tagoudjeu. (2018) An Asymptotic Preserving Scheme for Kinetic Models for Chemotaxis Phenomena. Communications in Applied and Industrial Mathematics 9:2, pages 61-75.
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M. Eskandari & S.S. Nourazar. (2018) On the time relaxed Monte Carlo computations for the flow over a flat nano-plate. Computers & Fluids 160, pages 219-229.
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Raluca EftimieRaluca Eftimie. 2018. Hyperbolic and Kinetic Models for Self-organised Biological Aggregations. Hyperbolic and Kinetic Models for Self-organised Biological Aggregations 195 226 .
M. Eskandari & S.S. Nourazar. (2017) On the time relaxed Monte Carlo computations for the lid-driven micro cavity flow. Journal of Computational Physics 343, pages 355-367.
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Lei Wu, Jun Zhang, Jason M. Reese & Yonghao Zhang. (2015) A fast spectral method for the Boltzmann equation for monatomic gas mixtures. Journal of Computational Physics 298, pages 602-621.
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Russel Caflisch. 2015. Encyclopedia of Applied and Computational Mathematics. Encyclopedia of Applied and Computational Mathematics 968 972 .
G. Dimarco & L. Pareschi. (2014) Numerical methods for kinetic equations. Acta Numerica 23, pages 369-520.
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MATHIAS ROUSSET & GIOVANNI SAMAEY. (2013) SIMULATING INDIVIDUAL-BASED MODELS OF BACTERIAL CHEMOTAXIS WITH ASYMPTOTIC VARIANCE REDUCTION. Mathematical Models and Methods in Applied Sciences 23:12, pages 2155-2191.
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M. Hossein Gorji & Patrick Jenny. (2013) A Fokker–Planck based kinetic model for diatomic rarefied gas flows. Physics of Fluids 25:6.
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Gregg A. Radtke, Jean-Philippe M. Péraud & Nicolas G. Hadjiconstantinou. (2013) On efficient simulations of multiscale kinetic transport. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 371:1982, pages 20120182.
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Giacomo Dimarco & Lorenzo Pareschi. (2013) Asymptotic Preserving Implicit-Explicit Runge--Kutta Methods for Nonlinear Kinetic Equations. SIAM Journal on Numerical Analysis 51:2, pages 1064-1087.
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Pouyan Jahangiri, Amir Nejat, Jila Samadi & Ali Aboutalebi. (2012) A high-order Monte Carlo algorithm for the direct simulation of Boltzmann equation. Journal of Computational Physics 231:14, pages 4578-4596.
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Anaïs Crestetto, Nicolas Crouseilles & Mohammed Lemou. (2012) Kinetic/fluid micro-macro numerical schemes for Vlasov-Poisson-BGK equation using particles. Kinetic & Related Models 5:4, pages 787-816.
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Giacomo Dimarco & Lorenzo Pareschi. (2011) Exponential Runge–Kutta Methods for Stiff Kinetic Equations. SIAM Journal on Numerical Analysis 49:5, pages 2057-2077.
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S. S. Nourazar & A. A. Ganjaei. (2010) A new scheme developed for the numerical simulation of the Boltzmann equation using the direct simulation monte-carlo scheme for the flow about a sphere. Journal of Mechanical Science and Technology 24:10, pages 1989-1996.
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A. A. Ganjaei & S. S. Nourazar. (2009) A new algorithm for the simulation of the boltzmann equation using the direct simulation monte-carlo method. Journal of Mechanical Science and Technology 23:10, pages 2861-2870.
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A. A. Ganjaei & S. S. Nourazar. (2009) Numerical simulation of a binary gas flow inside a rotating cylinder. Journal of Mechanical Science and Technology 23:10, pages 2848-2860.
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P. Degond, F. Deluzet, A. Sangam & M.-H. Vignal. (2009) An Asymptotic Preserving scheme for the Euler equations in a strong magnetic field. Journal of Computational Physics 228:10, pages 3540-3558.
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Russel Caflisch, Han Chen, Erding Luo & Lorenzo Pareschi. (2006) A Hybrid Method that Interpolates Between DSMC and CFD. A Hybrid Method that Interpolates Between DSMC and CFD.
Lorenzo Pareschi & Stefano Trazzi. (2005) Numerical solution of the Boltzmann equation by time relaxed Monte Carlo (TRMC) methods. International Journal for Numerical Methods in Fluids 48:9, pages 947-983.
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Russel E. Caflisch & Lorenzo Pareschi. 2004. Transport in Transition Regimes. Transport in Transition Regimes 57 73 .
S. Cordier & S. Mancini. 2003. Numerical Mathematics and Advanced Applications. Numerical Mathematics and Advanced Applications 447 457 .
Lorenzo Pareschi & Giovanni Russo. (2001) Time Relaxed Monte Carlo Methods for the Boltzmann Equation. SIAM Journal on Scientific Computing 23:4, pages 1253-1273.
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