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Hybrid Navier-Stokes/DSMC Simulations of Gas Flows with Rarefied-Continuum Transitions

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Advanced Computational Methods in Science and Engineering

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 71))

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Abstract

Numerical simulations are an important tool for the design and optimization of gas flow equipment in many areas of science and technology. Most gas flows can be simulated using the continuum transport equations (Navier-Stokes), which describe the transport of mass, momentum and energy. These equations are based on the hypothesis that the mean free path length λ of the gas molecules is very small in comparison to a characteristic dimension L of the flow. This dimension can be either a physical dimension, e.g. a pipe diameter, or a flow dimension, e.g. the gradient length scale \( \frac{1}{\phi }\frac{{\partial \phi }}{{\partial x}} \) on which some flow property φ changes significantly. The dimensionless Knudsen number Kn can be used to describe this situation:

$$ Kn = \frac{\lambda }{L}. $$

When Kn < 0.01, gas molecules travel only a small distance (compared to the geometry and flow dimensions) between collisions. For internal flows this means that molecules only very rarely collide with walls, and the flow is dominated by the characteristics of the inter-molecular collisions. As a result, the gas will be in local equilibrium and the velocity distribution of its molecules will be Maxwellian.

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References

  1. Boltzmann L (1872) Weitere Studien ueber das Waermegleichgewicht under Gasmolekuelen. In: Sitzungsberichte Akademie der Wissenschaften Wien, 66:275–370

    Google Scholar 

  2. Maxwell J C (1879) On stresses in rarefied gases arising from inequalities of temperature. Philos. Trans. R. Soc. London, Ser. B 170:231

    Article  Google Scholar 

  3. Alder B (1997) Highly discretized dynamics. Physica A 240:193–195

    Article  Google Scholar 

  4. Hadjiconstantinou N G (2003) Comment on Cercignani's second-order slip coefficient. Physics of Fluids 15:2352–2354

    Article  MathSciNet  Google Scholar 

  5. Hadjiconstantinou N G (2004) Validation of a second-order slip model for transition-regime, gaseous flows. In: 2nd Int. Conf. on Microchannels and Minichannels, Rochester, New York, USA.

    Google Scholar 

  6. Bird G A (1998) Molecular gas dynamics and Direct Simulation Monte Carlo. Clarendon Press, Oxford.

    Google Scholar 

  7. Sharipov F (2003) Hypersonic flow of rarefied gas near the Brazilian satellite during its re-entry into atmosphere. Brazilian Journal of Physics, vol.33, no.2

    Google Scholar 

  8. Aktas O, Aluru N R (2002) A combined Continuum/DSMC technique for multiscale analysis of microfluidic filters. Journal of Computational Physics 178:342–372

    Article  MATH  Google Scholar 

  9. Cai C, Boyd I D (2005) 3D simulation of Plume flows from a cluster of plasma thrusters. In: 36th AIAA Plasmadynamics and Laser Conference, Toronto, Ontario, Canada, AIAA-2005-4662

    Google Scholar 

  10. van de Sanden M C M, Severens R J, Gielen J W A M, Paffen R M J, Schram D C (1996) Deposition of a-Si:H and a-C:H using an expanding thermal arc plasma. Plasma sources Science and Technology 5:268–274

    Article  Google Scholar 

  11. Hadjiconstantinou N G (1999) Hybrid Atomistic-Continuum formulations and moving contact-line problem. Journal of Computational Physics 154:245–265

    Article  MATH  Google Scholar 

  12. Le Tallec P, Mallinger F (1997) Coupling Boltzmann and Navier-Stokes equations by half fluxes. Journal of Computational Physics 136:51–67

    Article  MATH  MathSciNet  Google Scholar 

  13. Wijesinghe H S, Hadijconstantinou N G (2004) Discussion of hybrid Atomistic-Continuum scheme method for multiscale hydrodynamics. International Journal for Multiscale Computational Engineering 2 no.2:189–202

    Article  Google Scholar 

  14. Roveda R, Goldstein D B, Varghese P L (1998) Hybrid Euler/particle approach for continuum/rarefied flows. J. Spacecraft Rockets 35:258

    Article  Google Scholar 

  15. Garcia A L, Bell J B, Crutchfield W Y, Alder B J (1999) Adaptive mesh and algorithm refinement using Direct Simulation Monte Carlo. Journal of Computational Physics 154:134–155

    Article  MATH  Google Scholar 

  16. Glass C E, Gnoffo P A (2002) A 3-D coupled CFD-DSMC solution method for simulating hypersonic interacting flow. In: 8th AIAA/ASME Joint Thermophysics and Heat Transfer Conference, AIAA Paper 2002–3099,

    Google Scholar 

  17. Wu J S, Lian Y Y, Cheng G, Koomullil R P, Tseng K C (2006) Development and verification of a coupled DSMC-NS scheme using unstructured mesh. Journal of Computational Physics 219:579–607

    Article  MATH  Google Scholar 

  18. Schwartzentruber T E, Scalabrin L C, Boyd I D (2006) Hybrid Particle-Continuum Simulations of Non-Equilibrium Hypersonic Blunt Body Flows. AIAA Paper, San Francisco, CA, AIAA-2006–3602

    Google Scholar 

  19. Schwartzentruber T E, Boyd I D (2006) A Hybrid particle-continuum method applied to shock waves. Journal of Computational Physics 215 No.2:402–416

