Abstract
This paper presents a comparative study of divergence cleaning methods of magnetic field in the solar coronal three-dimensional numerical simulation. For such purpose, the diffusive method, projection method, generalized Lagrange multiplier method and constrained-transport method are used. All these methods are combined with a finite-volume scheme based on a six-component grid system in spherical coordinates. In order to see the performance between the four divergence cleaning methods, solar coronal numerical simulation for Carrington rotation 2056 has been studied. Numerical results show that the average relative divergence error is around $10^{-4.5}$ for the constrained-transport method, while about $10^{-3.1}- 10^{-3.6}$ for the other three methods. Although there exist some differences in the average relative divergence errors for the four employed methods, our tests show they can all produce basic structured solar wind.
Highlights
Magnetohydrodynamics (MHD) equations are presently the only system available to selfconsistently describe large-scale dynamics of space plasmas, and numerical MHD simulations has enabled us to capture the basic structures of the solar wind plasma flow and transient phenomena
We present the numerical results from Carrington rotation (CR) 2056 for the solar coronal numerical simulation with these four methods to maintain the divergence-free constraint
To see the differences with the four divergence cleaning methods in solar corona simulation, Figures 2–5 show the magnetic field lines, radial speed vr, and number density N on two different meridional planes at φ = 180◦ − 0◦ and φ = 270◦ − 90◦ from 1 to 20 Rs, where the arrowheads on the black lines stand for the magnetic field directions
Summary
Magnetohydrodynamics (MHD) equations are presently the only system available to selfconsistently describe large-scale dynamics of space plasmas, and numerical MHD simulations has enabled us to capture the basic structures of the solar wind plasma flow and transient phenomena. Different from the usual computational fluid mechanics, the MHD scheme has to be designed so as to guarantee the divergence free constraint of the magnetic field in two or three-dimensional MHD calculations. The eight-wave formulation approach, suggested by Powell et al (1993, 1999), is to solve the MHD equations with the additional source terms that are proportional to ∇ · B without modifying the MHD solver In this approach, divergence of the magnetic can be controlled to a truncation error and the robustness of a MHD code can be improved (Hayashi, 2005; Jiang et al, 2012a,b). The CT method sustains a specified discretization of the magnetic field divergence around the machine round off error as long as the boundary and initial conditions are compatible with the constraints (Ziegler, 2011, 2012; Feng et al, 2014)
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