Towards adaptive kinetic-fluid simulations of weakly ionized plasmas

Journal of Computational Physics

Volumn 231, Issue 3, 2012, Pages 839-869

  Kolobov, V I ^a   Arslanbekov, R R ^a  

^a CFD RESEARCH CORPORATION   (United States)

Author keywords

Adaptive Mesh and Algorithm Refinement; Boltzmann kinetic equation; Eulerian Vlasov solvers; Octree Cartesian mesh; Runaway electrons; Unified Flow Solver; Weakly ionized plasma

Indexed keywords

BOLTZMANN EQUATION; COLLISIONAL PLASMAS; ELECTRIC DISCHARGES; ELECTRONS; FLOW OF GASES; FLOW SIMULATION; GASES; INTEGRAL EQUATIONS; IONIZATION OF GASES; KINETIC ENERGY; KINETIC THEORY; MAGNETOHYDRODYNAMICS; MESH GENERATION; PLASMA SIMULATION; VLASOV EQUATION;

ADAPTIVE MESH REFINEMENT; ALGORITHM REFINEMENT; BOLTZMANN KINETIC EQUATIONS; CARTESIAN MESH; EULERIAN; EULERIAN VLASOV SOLVER; OCTREE CARTESIAN MESH; OCTREES; RUNAWAY ELECTRONS; UNIFIED FLOW SOLVERS; WEAKLY IONIZED PLASMA;

KINETICS;

EID: 82455162339     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2011.05.036     Document Type: Article

References (121)

