Citation: | WANG Tenglong, FENG Xueshang, LI Caixia, LIU Xiaojing. Numerical Simulation for Solar Wind Background by Entropy Conservation Scheme[J]. Chinese Journal of Space Science, 2019, 39(4): 417-431. doi: 10.11728/cjss2019.04.417 |
[1] |
BRACKBILL J U, BARNES D C. The effect of nonzero a·±b B on the numerical solution of the magnetohydrodynamic equations[J]. J. Comput. Phys., 1980, 35(3):426-430
|
[2] |
TOTH G. The a·±b B constraint in shock-capturing magnetohydrodynamics codes[J]. J. Comput. Phys., 2000, 161(2):605-652
|
[3] |
BALSARA D S, KIM J. A comparison between divergence-cleaning and staggered-mesh formulations for numerical magnetohydrodynamics[J]. Astrophys. J., 2004, 602(2):1079
|
[4] |
GUILLET T, TEYSSIER R. A simple multigrid scheme for solving the poisson equation with arbitrary domain boundaries[J]. J. Comput. Phys., 2011, 230(12):4756-4771
|
[5] |
EVANS C R, HAWLEY J F. Simulation of magnetohydrodynamic flows-a constrained transport method[J]. Astrophys. J., 1988, 332:659-677
|
[6] |
YEE K. Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media[J]. IEEE Trans. Anten. Propag., 1966, 14(3):302-307
|
[7] |
BALSARA D S. Second-order-accurate schemes for magnetohydrodynamics with divergence-free reconstruction[J]. Astrophys. J. Supp. Ser., 2004, 151(1):149
|
[8] |
DAI W, WOODWARD P R. A simple finite difference scheme for multidimensional magnetohydrodynamical equations[J]. J. Comput. Phys., 1998, 142(2):331-369
|
[9] |
POWELL K G, ROE P L, LINDE T J, et al. A solution-adaptive upwind scheme for ideal magnetohydrodynamics[J]. J. Comput. Phys., 1999, 154(2):284-309
|
[10] |
DEDNER A, KEMM F, KRONER D, et al. Hyperbolic divergence cleaning for the MHD equations[J]. J. Comput. Phys., 2002, 175(2):645-673
|
[11] |
FENG X, ZHANG M, ZHOU Y. A new three-dimensional solar wind model in spherical coordinates with a six-component grid[J]. Astrophys. J. Suppl. Ser., 2014, 214(1):6
|
[12] |
FENG X, LI C, XIANG C, et al. Data-driven modeling of the solar corona by a new three-dimensional path-conservative osher-solomon MHD model[J]. Astrophys. J. Supp. Ser., 2017, 233(1):10
|
[13] |
GODUNOV S K. A difference method for numerical calculation of discontinuous solutions of the equations of hydrodynamics[J]. Matemat. Sbornik, 1959, 89(3):271-306
|
[14] |
TORO E F. Riemann Solvers and Numerical Methods for Fluid Dynamics:A Practical Introduction[M]. Berlin, Herdelberg:Springer, 2009
|
[15] |
CONSTANTINE D. Hyperbolic Conservation Laws in Continuum Physics[M]. Berlin, Herdelberg Springer, 2016
|
[16] |
TADMOR E. Numerical viscosity and the entropy condition for conservative difference schemes[J]. Math. Comput., 1984, 43(168):369-381
|
[17] |
ISMAIL F, ROE P L. Affordable, entropy-consistent Euler flux functions ii:entropy production at shocks[J]. J. Comput. Phys., 2009, 228(15):5410-5436
|
[18] |
DERIGS D, WINTERS A R, GASSNER G J, et al. Ideal GLM-MHD:about the entropy consistent nine-wave magnetic field divergence diminishing ideal magnetohydrodynamics equations[J]. J. Comput. Phys., 2018, 364:420-467
|
[19] |
CHANDRASHEKAR P, KLINGENBERG C. Entropy stable finite volume scheme for ideal compressible MHD on 2-d cartesian meshes[J]. SIAM J. Num. Anal., 2016, 54(2):1313-1340
|
[20] |
WINTERS A R, DERIGS D, GASSNER G J, et al. A uniquely defined entropy stable matrix dissipation operator for high mach number ideal mhd and compressible euler simulations[J]. J. Comput. Phys., 2017, 332:274-289
|
[21] |
TRICCO T S, PRICE D J. Constrained hyperbolic divergence cleaning for smoothed particle magnetohydrodynamics[J]. J. Comput. Phys., 2012, 231(21):7214-7236
|
[22] |
FENG X, XIANG C, ZHONG D, et al. Sip-cese MHD model of solar wind with adaptive mesh refinement of hexahedral meshes[J]. Comput. Phys. Commun., 2014, 185(7):1965-1980
|
[23] |
FENG X, YANG L, XIANG C, et al. Three-dimensional solar wind modeling from the Sun to Earth by a SIP-CESE MHD model with a six-component grid[J]. Astrophys. J., 2010, 723(1):300
|
[24] |
FREY A, HALL C, PORSCHING T. Some results on the global inversion of bilinear and quadratic isoparametric finite element transformations[J]. Math. Comput., 1978, 32(143):725-749
|
[25] |
IVAN L, DE STERCK H, SUSANTO A, et al. High-order central ENO finite-volume scheme for hyperbolic conservation laws on three-dimensional cubed-sphere grids[J]. J. Comput. Phys., 2015, 282:157-182
|
[26] |
VENKATAKRISHNAN V. Convergence to steady state solutions of the euler equations on unstructured grids with limiters[J]. J. Comput. Phys., 1995, 118(1):120-130
|
[27] |
HOPKINS P F. A constrained-gradient method to control divergence errors in numerical mhd[J]. Mon. Not. R. Astron. Soc., 2016, 462(1):576-587
|
[28] |
TADMOR E. The numerical viscosity of entropy stable schemes for systems of conservation laws[J]. Math. Comput., 1987, 49(179):91-103
|
[29] |
BARTH T J. Numerical methods for gas dynamic systems on unstructured meshes[M]//An Introduction to Recent Developments in Theory and Numerics for Conservation Laws. Berlin:Springer, 1999:195-285
|
[30] |
PARKER E N. Dynamics of the interplanetary gas and magnetic fields[J]. Astrophys. J., 1958, 128:664
|
[31] |
ALTSCHULER M D, NEWKIRK G. Magnetic fields and the structure of the solar corona[J]. Solar Phys., 1969, 9(1):131-149
|
[32] |
SHIOTA D, KATAOKA R, MIYOSHI Y, et al. Inner heliosphere MHD modeling system applicable to space weather forecasting for the other planets[J]. Space Weather, 2014, 12(4):187-204
|