[1]
National Research Council, Plasma science: advancing knowledge in the national interest. National Academies Press (2008).
[2]
Chen F. F., Introduction to plasma physics and controlled fusion. Plenum Press, New York and London, 2nd edition (1974).
[3]
Vahedi V. and Surendra M., “A Monte Carlo collision model for the particle-in-cell method: applications to argon and oxygen discharges,” Comput. Phys. Commun., vol. 87 (1995), no. 1, pp. 179–198.
[4]
Filbet F. and Sonnendrücker E., “Comparison of Eulerian Vlasov solvers,” Comput. Phys. Commun., vol. 150 (2003), no. 3, pp. 247–266.
[5]
Filbet F., Sonnendrücker E., and Bertrand P., “Conservative numerical schemes for the Vlasov equation,” J. Comput. Phys., vol. 172 (2001), no. 1, pp. 166–187.
[6]
Degon P., Deluzet F., Navoret F., and Sun A.B., “Asymptotic-preserving particle-in-cell method for the VlasovCPoisson system near quasineutrality,” J. Comput. Phys., vol. 229 (2010), no. 1, pp. 5630–5652.
[7]
Degon P., Deluzet F., Navoret F., and Sun A.B., “Asymptotic-preserving particle-in-cell method for the VlasovCMaxwell systemin the quasi-neutral limit,” J. Comput. Phys., vol. 330 (2017), no. 1, pp. 467–492.
[8]
Degon P., Deluzet F., “Asymptotic-Preserving methods and multiscale models for plasma physics,” arXiv preprint, (2016).
[9]
Qiu J.-M. and Shu C.-W., “Conservative semi-Lagrangian finite difference WENO formulations with applications to the Vlasov equation,” Commun. Comput. Phys., vol. 10 (2011), no. 4, p. 979.
[10]
Guo W. and Qiu J.-M., “Hybrid semi-Lagrangian finite element-finite differencemethods for the Vlasov equation,” J. Comput. Phys., vol. 234 (2013), pp. 108–132.
[11]
Xiong T., Qiu J.-M., Xu Z., and Christlieb A., “High order maximum principle preserving semi-Lagrangian finite differenceWENO schemes for the Vlasov equation,” J. Comput. Phys., vol. 273 (2014), pp. 618–639.
[12]
Powell K. G., Roe P. L., Linde T. J., Gombosi T. I., and De Zeeuw D. L., “A solution-adaptive upwind scheme for ideal magnetohydrodynamics,” J. Comput. Phys., vol. 154 (1999), no. 2, pp. 284–309.
[13]
Brio M. and Wu C. C., “An upwind differencing scheme for the equations of ideal magnetohydrodynamics,” J. Comput. Phys., vol. 75 (1988), no. 2, pp. 400–422.
[14]
Xu K., “Gas-kinetic theory-based flux splitting method for ideal magnetohydrodynamics,” J. Comput. Phys., vol. 153 (1999), no. 2, pp. 334–352.
[15]
Araya D. B., Ebersohn F. H., Anderson S. E., and Girimaji S. S., “Magneto-gas kineticmethod for nonideal magnetohydrodynamics flows: verification protocol and plasma jet simulations,” J. Fluids Eng., vol. 137 (2015), no. 8, p. 081302.
[16]
Shumlak U. and Loverich J., “Approximate Riemann solver for the two-fluid plasma model,” J. Comput. Phys., vol. 187 (2003), no. 2, pp. 620–638.
[17]
Hakim A., Loverich J., and Shumlak U., “A high resolution wave propagation scheme for ideal two-fluid plasma equations,” J. Comput. Phys., vol. 219 (2006), no. 1, pp. 418–442.
[18]
Loverich J. and Shumlak U., “Adiscontinuous Galerkinmethod for the full two-fluid plasma model,” J. Comput. Phys., vol. 169 (2005), no. 1, pp. 251–255.
[19]
Loverich J., Hakim A., and Shumlak U., “A discontinuous Galerkin method for ideal twofluid plasma equations,” J. Comput. Phys., vol. 9 (2011), no. 02, pp. 240–268.
[20]
Srinivasan B. and Shumlak U., “Analytical and computational study of the ideal full twofluid plasma model and asymptotic approximations for Hall-magnetohydrodynamics,” Phys. Plasmas, vol. 18 (2011), no. 9, p. 092113.
[21]
Crestetto A., Crouseilles N., and Lemou M., “Kinetic/fluid micro-macro numerical schemes for Vlasov-Poisson-BGK equation using particles,” Kin. Rel. Mod., vol. 5 (2012), no. 4, pp. 787–816.
[22]
Dimarco G., Mieussens L., and Rispoli V., “An asymptotic preserving automatic domain decomposition method for the Vlasov-Poisson-BGK system with applications to plasmas,” J. Comput. Phys., vol. 274 (2014), pp. 122–139.
[23]
Jin S. and Yan B., “A class of asymptotic-preserving schemes for the Fokker-Planck-Landau equation,” J. Comput. Phys., vol. 230 (2011), no. 17, pp. 6420–6437.