1. Cercignani C. The Boltzmann Equation and its Applications 1988, Springer-Verlag.
2. Sone Y. Kinetic Theory and Fluid Dynamics 2002, Burkhausen, Boston.
3. Birdsall C.K., Langdon A.B. Plasma Physics via Computer Simulations 2004, Taylor and Fransis.
4. Verboncoeur J.P. Particle simulation of plasmas: review and advances. Plasma Phys. Control. Fusion 2005, 47:A231.
5. Bird G.A. Molecular Gas Dynamics and the Direct Simulation of Gas Flows 1994, Oxford Science Publications.
6. I.D. Boyd, Direct simulation monte carlo for atmospheric entry, in: Non-equilibrium Gas Dynamics from Physical Models to Hypersonic Flights, RTO-EN-AVT-162, 2009.
7. Aristov V.V. Direct Methods for Solving the Boltzmann Equation and Study of Non-Equilibrium Flows 2001, Kluwer Academic Publishers, Dordrecht.
8. Tcheremissine F.G. Direct numerical solution of the Boltzmann equation. AIP Conf. Proc. 2005, 762:677-685.
9. Tcheremissine F.G. Solution of the Boltzmann equation for high-speed flows. Comput. Math. Math. Phys. 2006, 46:315.
10. Tcheremissine F.G. Solution of the Boltzmann equation for low-speed flows. Transport Theory Stat. Phys. 2008, 37:564.
11. Eulerian Codes for the Numerical Solution of the Kinetic Equations of Plasmas 2010, Nova Publishers. M. Shoucri (Ed.).
12. Modeling and Computational methods for Kinetic Equations 2004, 356. Birkhauser, Boston. P. Degond, L. Pareschi, G. Russo (Eds.).
13. Mouhot C., Pareschi L. Fast algorithms for computing the Boltzmann collision operator. Math. Comput. 2006, 75:1833.
14. Kowalczyk P., et al. Numerical solutions of the Boltzmann equation: comparison of different algorithms. Eur. J. Mech. B 2008, 27:62.
15. Ibragimov I., Rjasanov S. Three way decomposition for the Boltzmann equation. J. Comput. Math. 2009, 27:184.
16. Electron Kinetics and Applications of Glow Discharges. NATO ASI Series 1998, vol. 367. Kluwer Academic Publishers. U. Kortshagen, L.D. Tsendin (Eds.).
17. Kushner M.J. Hybrid modelling of low temperature plasmas for fundamental investigation and equipment design. J. Phys. D. 2009, 42:194013.
18. Wijesinghe H.S., Hadjiconstantinou N.G. A discussion of hybrid atomistic-continuum methods for multiscale hydrodynamics. Int. J. Multiscale Comput. Eng. 2004, 2:189.
19. Kolobov V.I., Bayyuk S.A., Arslanbekov R.R., Aristov V.V., Frolova A.A., Zabelok S.A. Construction of a unified continuum/kinetic solver for aerodynamic problems. AIAA J. Spacecraft Rockets 2005, 42:598-605.
20. Bourgat J.F., Le Tallec P., Tidriri M.D. Coupling Boltzmann and Navier-Stokes equations by friction. J. Comput. Phys. 1996, 127:227.
21. Tiwari S., Klar A. An adaptive domain decomposition procedure for Boltzmann and Euler equations. J. Comput. Appl. Math. 1998, 90:223.
22. Le Tallec P., Mallinger F. Coupling Boltzmann and Navier-Stokes equations by half fluxes. J. Comput. Phys. 1997, 136:51.
23. Tiwari S. Coupling of the Boltzmann and Euler equations with automatic domain decomposition. J. Comput. Phys. 1998, 144:710.
24. T. Ohsawa, T. Ohwada, Deterministic hybrid computation of rarefied gas flows, in: Rarefied Gas Dynamics: 23rd International Symposium, Andrew D. Ketsdever, E.P. Munz, (Eds.), AIP Conference Proceedings vol. 663, 2003, pp. 931-938.
25. Schwartzentruber T.E., Scalabrin L.C., Boyd I.D. A modular particle-continuum numerical method for hypersonic non-equilibrium gas flows. J. Comput. Phys. 2007, 225:1159.
26. Degond P., Dimarco G., Mieussens L. A multiscale kinetic-fluid solver with dynamic localization of kinetic effects. J. Comput. Phys. 2010, 229:4907.
27. Beylich A.E. Solving the kinetic equation for all Knudsen numbers. Phys. Fluids 2000, 12:444.
28. Crouseilles N., Degond P., Lemou M. A hybrid kinetic/fluid models for solving the gas dynamics Boltzmann-BGK equation. J. Comput. Phys. 2004, 199:776.
29. Iza H.C.Kim.F., Yang S.S., Radmilovic-Radjenovic M., Lee J.K. Particle and fluid simulations of low temperature plasma discharges: benchmark and kinetic effects. J. Phys. D 2005, 38:R283.
30. Tsendin L. Nonlocal electron kinetics in gas-discharge plasma. Physics -Uspekhi 2010, 53:133.
31. D.B. Hash, H.A. Hassan, Two-dimensional coupling issues of hybrid DSMC/Navier-Stokes solvers, in: AIAA Paper 97-2507, 1997.
32. H.A. Carlson, R. Roveda, I.D. Boyd, G.V. Candler, A hybrid CFD-DSMC method of modeling continuum-rarefied flows, in: AIAA Paper 2004-1180, 2004.
