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
    TOTH G. The a·±b B constraint in shock-capturing magnetohydrodynamics codes[J]. J. Comput. Phys., 2000, 161(2):605-652
    BALSARA D S, KIM J. A comparison between divergence-cleaning and staggered-mesh formulations for numerical magnetohydrodynamics[J]. Astrophys. J., 2004, 602(2):1079
    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
    EVANS C R, HAWLEY J F. Simulation of magnetohydrodynamic flows-a constrained transport method[J]. Astrophys. J., 1988, 332:659-677
    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
    BALSARA D S. Second-order-accurate schemes for magnetohydrodynamics with divergence-free reconstruction[J]. Astrophys. J. Supp. Ser., 2004, 151(1):149
    DAI W, WOODWARD P R. A simple finite difference scheme for multidimensional magnetohydrodynamical equations[J]. J. Comput. Phys., 1998, 142(2):331-369
    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
    DEDNER A, KEMM F, KRONER D, et al. Hyperbolic divergence cleaning for the MHD equations[J]. J. Comput. Phys., 2002, 175(2):645-673
    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
    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
    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
    TORO E F. Riemann Solvers and Numerical Methods for Fluid Dynamics:A Practical Introduction[M]. Berlin, Herdelberg:Springer, 2009
    CONSTANTINE D. Hyperbolic Conservation Laws in Continuum Physics[M]. Berlin, Herdelberg Springer, 2016
    TADMOR E. Numerical viscosity and the entropy condition for conservative difference schemes[J]. Math. Comput., 1984, 43(168):369-381
    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
    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
    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
    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
    TRICCO T S, PRICE D J. Constrained hyperbolic divergence cleaning for smoothed particle magnetohydrodynamics[J]. J. Comput. Phys., 2012, 231(21):7214-7236
    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
    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
    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
    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
    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
    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
    TADMOR E. The numerical viscosity of entropy stable schemes for systems of conservation laws[J]. Math. Comput., 1987, 49(179):91-103
    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
    PARKER E N. Dynamics of the interplanetary gas and magnetic fields[J]. Astrophys. J., 1958, 128:664
    ALTSCHULER M D, NEWKIRK G. Magnetic fields and the structure of the solar corona[J]. Solar Phys., 1969, 9(1):131-149
    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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