Hybrid block-AMR in cartesian and curvilinear coordinates: MHD applications

Holst, B. van der; Keppens, Rony

doi:10.1016/j.jcp.2007.05.007

Cited by 87 publications

(54 citation statements)

References 40 publications

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“…Many modern numerical schemes are usually established in Cartesian coordinates and can be directly used in solar wind modeling without any further modification. For these reasons, Cartesian coordinates (x, y, z) have also been widely used (Groth et al 2000;van der Holst & Keppens 2007;Kleimann et al 2009), for which numerics are faster, simpler (esp ecially with respect to multidimensional extension), and more stable. This is especially true for an MHD code built within a framework that allows for Cartesian AMR (e.g., Groth et al 2000;van der Holst & Keppens 2007;Kleimann et al 2009).…”

Section: Introductionmentioning

confidence: 99%

“…In order to adequately implement the Sun's spherical surface as an inner boundary on the Cartesian grid, a weighted averaging procedure (Kleimann et al 2009) was devised in order to handle the huge gradients (most notably of mass density) occurring at this boundary. To deal with the spherical surface inner boundary, an alternative method is to allow for arbitrary embedded boundaries in the Cartesian geometry by employing a cut-cell method (e.g., Zeeuw & Powell 1993;Groth et al 2000;van der Holst & Keppens 2007). The use of these procedures also contributes to a reduction of spurious departures from the problem's underlying symmetry, which results from the fact that the Sun's spherical boundary surface cannot be mapped to a Cartesian grid of finite cell spacing.…”

Section: Introductionmentioning

confidence: 99%

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THREE-DIMENSIONAL SOLARWINDMODELING FROM THE SUN TO EARTH BY A SIP-CESE MHD MODEL WITH A SIX-COMPONENT GRID

Feng

Yang

Cui

et al. 2010

ApJ

174

144

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The objective of this paper is to explore the application of a six-component overset grid to solar wind simulation with a three-dimensional (3D) Solar-InterPlanetary Conservation Element/Solution Element MHD model. The essential focus of our numerical model is devoted to dealing with: (1) the singularity and mesh convergence near the poles via the use of the six-component grid system, (2) the ∇ · B constraint error via an easy-to-use cleaning procedure by a fast multigrid Poisson solver, (3) the Courant-Friedrichs-Levy number disparity via the Courant-number insensitive method, (4) the time integration by multiple time stepping, and (5) the time-dependent boundary condition at the subsonic region by limiting the mass flux escaping through the solar surface. In order to produce fast and slow plasma streams of the solar wind, we include the volumetric heating source terms and momentum addition by involving the topological effect of the magnetic field expansion factor f S and the minimum angular distance θ b (at the photosphere) between an open field foot point and its nearest coronal hole boundary. These considerations can help us easily code the existing program, conveniently carry out the parallel implementation, efficiently shorten the computation time, greatly enhance the accuracy of the numerical solution, and reasonably produce the structured solar wind. The numerical study for the 3D steady-state background solar wind during Carrington rotation 1911 from the Sun to Earth is chosen to show the above-mentioned merits. Our numerical results have demonstrated overall good agreements in the solar corona with the Large Angle and Spectrometric Coronagraph on board the Solar and Heliospheric Observatory satellite and at 1 AU with WIND observations.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

THREE-DIMENSIONAL SOLARWINDMODELING FROM THE SUN TO EARTH BY A SIP-CESE MHD MODEL WITH A SIX-COMPONENT GRID

Feng

Yang

Cui

et al. 2010

ApJ

174

144

View full text Add to dashboard Cite

show abstract

“…Expressions for the wave speeds, as obtained for different reference frames in relative motion to each other, have been used as basic ingredients for the current suite of relativistic magnetofluid codes. [4][5][6][7][8][9][10][11][12] Knowledge of the ͑fastest͒ characteristic speeds embedded in the relativistic MHD equations is essential to obtain time-step stability limits for explicit time-stepping strategies, while many modern RMHD codes use more complete information on all linear wave dynamics. This information is incorporated in the eigenvectors of the flux Jacobian, with the fluxes appearing in the governing hyperbolic equations for the conserved variables, typically formulated in a 3 + 1 formulation where a fixed laboratory frame is selected.…”

Section: Introduction: Relativistic Mhdmentioning

confidence: 99%

Linear wave propagation in relativistic magnetohydrodynamics

Keppens

Méliani

2008

Physics of Plasmas

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The properties of linear Alfvén, slow, and fast magnetoacoustic waves for uniform plasmas in relativistic magnetohydrodynamics ͑MHD͒ are discussed, augmenting the well-known expressions for their phase speeds with knowledge on the group speed. A 3 + 1 formalism is purposely adopted to make direct comparison with the Newtonian MHD limits easier and to stress the graphical representation of their anisotropic linear wave properties using the phase and group speed diagrams. By drawing these for both the fluid rest frame and for a laboratory Lorentzian frame which sees the plasma move with a three-velocity having an arbitrary orientation with respect to the magnetic field, a graphical view of the relativistic aberration effects is obtained for all three MHD wave families. Moreover, it is confirmed that the classical Huygens construction relates the phase and group speed diagram in the usual way, even for the lab frame viewpoint. Since the group speed diagrams correspond to exact solutions for initial conditions corresponding to a localized point perturbation, their formulae and geometrical construction can serve to benchmark current high-resolution algorithms for numerical relativistic MHD.

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“…in the BATS-R-US code (Powell et al, 1999), or in the AMR-VAC code (van der Holst and Keppens, 2007). Currently, only two groups have developed advanced 3D coupled MHD models to model a CME event from its initiation up to the interaction with the magnetosphere of the Earth: the CORHEL model at the University of Boston and the Space Weather Modeling Framework (SWMF) (Tó th et al, 2005) at the University of Michigan.…”

Section: Discussionmentioning

confidence: 99%

Models for coronal mass ejections

Jacobs

Poedts

2011

Journal of Atmospheric and Solar-Terrestrial Physics

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a b s t r a c tCoronal mass ejections (CMEs) play a key role in space weather. The mathematical modelling of these violent solar phenomena can contribute to a better understanding of their origin and evolution and as such improve space weather predictions. We review the state-of-the-art in CME simulations, including a brief overview of current models for the background solar wind as it has been shown that the background solar wind affects the onset and initial evolution of CMEs quite substantially. We mainly focus on the attempt to retrieve the initiation and propagation of CMEs in the framework of computational magnetofluid dynamics (CMFD). Advanced numerical techniques and large computer resources are indispensable when attempting to reconstruct an event from Sun to Earth. Especially the simulations developed in dedicated event studies yield very realistic results, comparable with the observations. However, there are still a lot of free parameters in these models and ad hoc source terms are often added to the equations, mimicking the physics that is not really understood yet in detail.

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Hybrid block-AMR in cartesian and curvilinear coordinates: MHD applications

Cited by 87 publications

References 40 publications

THREE-DIMENSIONAL SOLARWINDMODELING FROM THE SUN TO EARTH BY A SIP-CESE MHD MODEL WITH A SIX-COMPONENT GRID

THREE-DIMENSIONAL SOLARWINDMODELING FROM THE SUN TO EARTH BY A SIP-CESE MHD MODEL WITH A SIX-COMPONENT GRID

Linear wave propagation in relativistic magnetohydrodynamics

Models for coronal mass ejections

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