A 3D MHD model of astrophysical flows: Algorithms, tests and parallelisation

Caunt, S. E.; Korpi, M. J.

doi:10.1051/0004-6361:20010157

Cited by 54 publications

(60 citation statements)

References 42 publications

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“…SAC is the reconfigurable multi-dimensional ideal MHD solver which is designed to simulate the nonlinear interaction of an arbitrary perturbation with a gravitationally stratified background model, i.e., a model of the solar atmosphere, in magnetohydrostatic equilibrium. The code uses variable separation and hyperdiffusive and hyper-resistive terms (Stein & Nordlund 1998;Caunt & Korpi 2001;Vögler et al 2005;Shelyag et al 2008) to stabilize the solution against numerical instabilities and imperfections in the background model, caused by truncation errors. The main advantage of the implemented numerical technique is that it allows us to robustly simulate the macroscopic processes in a gravitationally stratified, magnetized plasma.…”

Section: Numerical Methods and Modelmentioning

confidence: 99%

Numerical Modeling of Footpoint-Driven Magneto-Acoustic Wave Propagation in a Localized Solar Flux Tube

Fedun

Shelyag

Erdélyi

2010

ApJ

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In this paper, we present and discuss results of two-dimensional simulations of linear and nonlinear magnetoacoustic wave propagation through an open magnetic flux tube embedded in the solar atmosphere expanding from the photosphere through to the transition region and into the low corona. Our aim is to model and analyze the response of such a magnetic structure to vertical and horizontal periodic motions originating in the photosphere. To carry out the simulations, we employed our MHD code SAC (Sheffield Advanced Code). A combination of the VALIIIC and McWhirter solar atmospheres and coronal density profiles were used as the background equilibrium model in the simulations. Vertical and horizontal harmonic sources, located at the footpoint region of the open magnetic flux tube, are incorporated in the calculations, to excite oscillations in the domain of interest. To perform the analysis we have constructed a series of time-distance diagrams of the vertical and perpendicular components of the velocity with respect to the magnetic field lines at each height of the computational domain. These time-distance diagrams are subject to spatio-temporal Fourier transforms allowing us to build ω-k dispersion diagrams for all of the simulated regions in the solar atmosphere. This approach makes it possible to compute the phase speeds of waves propagating throughout the various regions of the solar atmosphere model. We demonstrate the transformation of linear slow and fast magneto-acoustic wave modes into nonlinear ones, i.e., shock waves, and also show that magneto-acoustic waves with a range of frequencies efficiently leak through the transition region into the solar corona. It is found that the waves interact with the transition region and excite horizontally propagating surface waves along the transition region for both types of drivers. Finally, we estimate the phase speed of the oscillations in the solar corona and compare it with the phase speed derived from observations.

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Section: Numerical Methods and Modelmentioning

confidence: 99%

Numerical Modeling of Footpoint-Driven Magneto-Acoustic Wave Propagation in a Localized Solar Flux Tube

Fedun

Shelyag

Erdélyi

2010

ApJ

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“…In a similar manner to Stein and Nordlund (1998) and Caunt and Korpi (2001), in order to damp high-frequency numerical noise on subgrid scales, the physical diffusive terms in the equations of momentum and energy are replaced by artificial equivalents. In the induction equation, the magnetic-diffusion term is retained, with η being replaced by an artificial value.…”

Section: The Iac Mhd Codementioning

confidence: 99%

“…In particular, the method has been used to study the absorption of p-mode power by active regions (Braun, Duvall, and Labonte, 1988;Bogdan et al, 1993;Chen, Chou, and TON Team, 1996). In this procedure, the wave signal of the p modes is decomposed into inward-and outward-propagating modes in an annular region surrounding a sunspot.…”

