
Mathematics in Engineering, 2020, 2(2): 203229. doi: 10.3934/mine.2020010
Research article Special Issues
Export file:
Format
 RIS(for EndNote,Reference Manager,ProCite)
 BibTex
 Text
Content
 Citation Only
 Citation and Abstract
Interaction of rigid body motion and rarefied gas dynamics based on the BGK model
1 Department of Mathematics, Technische Universität Kaiserslautern, ErwinSchrödingerStraße, 67663 Kaiserslautern, Germany
2 Fraunhofer ITWM, Fraunhoferplatz 1, 67663 Kaiserslautern, Germany
3 Department of Mathematics and Computer Science, University of Catania, Italy
^{†}This contribution is part of the Special Issue: Nonlinear models in applied mathematics
Guest Editor: Giuseppe Maria Coclite
Link: https://www.aimspress.com/newsinfo/1213.html
Received: , Accepted: , Published:
Special Issues: Nonlinear models in applied mathematics
References
1. Avesani D, Dumbser M, Bellin A (2014) A new class of MovingLeastSquares WENOSPH schemes. J Comput Phys 270: 278299.
2. Arslanbekov RR, Kolobov VI, Frolova AA (2011) Immersed Boundary Method for Boltzmann and NavierStokes Solvers with Adaptive Cartesian Mesh. AIP Conference Proceedings 1333: 873877.
3. Babovsky H (1989) A convergence proof for Nanbu's Boltzmann simulation scheme. Eur J Mech 8: 4155.
4. Baier T, Tiwari S, Shrestha S, et al. (2018) Thermophoresis of Janus particles at large Knudsen numbers. Phys Rev Fluids 3: 094202.
5. Bird G (1995) Molecular Gas Dynamics and the Direct Simulation of Gas Flows, Oxford: Clarendon Press.
6. Cercignani C, Illner R, Pulvirenti M (2013) The Mathematical Theory of Dilute Gases, Springer Science & Business Media.
7. Chapman S, Cowling TW (1970) The Mathematical Theory of NonUniform Gases, England: Cambridge University Press.
8. Chertock A, Coco A, Kurganov A, et al. (2018) A secondorder finitedifference method for compressible fluids in domains with moving boundaries. Commun Comput Phys 23: 230263.
9. Chu CK (1965) Kinetictheoretic description of the formation of a shock wave. Phys Fluids 8: 1222.
10. Dechristé G, Mieussens L (2012) Numerical simulation of micro flows with moving obstacles. Journal of Physics: Conference Series 362: 012030.
11. Dechristé G, Mieussens L (2016) A Cartesian cut cell method for rarefied flow simulations around moving obstacles. J Comput Phys 314: 454488.
12. Degond P, Dimarco G, Pareshi L (2011) The moment guided Monte Carlo method. Int J Numer Meth Fluids 67: 189213.
13. Frangi A, Frezzotti A, Lorenzani S (2007) On the application of the BGK kinetic model to the analysis of gasstructure interactions in MEMS. Comput Struct 85: 810817.
14. Groppi M, Russo G, Stracquadanio G (2007) High order semiLagrangian methods for the BGK equation. Commun Math Sci 14: 289417.
15. Groppi M, Russo G, Stracquadanio G (2018) SemiLagrangian Approximation of BGK Models for Inert and Reactive Gas Mixtures, In: Goncalves P, Soares AJ, From Particle Systems to Partial Differential Equations, Springer.
16. Karniadakis G, Beskok A, Aluru N (2005) Microflows and Nanoflows: Fundamentals and Simulations, New York: Springer.
17. Kuhnert J (1999) General smoothed particle hydrodynamics, PhD Thesis, University of Kaiserslautern, Germany.
18. Li Q, Luo KH, Li XJ (2012) Forcing scheme in pseudopotential lattice Boltzmann model for multiphase flows. Phys Rev E 86: 278299.
19. Neunzert H, Struckmeier J (1995) Particle methods for the Boltzmann equation. Acta Numer 4: 417457.
20. Pareshi L, Russo G (2000) Numerical solution of the Boltzmann equation I: Spectrally accurate accurate approximation of the collision operator. SIAM J Numer Anal 37: 12171245.
21. Peskin CS (1972) Flow patterns around heart valves: A digital computer method for solving the equations of motion, PhD thesis, Albert Einstein College of Medicine.
22. Russo G, Filbet F (2009) SemiLagrangian schemes applied to moving boundary problems for the BGK model of rarefied gas dynamics. Kinet Relat Mod, AIMS 2: 231250.
23. Shan X, Chen H (1993) Latticeemph Boltzmann model for simulating flows with multiple phases and components. Phys Rev E 47: 18151819.
24. Shrestha S, Tiwari S, Klar A, et al. (2015) Numerical simulation of a moving rigid body in a rarefied gas. J Comput Phys 292: 239252.
25. Shrestha S, Tiwari S, Klar A (2015) Comparison of numerical simulations of the Boltzmann and the NavierStokes equations for a moving rigid circular body in a micro scaled cavity. Int J Adv Eng Sci Appl Math 7: 3850.
26. Sonar T (2005) Difference operators from interpolating moving least squares and their deviation from optimality. ESAIM: Math Model Num 39: 883908.
27. Tiwari S, Klar A, Russo G (2019) A meshfree method for solving BGK model of rarefied gas dynamics. Int J Adv Eng Sci Appl Math 11: 187197.
28. Tiwari S, Klar A, Hardt S (2009) A particleparticle hybrid method for kinetic and continuum equations. J Comput Phys 228: 71097124.
29. Tiwari S, Klar A, Hardt S (2013) Coupled solution of the Boltzmann and NavierStokes equations in gasliquid two phase flow. Comput Fluids 71: 283296.
30. Tsuji T, Aoki K (2013) Moving boundary problems for a rarefied gas: Spatially one dimensional case. J Comput Phys 250: 574600.
31. Tsuji T, Aoki K (2014) Gas motion in a microgap between a stationary plate and a plate oscillating in its normal direction. Microfluid Nanofluid 16: 10331045.
32. Xiong T, Russo G, Qiu JM (2019) Conservative multidimensional semiLagrangian finite difference scheme: Stability and applications to the kinetic and fluid simulations, J Sci Comput 79: 12411270.
33. Yomsatieanku W (2010) Highorder nonoscillatory schemes using meshfree interpolating moving least squares reconstruction for hyperbolic conservation laws, PhD Thesis, TU CaroloWilhelmina zu Braunschweig, Germany.
© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)