Application of discrete kinetic model for Euler-Poisson system to plasma aerodynamics problems

In this work authors examine plasma layer decay in spherical symmetric case using lattice Boltzmann method for Euler-Poisson equations. Effects of external electrical field on plasma decay are shown.

numerical methods, lattice Boltzmann method, Euler-Poisson equations

Применение дискретной кинетической модели для системы уравнений Эйлера-Пуассона к задачам плазменной аэродинамики

В работе рассмотрен распад плазменного слоя в сферически-симметричном случае на основе решения уравнений Эйлера-Пуассона с помощью метода решеточных уравнений Больцмана. Показано влияние внешнего поля на распад плазменного слоя.

численные методы, решеточный метод Больцмана, уравнения Эйлера-Пуассона

1. D. Wang, Z. Wang “Large BV solutions to the compressible isothermal Euler–Poisson equations with spherical symmetry,” Nonlinearity, vol. 19, pp. 1985-2004, Aug. 2006.
2. G-Q. Chen, T-H. Li, “Global entropy solutions in L∞ to the Euler equations and Euler-Poisson equations for isothermal fluids with spherical symmetry,” Methods Appl. Anal., vol. 10, no. 2, pp. 215-244, 2003.
3. C. Chainais-Hillairet, Y.-J. Peng, I. Violet, “Numerical solutions of Euler-Poisson systems for potential flows,” Appl. Numer. Math., vol. 59, pp. 301-315, 2009.
4. D.A. Wolf-Gladrow, Lattice-Gas Cellular Automata and Lattice Boltzmann Models – An Introduction, Berlin, Germany: Springer, 2000.
5. S. Chen, G.D. Doolen, “Lattice Boltzmann method for fluid flows,” Annu. Rev. Fluid Mech., vol. 30, pp. 329-364, Jan. 1998
6. X. Shan, X. He, “Discretization of the Velocity Space in the Solution of the Boltzmann Equation,” Phys. Rev. Lett., vol. 80, no. 1, pp. 65-68, Jan. 1998.
7. X. Xe, L.S. Luo, “A priory derivation of the lattice Boltzmann equation,” Phys. Rev. E, vol. 55, no. 6, pp. R6333-R6336, Jun. 1997.
8. X. Shan, X.-F. Yuan, H. Chen, “Kinetic theory representation of hydrodynamics: a way beyond the Navier-Stokes equation,” J. Fluid Mech., vol. 550, pp. 413–441, Mar. 2006
9. T. Kihara, M.H. Taylo., J.O. Hirshfelder, “Transport properties for gases assuming inverse power intermolecular potentials,” Phys. Fluids, vol. 3, no 5, pp. 715-720, Sept. 1960.
10. C.H. Su, S.H. Lam, “Continuum Theory of Spherical Electrostatic Probes,” Phys. Fluids, vol. 6, no 10, pp. 1479-1491, Oct. 1963.
11. I.M. Cohen, “Characteristics of a Spherical Electrostatic Probe in a Bounded Plasma,” Phys. Fluid, vol. 13, no 4, pp. 889-894, Apr. 1970.
12. K. Toba, S. Sayano, “A continuum theory of electrostatic probes in a slightly ionized gas,” J. Plasma Physics, vol. 1, no. 4, pp. 407-423, 1967.
13. W.B. Bush, F.E. Fendell, “Continuum theory of spherical electrostatic probes (frozen chemistry),” J. Plasma Physics, vol. 4, no. 2, pp. 317-334, May 1970.
14. S.A. Self, C.H. Shih, “Theory and Measurements for Ion Collection by a Spherical Probe in a Collisional Plasma,” Phys. Fluids, vol. 11, no 7, pp. 1532-1545, July 1968.
15. L. Patacchini, I.H. Hutchinson, “Continuum-plasma solution surrounding nonemitting spherical bodies,” Phys. Plasmas, vol. 16, pp. 062101, 2009.
16. K.K. Niyogi, I M. Cohen, “Continuum electrostatic probe theory with magnetic field” Phys. Fluids, vol 16, no 1. pp 69, Jan 1973;
17. Y.S. Chou, L. Talbot, D.R. Willis, “Kinetic Theory of a Spherical Electrostatic Probe in a Stationary Plasma,” Phys. Fluids, vol. 9, no 11, pp. 2150-2167, Nov. 1966.
18. B.B. Hamel, “Kinetic Model for Binary Gas Mixture,” Phys. Fluids, vol. 8, no. 3, pp. 418-425, Mar. 1965.
19. V.I. Krylov “Chapter 7” in Approximate Calculation of Integrals [Priblijennoe Vichislenie Inte-gralov], Russia, Moscow: Nauka, 1967, pp. 140-142.
20. G. Capdewille, “A Hermite Upwind WENO scheme for solving hyperbolic equations,” J. Comp. Phys., 227 (2008), pp. 2430-2454
21. S. Pieraccini1 and G. Puppo, “Implicit–Explicit Schemes for BGK Kinetic Equations”, Journal of Scientific Computing, Vol. 32, No. 1, July 2007