    Article  MathSciNet  Google Scholar 

  20. Chapman S, Cowling T G (1960) The Mathematical Theory of Non-Uniform Gases. Cambridge University Press, Cambridge.

    MATH  Google Scholar 

  21. Grad H (1949) On the kinetic theory of rarefied gases. Commun. Pure Appl. Math. 2:331

    Article  MATH  MathSciNet  Google Scholar 

  22. Patterson G N (1956), Molecular flow of gases. Wiley, New York.

    MATH  Google Scholar 

  23. Chou S Y, Baganoff D (1997) Kinetic flux-vector splitting for the Navier-Stokes equations. Journal of Computational Physics 130:217–230

    Article  MATH  Google Scholar 

  24. Garcia A L, Alder B J (1998) Generation of the Chapman-Enskog distribution. Journal of Computational Physics 140:66–70

    Article  MATH  MathSciNet  Google Scholar 

  25. van Leer B (1979) Towards the ultimate conservative difference scheme V. a second order sequel to Godunov's method. Journal of Computational Physics 32:101–136

    Article  Google Scholar 

  26. Roe P L (1981) Approximate Riemann solvers, parameter vectors and difference schemes. Journal of Computational Physics 43:357–372

    Article  MATH  MathSciNet  Google Scholar 

  27. Lou T, Dahlby D C, Baganoff D (1998) A numerical study comparing kinetic flux-vector splitting for the Navier-Stokes equations with a particle method. Journal of Computational Physics 145:489–510

    Article  MATH  Google Scholar 

  28. Hirschfelder J O, Curtis C F, Bird R B (1954) Molecular Theory of Gasses and Liquids, Wiley, New York

    Google Scholar 

  29. Dorsman R (2007) Numerical Simulations of Rarefied Gas Flows in Thin Film Processes. PhD Thesis, Delft University of Technology, The Netherlands

    Google Scholar 

  30. Wagner W (1992) A convergence proof for Bird's direct simulation method for the Boltzmann equation. Journal of Statistical Physics 66:1011–1044

    Article  MATH  MathSciNet  Google Scholar 

  31. Bhatnagar P L, Gross E P, Krook M (1954) A model for collision processes in gases. Physical Review 94:511–525

    Article  MATH  Google Scholar 

  32. Nance R P, Hash D B, Hassan H A (1998) Role of boundary condition in Monte Carlo simulation of microelectromechanical system. J.Thermophys.Heat Trans. 12

    Google Scholar 

  33. Bird G A (1981) Monte Carlo simulation in an engineering context. In: Fischer S S (ed) 12th International Symposium Rarefied Gas Dynamics – part 1:239–255

    Google Scholar 

  34. Koura K, Matsumoto H (1991) Variable soft sphere molecular model for air species. Physics of Fluids 3:2459–2465

    Article  MATH  Google Scholar 

  35. Koura K, Matsumoto H (1992) Variable soft sphere molecular model for inverse-power-law or Lennard-Jones potential. Physics of Fluids 4:1083–1085

    Article  Google Scholar 

  36. Wang W L, Boyd I D (2002) Continuum breakdown in hypersonic viscous flows. In: 40th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV

    Google Scholar 

  37. Mott-Smith H M (1951) The solution of the Boltzmann equation for a shock wave. Phys. Rev. 82 (6) 885–892

    Article  MATH  MathSciNet  Google Scholar 

  38. Hash D, Hassan H (1996) A decoupled DSMC/Navier-Stokes analysis of a transitional flow experiment. AIAA Paper 96–0353

    Google Scholar 

  39. Yohung S, Chan W K (2004) Analytical modelling of Rarefied Poiseuille flow in microchannels. J.Vac.Sci.Technol. A 22(2)

    Google Scholar 

  40. Cai C, Boyd I D, Fan J (2000) Direct simulation method for low-speed microchannel flows. J.Thermophysics and Heat Transfer 14 No.3

    Google Scholar 

  41. Selezneva S E, Boulos M I, van de Sanden M C M, Engeln R, Schram D C (2002) Stationary supersonic plasma expansion: continuum fluid mechanics versus Direct Simulation Monte Carlo method. J. Phys. D: Appl. Phys. 35:1362–1372

    Article  Google Scholar 

  42. Engeln R, Mazouffre S, Vankan P, Schram D C, Sadeghi N (2001) Flow dynamics and invasion by background gas of a supersonically expanding thermal plasma. Plasma Sources Sci. Technol. 10:595

    Google Scholar 

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Authors and Affiliations

  1. Department of Multi-Scale Physics … J.M.Burgers Centre for Fluid Mechanics, Delft University of Technology, Prins Bernhardlaan 6, 2628 BW, Delft, The Netherlands

    G. Abbate & C. R. Kleijn

  2. Department of Materials Science and Engineering, Delft University of Technology, Mekelweg 2, 2628 CD, Delft, The Netherlands

    B. J. Thijsse

Authors
  1. G. Abbate
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  2. B. J. Thijsse
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  3. C. R. Kleijn
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Correspondence to G. Abbate .

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Editors and Affiliations

  1. Scientific Computing &, Centrum Wiskunde & Informatica, Science Park 123, Amsterdam, 1098 XG, Netherlands

    Barry Koren

  2. Inst. Applied Mathematics, Delft University of Technology, Mekelweg 4, Delft, 2628 CD, Netherlands

    Kees Vuik

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© 2009 Springer-Verlag Berlin Heidelberg

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Abbate, G., Thijsse, B.J., Kleijn, C.R. (2009). Hybrid Navier-Stokes/DSMC Simulations of Gas Flows with Rarefied-Continuum Transitions. In: Koren, B., Vuik, K. (eds) Advanced Computational Methods in Science and Engineering. Lecture Notes in Computational Science and Engineering, vol 71. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03344-5_14

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