Section: Moat Flow: Hankel Analysismentioning

confidence: 99%

Modeling the Subsurface Structure of Sunspots

et al. 2010

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While sunspots are easily observed at the solar surface, determining their subsurface structure is not trivial. There are two main hypotheses for the subsurface structure of sunspots: the monolithic model and the cluster model. Local helioseismology is the only means by which we can investigate subphotospheric structure. However, as current linear inversion techniques do not yet allow helioseismology to probe the internal structure with sufficient confidence to distinguish between the monolith and cluster models, the development of physically realistic sunspot models are a priority for helioseismologists. This is because they are not only important indicators of the variety of physical effects that may influence helioseismic inferences in active regions, but they also enable detailed assessments of the validity of helioseismic interpretations through numerical forward modeling. In this article, we provide a critical review of the existing sunspot models and an overview of numerical methods employed to model wave propagation through model sunspots. We then carry out a helioseismic analysis of the sunspot in Active Region 9787 and address the serious inconsistencies uncovered by Gizon et al. (2009aGizon et al. ( , 2009b. We find that this sunspot is most probably associated with a shallow, positive wave-speed perturbation (unlike the traditional two-layer model) and that travel-time measurements are consistent with a horizontal outflow in the surrounding moat.

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“…These terms are implemented to stabilise the solution against numerical instabilities, and they are extensively described in e.g., Caunt & Korpi (2001), Vögler et al (2005), Shelyag et al (2008), and references therein. Equations (2)-(11) are solved using a fourth-order central difference scheme for the spatial derivatives and are advanced in time by implementing a fourth order Runge-Kutta numerical method.…”

Section: Simulation Modelmentioning

confidence: 99%

“…The 2D box is 180 Mm wide and 50 Mm deep, and has a resolution of 960 × 1000 grid points; the upper boundary of the domain is at the solar surface R = R . We employ the simplest type of "open" boundary conditions, assuming that all of the spatial derivatives of the variables, which are advanced in time, are set to be zero across the boundaries of the domain (Caunt & Korpi 2001;Shelyag et al 2008). The perturbation source is located in the upper-middle (500 km below the upper boundary) of the simulation box.…”

Section: Simulation Modelmentioning

confidence: 99%

Acoustic wave propagation in the solar sub-photosphere with localised magnetic field concentration: effect of magnetic tension

Shelyag¹,

Zharkov²,

Fedun³

et al. 2009

A&A

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Aims. We analyse numerically the propagation and dispersion of acoustic waves in the solar-like sub-photosphere with localised nonuniform magnetic field concentrations, mimicking sunspots with various representative magnetic field configurations. Methods. Numerical simulations of wave propagation through the solar sub-photosphere with a localised magnetic field concentration are carried out using SAC, which solves the MHD equations for gravitationally stratified plasma. The initial equilibrium density and pressure stratifications are derived from a standard solar model. Acoustic waves are generated by a source located at the height corresponding approximately to the visible surface of the Sun. By means of local helioseismology we analyse the response of vertical velocity at the level corresponding to the visible solar surface to changes induced by magnetic field in the interior. Results. The results of numerical simulations of acoustic wave propagation and dispersion in the solar sub-photosphere with localised magnetic field concentrations of various types are presented. Time-distance diagrams of the vertical velocity perturbation at the level corresponding to the visible solar surface show that the magnetic field perturbs and scatters acoustic waves and absorbs the acoustic power of the wave packet. For the weakly magnetised case, the effect of magnetic field is mainly thermodynamic, since the magnetic field changes the temperature stratification. However, we observe the signature of slow magnetoacoustic mode, propagating downwards, for the strong magnetic field cases.

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A 3D MHD model of astrophysical flows: Algorithms, tests and parallelisation

Cited by 54 publications

References 42 publications

Numerical Modeling of Footpoint-Driven Magneto-Acoustic Wave Propagation in a Localized Solar Flux Tube

Numerical Modeling of Footpoint-Driven Magneto-Acoustic Wave Propagation in a Localized Solar Flux Tube

Modeling the Subsurface Structure of Sunspots

Acoustic wave propagation in the solar sub-photosphere with localised magnetic field concentration: effect of magnetic tension

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