March  2009, 2(1): 231-250. doi: 10.3934/krm.2009.2.231

Semilagrangian schemes applied to moving boundary problems for the BGK model of rarefied gas dynamics

1. 

Dipartimento di Matematica e Informatica, Università di Catania, Viale Andrea Doria 6, 95125 Catania, Italy

2. 

Université de Lyon, UL1, INSAL, ECL, CNRS, UMR5208, Institut Camille Jordan, 43 boulevard 11 novembre 1918, F-69622 Villeurbanne cedex, France

Received  November 2008 Revised  December 2008 Published  January 2009

In this paper we present a new semilagrangian scheme for the numerical solution of the BGK model of rarefied gas dynamics, in a domain with moving boundaries, in view of applications to Micro Electro Mechanical Systems (MEMS). The source term is treated implicitly, which makes the scheme Asymptotic Preserving in the limit of small Knudsen number. Because of its Lagrangian nature, no stability restriction is posed on the CFL number, which is determined only by accuracy requirements. The method is tested on a one dimensional piston problem. The solution for small Knudsen number is compared with the results obtained by the numerical solution of the Euler equation of gas dynamics.
Citation: Giovanni Russo, Francis Filbet. Semilagrangian schemes applied to moving boundary problems for the BGK model of rarefied gas dynamics. Kinetic and Related Models, 2009, 2 (1) : 231-250. doi: 10.3934/krm.2009.2.231
[1]

Raffaele Esposito, Mario Pulvirenti. Rigorous validity of the Boltzmann equation for a thin layer of a rarefied gas. Kinetic and Related Models, 2010, 3 (2) : 281-297. doi: 10.3934/krm.2010.3.281

[2]

Yue Qiu, Sara Grundel, Martin Stoll, Peter Benner. Efficient numerical methods for gas network modeling and simulation. Networks and Heterogeneous Media, 2020, 15 (4) : 653-679. doi: 10.3934/nhm.2020018

[3]

Jiangshan Wang, Lingxiong Meng, Hongen Jia. Numerical analysis of modular grad-div stability methods for the time-dependent Navier-Stokes/Darcy model. Electronic Research Archive, 2020, 28 (3) : 1191-1205. doi: 10.3934/era.2020065

[4]

Xiaozhong Yang, Xinlong Liu. Numerical analysis of two new finite difference methods for time-fractional telegraph equation. Discrete and Continuous Dynamical Systems - B, 2021, 26 (7) : 3921-3942. doi: 10.3934/dcdsb.2020269

[5]

Nicolas Crouseilles, Giacomo Dimarco, Mohammed Lemou. Asymptotic preserving and time diminishing schemes for rarefied gas dynamic. Kinetic and Related Models, 2017, 10 (3) : 643-668. doi: 10.3934/krm.2017026

[6]

Asif Yokus, Mehmet Yavuz. Novel comparison of numerical and analytical methods for fractional Burger–Fisher equation. Discrete and Continuous Dynamical Systems - S, 2021, 14 (7) : 2591-2606. doi: 10.3934/dcdss.2020258

[7]

Sébastien Guisset. Angular moments models for rarefied gas dynamics. Numerical comparisons with kinetic and Navier-Stokes equations. Kinetic and Related Models, 2020, 13 (4) : 739-758. doi: 10.3934/krm.2020025

[8]

Emmanuel Frénod. Homogenization-based numerical methods. Discrete and Continuous Dynamical Systems - S, 2016, 9 (5) : i-ix. doi: 10.3934/dcdss.201605i

[9]

Konstantinos Chrysafinos. Error estimates for time-discretizations for the velocity tracking problem for Navier-Stokes flows by penalty methods. Discrete and Continuous Dynamical Systems - B, 2006, 6 (5) : 1077-1096. doi: 10.3934/dcdsb.2006.6.1077

[10]

Xiaobing Feng, Shu Ma. Stable numerical methods for a stochastic nonlinear Schrödinger equation with linear multiplicative noise. Discrete and Continuous Dynamical Systems - S, 2022, 15 (4) : 687-711. doi: 10.3934/dcdss.2021071

[11]

Ching-Shan Chou, Yong-Tao Zhang, Rui Zhao, Qing Nie. Numerical methods for stiff reaction-diffusion systems. Discrete and Continuous Dynamical Systems - B, 2007, 7 (3) : 515-525. doi: 10.3934/dcdsb.2007.7.515

[12]

Emmanuel Frénod. An attempt at classifying homogenization-based numerical methods. Discrete and Continuous Dynamical Systems - S, 2015, 8 (1) : i-vi. doi: 10.3934/dcdss.2015.8.1i

[13]

Sebastián J. Ferraro, David Iglesias-Ponte, D. Martín de Diego. Numerical and geometric aspects of the nonholonomic SHAKE and RATTLE methods. Conference Publications, 2009, 2009 (Special) : 220-229. doi: 10.3934/proc.2009.2009.220

[14]

Abdon Atangana, José Francisco Gómez-Aguilar, Jordan Y. Hristov, Kolade M. Owolabi. Preface on "New trends of numerical and analytical methods". Discrete and Continuous Dynamical Systems - S, 2020, 13 (3) : i-ii. doi: 10.3934/dcdss.20203i

[15]

Timothy Blass, Rafael de la Llave. Perturbation and numerical methods for computing the minimal average energy. Networks and Heterogeneous Media, 2011, 6 (2) : 241-255. doi: 10.3934/nhm.2011.6.241

[16]

Joseph A. Connolly, Neville J. Ford. Comparison of numerical methods for fractional differential equations. Communications on Pure and Applied Analysis, 2006, 5 (2) : 289-307. doi: 10.3934/cpaa.2006.5.289

[17]

Miguel Ángel Evangelista-Alvarado, José Crispín Ruíz-Pantaleón, Pablo Suárez-Serrato. On computational Poisson geometry II: Numerical methods. Journal of Computational Dynamics, 2021, 8 (3) : 273-307. doi: 10.3934/jcd.2021012

[18]

Holger Heumann, Ralf Hiptmair. Eulerian and semi-Lagrangian methods for convection-diffusion for differential forms. Discrete and Continuous Dynamical Systems, 2011, 29 (4) : 1471-1495. doi: 10.3934/dcds.2011.29.1471

[19]

Alexander V. Bobylev, Sergey V. Meleshko. On group symmetries of the hydrodynamic equations for rarefied gas. Kinetic and Related Models, 2021, 14 (3) : 469-482. doi: 10.3934/krm.2021012

[20]

Stéphane Brull, Pierre Charrier, Luc Mieussens. Gas-surface interaction and boundary conditions for the Boltzmann equation. Kinetic and Related Models, 2014, 7 (2) : 219-251. doi: 10.3934/krm.2014.7.219

2021 Impact Factor: 1.398

Metrics

  • PDF downloads (148)
  • HTML views (0)
  • Cited by (26)

Other articles
by authors

[Back to Top]