[24]
Dimarco G., Li Q., Pareschi L., and Yan B., “Numerical methods for plasma physics in collisional regimes,” J. Plasma Phys., vol. 81 (2015), no. 1, 305810106
[25]
Degond P., Deluzet F., Navoret L., Sun A.-B., and Vignal M.-H., “Asymptotic-preserving particle-in-cell method for the Vlasov–Poisson system near quasineutrality,” J. Comput. Phys., vol. 229 (2010), no. 16, pp. 5630–5652.
[26]
Xu K. and Huang J., “A unified gas-kinetic scheme for continuum and rarefied flows,” J. Comput. Phys., vol. 229 (2010), no. 20, pp. 7747–7764.
[27]
Huang J., Xu K., and Yu P., “A unified gas-kinetic scheme for continuum and rarefied flows II: Multi-dimensional cases,” Commun. Comput. Phys., vol. 12 (2012), no. 3, pp. 662–690.
[28]
Huang J., Xu K., and Yu P., “A unified gas-kinetic scheme for continuum and rarefied flows III: Microflow simulations,” Commun. Comput. Phys., vol. 14 (2013), no. 5, pp. 1147–1173.
[29]
Sun W., Jiang S., and Xu K., “An asymptotic preserving unified gas kinetic scheme for gray radiative transfer equations,” J. Comput. Phys., vol. 285 (2015), pp. 265–279.
[30]
Sun W., Jiang S., Xu K., and Li S., “An asymptotic preserving unified gas kinetic scheme for frequency-dependent radiative transfer equations,” J. Comput. Phys., vol. 302 (2015), pp. 222–238.
[31]
Guo Z. and Xu K., “Discrete unified gas kinetic scheme for multiscale heat transfer based on the phonon Boltzmann transport equation,” Int. J. Heat Mass, vol. 102 (2016), pp. 944–958.
[32]
Xu K., “Direct modeling for computational fluid dynamics: construction and application of unified gas-kinetic schemes,” World Scientific, Singapore (2015).
[33]
Andries P., Aoki K., and Perthame B., “A consistent BGK-type model for gas mixtures,” J. Stat. Phys., vol. 106 (2002), no. 5-6, pp. 993–1018.
[34]
Morse T.F., “Energy and momentum exchange between nonequipartition gases,” Phys. Fluids, vol. 6 (1963), no. 10, pp. 1420–1427.
[35]
Liu C., Xu K., Sun Q., and Cai Q., “A unified gas-kinetic scheme for continuum and rarefied flows IV: full Boltzmann andmodel equations,” J. Comput. Phys., vol. 314 (2016), pp. 305–340.
[36]
Munz C.-D., Omnes P., Schneider R., Sonnendrücker E., and Voss U., “Divergence correction techniques for Maxwell solvers based on a hyperbolic model,” J. Comput. Phys., vol. 161 (2000), no. 2, pp. 484–511.
[37]
LeVeque R.J., “ Finite volume methods for hyperbolic problems,” Cambridge university press (2002).
[38]
Orszag S. A. and Tang C.-M., “Small-scale structure of two-dimensional magnetohydrodynamic turbulence,” J. Fluid Mech., vol. 90 (1979), no. 01, pp. 129–143.
[39]
Tang H.-Z. and Xu K., “A high-order gas-kinetic method for multidimensional ideal magnetohydrodynamics,” J. Comput. Phys., vol. 165 (2000), no. 1, pp. 69–88.
[40]
Parker E.N., “Sweet's mechanism for merging magnetic fields in conducting fluids,” J. Geophys. Res., vol. 62 (1957), no. 4, pp. 509–520.
[41]
Birn J., Drake J., Shay M., Rogers B., Denton R., Hesse M., Kuznetsova M., Ma Z., Bhattacharjee A., Otto A., et al., “Geospace environmental modeling (GEM) magnetic reconnection challenge,” J. Geophys. Res.-Space, vol. 106 (2001), no. A3, pp. 3715–3719.
[42]
Hesse M., Birn J., and Kuznetsova M., “Collisionless magnetic reconnection: Electron processes and transportmodeling,” J. Geophys. Res.-Space, vol. 106 (2001), no. A3, pp. 3721–3735.
[43]
Birn J. and Hesse M., “Geospace environment modeling (GEM) magnetic reconnection challenge: Resistive tearing, anisotropic pressure and hall effects,” J. Geophys. Res.-Space, vol. 106 (2001), no. A3, pp. 3737–3750.
[44]
Ma Z. and Bhattacharjee A., “Hallmagnetohydrodynamic reconnection: The geospace environment modeling challenge,” J. Geophys. Res.-Space, vol. 106 (2001), no. A3, pp. 3773–3782.
[45]
Pritchett P., “Geospace environment modeling magnetic reconnection challenge: Simulations with a full particle electromagnetic code,” J. Geophys. Res.-Space, vol. 106 (2001), no. A3, pp. 3783–3798.
[46]
Kuznetsova M. M., Hesse M., and Winske D., “Collisionless reconnection supported by nongyrotropic pressure effects in hybrid and particle simulations,” J. Geophys. Res.-Space, vol. 106 (2001), no. A3, pp. 3799–3810.