Top

Journal of Scientific Computing

Published in:

15-12-2018

BGK Polyatomic Model for Rarefied Flows

Authors: Florian Bernard, Angelo Iollo, Gabriella Puppo

Published in: Journal of Scientific Computing | Issue 3/2019

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

In this work we present a new model of BGK type for polyatomic gases. The model incorporates the different relaxation rates of translational, rotational and/or vibrational modes characterizing polyatomic molecules using a BGK-type equation, and additional relaxation equations for the temperatures associated to each internal energy mode. We construct an efficient numerical scheme which is implicit in the relaxation terms, and test the model and the scheme on several problems, confirming the Asymptotic Preserving properties of the scheme, and comparing the results provided by the model with experimental and DSMC simulations, carried out on the full Boltzmann polyatomic equation.

previous article Error Analysis of a Fully Discrete Morley Finite Element Approximation for the Cahn–Hilliard Equation

next article Lowest-Order Weak Galerkin Finite Element Methods for Linear Elasticity on Rectangular and Brick Meshes

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Alsmeyer, H.: Density profiles in argon and nitrogen shock waves measured by the absorption of an electron beam. J. Fluid Mech. 74, 497–513 (1976)CrossRef

Andries, P., Bourgat, J.-F., Le Tallec, P., Perthame, B.: Numerical comparison between the Boltzmann and ES-BGK models for rarefied gases. Comput. Methods Appl. Mech. Eng. 191(31), 3369–3390 (2002)MathSciNetCrossRefMATH

Andries, P., Le Tallec, P., Perlat, J.-P., Perthame, B.: The Gaussian-BGK model of Boltzmann equation with small Prandtl number. Eur. J. Mech. B. Fluids 19(6), 813–830 (2000)MathSciNetCrossRefMATH

Andries, P., Perthame, B.: The ES-BGK model equation with correct Prandtl number. In: 22nd International Symposium on Rarefied Gas Dynamics. AIP Conference Proceeding vol. 585, p. 30, (2001)

Ascher, U.M., Ruuth, S.J., Spiteri, R.J.: Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations. Appl. Numer. Math. IMACS J. 25(2–3), 151–167 (1997)MathSciNetCrossRefMATH

Bernard, F.: Efficient asymptotic preserving schemes for BGK and ES-BGK models on cartesian grids. Politecnico di Torino, Université de Bordeaux, Theses (2015)

Bernard, F., Iollo, A., Puppo, G.: A local velocity grid approach for BGK equation. Commun. Comput. Phys. 16(4), 956–982 (2014)MathSciNetCrossRefMATH

Bernard, F., Iollo, A., Puppo, G.: Accurate asymptotic preserving boundary conditions for kinetic equations on cartesian grids. J. Sci. Comput. 65, 735–766 (2015)MathSciNetCrossRefMATH

Bhatnagar, P.L., Gross, E.P., Krook, M.: A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Phys. Rev. 94, 511–525 (1954)CrossRefMATH

10.

Borgnakke, C., Larsen, P.S.: Statistical collision model for Monte Carlo simulation of polyatomic gas mixture. J. Comput. Phys. 18, 405–420 (1975)CrossRef

11.

Brull, S., Schneider, J.: On the ellipsoidal statistical model for polyatomic gases. Contin. Mech. Thermodyn. 20(8), 489–508 (2009)MathSciNetCrossRefMATH

12.

Cabannes, H., Gatignol, R., Luol, L.-S.: The discrete Boltzmann equation. In: Lecture Notes at University of California, Berkley, pp. 1–65 (1980)

13.

Cercignani, C.: The Boltzmann Equation and Its Applications. Springer, Berlin (1988)CrossRefMATH

14.

Cercignani, C., Illner, R., Pulvirenti, M.: The Mathematical Theory of Dilute Gases. No. v. 106 in Applied Mathematical Sciences Series. Springer, Berlin (1994)CrossRefMATH

15.

Chu, C.K.: Kinetic-theoretic description of the formation of a shock wave. Phys. Fluids 8, 12–22 (1965)CrossRef

16.

Jin, S.: Asymptotic preserving (AP) schemes for multiscale kinetic and hyperbolic equations: a review. Riv. di Mat. della Univ. di Parma Ser. 73(2), 177–216 (2012)MathSciNetMATH

17.

Liu, C., Xu, K., Sun, Q., Cai, Q.: A unified gas-kinetic scheme for continuum and rarefied flows IV: full Boltzmann and model equations. J. Comput. Phys. 314, 305–340 (2016)MathSciNetCrossRefMATH

18.

Liu, S., Yu, P., Xu, K., Zhong, C.: Unified gas-kinetic scheme for diatomic molecular simulations in all flow regimes. J. Comput. Phys. 259(C), 96–113 (2014)MathSciNetCrossRefMATH

19.

Mieussens, L.: Discrete-velocity models and numerical schemes for the Boltzmann-BGK equation in plane and axisymmetric geometries. J. Comput. Phys. 162(2), 429–466 (2000)MathSciNetCrossRefMATH

20.

Pareschi, L., Russo, G.: Implicit-explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxation. J. Sci. Comput. 25(1), 129–155 (2005)MathSciNetCrossRefMATH

21.

Pieraccini, S., Puppo, G.: Implicit-explicit schemes for BGK kinetic equations. J. Sci. Comput. 32(1), 1–28 (2007)MathSciNetCrossRefMATH

22.

Pieraccini, S., Puppo, G.: Microscopically implicit-macroscopically explicit schemes for the BGK equation. J. Comput. Phys. 231, 299–327 (2011)MathSciNetCrossRefMATH

23.

Rykov, V.: A model kinetic equation for a gas with rotational degrees of freedom. Fluid Dyn. 6(10), 956–966 (1975)

24.

Semyonov, Y., Borisov, P., Suetin, P.: Investigation of heat transfer in rarefied gases over a wide range of Knudsen number. Int. J. Heat Mass Transf. 10, 1789–1799 (1984)CrossRef

25.

Shapiro, A.: The Dynamics and Thermodynamics of Compressible Fluid Flow. Ronald Press, New York (1953)

26.

Tantos, C., Frezzotti, A., Valougeorgis, D., Morini, G.L.: Conductive heat transfer in a rarefied polyatomic gas confined between coaxial cylinders. Int. J. Heat and Mass Transf. 79, 378–389 (1997)CrossRef

27.

Xu, K., Xin, H., Chunpei, C.: Multiple temperature kinetic model and gas-kinetic method for hypersonic non equilibrium flow computations. J. Comput. Phys. 227, 6779–6794 (2008)MathSciNetCrossRefMATH

Title: BGK Polyatomic Model for Rarefied Flows
Authors: Florian Bernard
Angelo Iollo
Gabriella Puppo
Publication date: 15-12-2018
Publisher: Springer US
Published in: Journal of Scientific Computing / Issue 3/2019
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-018-0864-x

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Springer Professional "Technik"

Other articles of this Issue 3/2019

A Contour-Integral Based Method for Counting the Eigenvalues Inside a Region

Variational Models for Joint Subsampling and Reconstruction of Turbulence-Degraded Images

An Regularization Method for Large Discrete Ill-Posed Problems

An Adaptive Infeasible-Interior-Point Method with the One-Norm Wide Neighborhood for Semi-definite Programming

Lowest-Order Weak Galerkin Finite Element Methods for Linear Elasticity on Rectangular and Brick Meshes

A Novel Stretch Energy Minimization Algorithm for Equiareal Parameterizations

Premium Partner