33. Baker L.L., Hadjiconstantinou N.G. Variance reduction for Monte Carlo solution of the Boltzmann equation. Phys. Fluids 2005, 17:051703.
34. Tiwari S., Klar A., Hardt S. A particle-particle hybrid method for kinetic and continuum equations. J. Comput. Phys. 2010, 228:7109.
35. Garsia A.L., Bell J.B., Crutchfield W.Y., Alder B.J. Adaptive mesh and algorithm refinement using direct simulation monte carlo. J. Comput. Phys. 1999, 54:134.
36. Popov S.P., Tcheremissine F.G. A conservative method for solving the Boltzmann equation with centrally symmetric interaction potentials. Comput. Math. Math. Phys. 1999, 39:156.
37. Succi S. The Lattice Boltzmann Equation for Fluid Dynamics and Beyond 2001, Oxford University Press.
38. N.M. Korobov, Exponential Sums and Their Applications, Springer, 2001, p. 232; Theoretico-Numerical Methods in Approximate Analysis, Moscow 2004 (in Russian).
39. Morris A.B., Varghese P.L., Goldstein D.B. Monte Carlo solution of the Boltzmann equation via a discrete velocity model. J. Comput. Phys. 2011, 230:1265.
40. Kloss Yu.Yu., Shuvalov P.V., Tcheremissine F.G. Solving Boltzmann equation on GPU. Proc. Comput. Sci. 2010, 1:1077.
41. A. Frezzotti, et al, Solving Kinetic Equations on GPUs, arXiv:0903.4044v1 [physics.comp-ph] 24 March, 2009.
42. Beylich A.E. Kinetics of thermalization in shock waves. Phys. Fluids 2002, 14:2683.
43. Ohwada T. Structure of normal shock waves on the basis of the Boltzmann equation for hard-spheres molecules. Phys. Fluids 1993, A5:217-234.
44. Aristov V.V. Method of adaptive meshes in velocity space for the intense shock wave problems. J. Comput. Math. Math. Phys. 1977, 17:261.
45. Heintz A., et al. Fast numerical method for the Boltzmann equation on non-uniform grids. J. Comput. Phys. 2008, 227:6681.
46. Kozuge S., Aoki K., Takata S. Shock wave structure of a binary gas mixture: finite-difference analysis of the Boltzmann equation for hard-sphere molecules. Eur. J. Mech. B - Fluids 2001, 20:87.
47. Raines A. Study of a shock wave structure in gas mixtures on the basis of the Boltzmann equation. Eur. J. Phys. B 2002, 21:599.
48. Josyula E., Vedula P., Bailey W.F., Suchyta C.J. Kinetic solution of the structure of a shock wave in a nonreactive gas mixture. Phys. Fluids 2011, 23:017101.
49. Schram P.P.J.M. Kinetic Theory of Gases and Plasmas 1991, Springer.
50. Tcheremissine F.G. Solution of the Wang-Chang-Uhlenbeck master equation. Doklady Phys. 2002, 47:872.
51. F.G. Tcheremissine, V.I. Kolobov, R.R. Arslanbekov, Simulation of shock wave structure in nitrogen with realistic rotational spectrum and molecular interaction potential, in: Proceedings of 25th Rarefied Gas Dynamics Symposium M.S. Ivanov, A.K. Rebrov, Novosibirsk (Eds.), 2007.
52. Koura K. Direct simulation Monte Carlo study of rotational nonequilibrium in shock wave and spherical expansion of nitrogen using classical trajectory calculations. Phys. Fluids 2002, 14:1689.
53. Rykov V.A., Titarev V.A., Shakhov E.M. J. Comput. Math. Math. Phys. 2007, 47:144.
54. Groppi M., Aoki K., Spiga G., Tritch V. Shock structure analysis in chemically reacting gas mixtures by a relaxation time kinetic model. Phys. Fluids 2008, 20:117103.
55. Starik A.M., Titova N.S., Arsentiev I.V. Comprehensive analysis of the effect of atomic and molecular metastable state excitation on air plasma composition behind strong shock waves. Plasma Sources Sci. Technol. 2010, 19:015007.
56. Shneider M.N., Barker P.F., Gimelshein S.F. Molecular transport in pulsed optical lattices. Appl. Phys. A 2007, 10.1007/s00339-007-4113-7.
57. V. Kolobov, et al, Unified Kinetic Approach for Simulations of Gas Flows in Rarefied and Continuum Regimes, Report AFRL-RB-WP-TR-2008-3031, 2008.
58. Kolobov V.I., Arslanbekov R.R., Aristov V.V., Frolova A.A., Zabelok S.A. Unified solver for rarefied and continuum flows with adaptive mesh and algorithm refinement. J. Comput. Phys. 2007, 223:589.
59. Samet H. The quadtree and related hierarchical data structures. Comput. Surv. 1984, 16:187.
60. Samet H. Foundations of Multidimensional and Metric Data Structures 2006, Elsevier.
61. Burstedde C., Wilcox L.C., Ghattas O. p4est: Scalable Algorithms for Parallel Adaptive Mesh Refinement on Forests of Octrees. SIAM Journal of Scientific Computing 2011, 33:1103-1133.
62. Norman M.L. The impact of AMR in numerical astrophysics and cosmology. Lecture Notes in Computational Science and Engineering 2005, Springer.
