Volume 39 Issue 4
Jul.  2019
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WANG Tenglong, FENG Xueshang, LI Caixia, LIU Xiaojing. Numerical Simulation for Solar Wind Background by Entropy Conservation Scheme[J]. Journal of Space Science, 2019, 39(4): 417-431. doi: 10.11728/cjss2019.04.417
Citation: WANG Tenglong, FENG Xueshang, LI Caixia, LIU Xiaojing. Numerical Simulation for Solar Wind Background by Entropy Conservation Scheme[J]. Journal of Space Science, 2019, 39(4): 417-431. doi: 10.11728/cjss2019.04.417

Numerical Simulation for Solar Wind Background by Entropy Conservation Scheme

doi: 10.11728/cjss2019.04.417
  • Received Date: 2018-05-08
  • Rev Recd Date: 2019-05-22
  • Publish Date: 2019-07-15
  • Background solar wind is a key factor for interplanetary disturbance propagation. Magnetohydrodynamic (MHD) simulation is an important tool for background solar wind study. In this paper an entropy conservation scheme is adopted. Ideal GLM-MHD is used to handle the magnetic divergence. The divergence of the magnetic field generated during the calculation is propagated outside the calculation domain with the maximum characteristic speed of MHD system. With the analytical divergence-free condition of magnetic field as additional constraint condition, the reconstruction of solution variables uses the constrained least squares method. The reconstructed magnetic field gradient is further modified by the way of iteration. The flux calculation adopts an entropy conservation scheme which satisfies the second law of thermodynamics. This formulation can ensure that the entropy does not increase in the calculation process, and the numerical stability can be guaranteed. The results show that numerical simulation for solar wind background by entropy conservation scheme can obtain more stable results.

     

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  • [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
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