63. Popinet S. Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries. J. Comput. Phys. 2003, 190:572.
64. Sagan H. Space Filling Curves 1994, Springer.
65. Stocco L., Schrack G. On spatial orders and location codes. IEEE Trans. Comput. 2009, 58:424.
66. Agbaglah G., et al. Parallel simulation of multiphase flows using octree adaptivity and the volume-of-fluid model. C.R. Mech. 2011, 10.1016/j.crme.2010.12.006.
67. Khokhlov A.M. Fully threaded tree algorithms for adaptive refinement fluid dynamics simulations. J. Comput. Phys. 1998, 143:519.
68. Muller S. Adaptive multiscale schemes for conservation laws. Lecture Notes on Computational Science and Engineering 2002, vol. 27. Springer.
69. Ji H., Lien F-S., Yee E. A new adaptive mesh refinement data a structure with an application to detonation. J. Comput. Phys. 2010, 229:8981.
70. D. Madeira, T. Leviner, GPU Octree and Optimized Search, VIII Brazilian Symposium on Games and Digital Entertainment, Rio de Janeiro , 2009.
71. Ohwada T. On the construction of kinetic schemes. J. Comput. Phys. 2002, 177:156.
72. Xu K., Chen J-C. A unified gas kinetic scheme for continuum and rarefied flows. J. Comput. Phys. 2010, 229:7747.
73. Aodun C.K., Clausen J.R. Lattice Boltzmann method for complex flows. Ann. Rev. Fluid Mech. 2010, 42:439.
74. W.J. Courier, An Adaptively Refined, Cartesian Cell-Based Scheme for the Euler and Navier-Stokes Equations, Ph.D. Thesis, University of Michigan, Ann Arbor, 1993.
75. J.D. Lee, S.M. Ruffin, Development of a turbulent wall-function based viscous Cartesian-grid methodology, in: AIAA-2007-1326, 2007.
76. Peskin C.S. The immersed boundary method. Acta Numer. 2002, 1.
77. Mittal R., Iaccarino G. Immersed boundary methods. Ann. Rev. Fluid Mech. 2005, 37:239.
78. Dillon R., Li Zhilin An introduction to the immersed boundary and the immersed interface methods. Interface Problems and Methods in Biological and Physical Flows 2009, World Scientific Publishing Co.
79. de Tullio M.D., et al. An immersed boundary method for compressible flows using local grid refinement. J. Comput. Phys. 2007, 225:2098.
80. Ghias R., Mittal R., Dong H. " A sharp interface immersed boundary method for compressible viscous flows. J. Comput. Phys. 2007, 225:528.
81. R.R. Arslanbekov, V.I. Kolobov, A.A. Frolova, Immersed boundary method for Boltzmann and Navier-Stokes solvers with adaptive cartesian mesh, in: 27th International Symposium On Rarefied Gas Dynamics, AIP Conf. Proc. vol. 1333, 2011, pp. 873-877, doi:10.1063/1.3562755.
82. Dellacherie S. Coupling of the Wang Chang-Uhlenbeck equations with the multispecies Euler system. J. Comput. Phys. 2003, 189:239.
83. V.I. Kolobov, K. Ikeda, T. Okumira, 3D simulations of an industrial ICP reactor with comparison to experimental data, in: 30th IEEE International Conference on Plasma Science, Plasma Science, 2003. ICOPS 2003. IEEE Conference Record - Abstracts The 30th International Conference on Plasma Science, 2003, p. 460.
84. Georghiou G.E., Papadakis A.P., Morrow R., Metaxas A C Numerical modeling of atmospheric pressure gas discharges leading to plasma production. J. Phys. D 2005, 38:R303.
85. Wang C-C., Roy S. Three-dimensional simulation of a microplasma pump. J. Phys. D 2009, 42:185206.
86. Colella P., Dorr M.R., Wake D.D. Numerical solution of plasma fluid equations using locally refined grids. J. Comput. Phys. 1999, 152:550.
87. Unfer T., Boeuf J-P., et al. Multi-scale gas discharge simulations using asynchronous adaptive mesh refinement. Comput. Phys. Commun. 2010, 181:247.
88. Min W-G., et al. A study of the streamer simulation using adaptive mesh generation and FEM-FCT. IEEE Trans. Magn. 2001, 37:3141.
89. Montijn C., et al. An adaptive grid refinement strategy for the simulation of negative streamers. J. Comput. Phys. 2006, 219:801.
90. Nikandrov D.S., Arslanbekov R.R., Kolobov V.I. Streamer simulations with dynamically adaptive Cartesian mesh. IEEE TPS 2008, 36:932.
91. Pancheshnyi S., Segur P., Capeillere J., Bourdon A. Numerical simulation of filamentary discharges with parallel adaptive mesh refinement. J. Comput. Phys. 2008, 227:6574.
92. D'yakonov M.I., Kachorovskii V.Y. Streamer discharge in a homogeneous field. Sov. Phys. JETP 1989, 68:1070.
93. Akishev Yu, et al. Negative corona, glow and spark discharges in ambient air and transitions between them. Plasma Sources Sci. Technol. 2005, 14:S18.
94. Tardiveau P., Moreau N., Bentaleb S., et al. Diffuse mode and diffuse-to-filamentary transition in a high pressure nanosecond scale corona discharge under high voltage. J. Phys. D 2009, 42:175202.
95. Tran T.N., Golosnoy I.O., Levin P.L., Georghiou G.E. Numerical modeling of negative corona discharges in air with experimental validation. J.Phys. D 2010, 44:015203.
96. Chanrion O., Neubert T. Production of runaway electrons by negative streamer discharges. J. Geophys. Res. 2010, 115:A00E32. 10.1029/2009JA014774.
97. Babaeva N.Yu., Kushner M.J. Effect of inhomogeneities on streamer propagation. Plasma Sources Sci. Technol 2009, 18:035009.
98. Li C., Ebert U., Hundsdorfer W. Spatially hybrid simulations for streamer discharges with generic features of pulled fronts. J. Comput. Phys. 2010, 229:200.
99. Shoucri M. Numerical Solution of Hyperbolic Differential Equations 2008, Nova Science Publishers.
100. V.I. Kolobov, R.R. Arslanbekov, A.A. Frolova, Multi-scale simulations of gas flows: effect of external forces, rarified gas dynamics, in: Proceedings of the 26th International Symposium on Rarified Gas Dynamics, AIP Conference Proceedings, vol. 1084, 2008, pp. 441-446.
101. Godyak V.A. Hot plasma effects in gas discharge plasma. Phys. Plasmas 2005, 12:055501.
102. Shoucri M., Matte J.P., Cote A. Numerical simulation of an inductively coupled discharge using an Eulerian Vlasov code. J. Phys. D 2003, 36:2083.
103. E. Sonnendrücker, Adaptive methods for the Vlasov equation, in: MAMCDP09 workshop, 2009.
104. O. Hoenen, E. Violard, An Efficient Data Structure for an Adaptive Vlasov Solver, research report, http://icps.u-strasbg.fr/pub_list.php?authors=hoenen&pres=0.
105. V.I. Kolobov, R.R. Arslanbekov, A.A. Frolova, Boltzmann solver with adaptive mesh in velocity space, in: 27th International Symposium on Rarefied Gas Dynamics, AIP Conf. Proc., vol. 1333, 2011, pp. 928-933, doi:10.1063/1.3562764.
106. Kudryavtsev A.A., Smirnov A.S., Tsendin L.D. Physics of Glow Discharges 2010, (in Russian).
107. Kingham R.J., Bell A.R. An implicit Vlasov-Fokker-Planck code to model non-local electron transport in 2-D with magnetic fields. J. Comput. Phys. 2004, 194:1.
108. Kolobov V.I. Fokker Planck modeling of electron kinetics in plasmas and semiconductors. Comput. Mater. Sci. 2003, 28:302.
109. Tsendin L.D. Electron distribution function of weakly ionized plasmas in nonuniform electric fields. Sov. J. Plasma Phys. 1982, 8:96.
110. Albritton J.R. Laser absorption and heat transport by non-Maxwell-Boltzmann electron distribution. Phys. Rev. Lett. 1983, 50:2078.
111. Liang W., Goldsman N., Meyergoyz I. 2-D MOSFET modeling including surface effects and impact ionization by self-consistent solution of the boltzmann, poisson, and hole-continuity equations. IEEE Trans. Electron Devices 1997, 44:257.
112. Rahmat K., White J., Antoniadis D.A. Simulation of semiconductor devices using a Galerkin/SHE approach to solving the coupled Poisson-Boltzmann system. IEEE Trans. Comput. Aided Des. Integr. circuits Syst. 1996, 15:1181.
113. Kolobov V.I., Arslanbekov R.R. Simulation of electron kinetics in gas discharges. IEEE Trans. Plasma Sci. 2006, 34:895.
114. Kolobov V.I., Godyak V.A. Non-local electron kinetics in collisional gas discharge plasmas. IEEE Trans. Plasma Sci. 1995, 23:503.
115. Kolobov V.I. Striations in rare gas plasmas (Topical Review). J. Phys. D. 2006, 39:R487-R506.
116. Kolobov V.I., Tsendin L.D. Analytic model of short gas discharge in light gases. Phys. Rev. A 1992, 46:7837.
117. Symbalisty E.M.D., Russel-Dupre R-A., Yukhimuk V.A. Finite volume solution of the relativistic Boltzmann equation for electron avalanche studies. IEEE Trans. Plasma Sci. 1998, 26:1575.
118. Solovyev A.A., et al. Electron kinetic effects in atmospheric breakdown by an intense electromagnetic pulse. Phys. Rev. E 1999, 60:7360.
119. Nikandrov D.S. Formation of distribution function of runaway electrons in strong field of pulsed gas discharges. Tech. Phys. 2008, 53:1565.
120. Lehtinen N.G., Bell T.F., Inan U.S. Monte Carlo simulation of runaway MeV electron breakdown with application to red sprites and terrestrial gamma ray flashes. J. Geophys. Res. 1999, 104:24,69.
121. Bakhtiari M. Revisiting the momentum-space study of runaway electrons during lightning initiation. J. Phys. D. 2009, 42:015209.