|Reference||Type||MHD||Resolution||Box size (Mm3)||Duration|
|Cattaneo et al. (2001)||I-Bouss.||Yes||10242 × 96||30 × 30 × 1.5||35 sh|
|DeRosa et al. (2002)||I-Anel.||No||1024 × 512 × 128||4400 × 4 400 × 56||80 d|
|Miesch et al. (2008)||I-Anel.||No||2048 × 1024 × 257||4400 × 4400 × 190||560 d|
|Rieutord et al. (2002)||R||No||3152 × 82||30 × 30 × 3.2||7 sh|
|Rincon et al. (2005)||I-Poly.||No||10242 × 82||64 × 64 × 1.5||15 sh|
|Ustyugov (2008)||R||No||6002 × 168||60 × 60 × 20||24 sh|
|Ustyugov (2009)||R||Yes||6002 × 204||60 × 60 × 20||24 sh|
|Stein et al. (2009a)||R||No||10002 × 500||96 × 96 × 20||64 sh|
|Stein et al. (2009b)||R||Yes||5002 × 500||48 × 48 × 20||48 sh|
The most recent large-scale three-dimensional models represent numerical tours de force and are increasingly successful at reproducing observational features of solar surface magnetoconvection in the granulation to supergranulation range. One of their main achievements has been the test of standard helioseismic diagnostic tools with numerical data sets: the results compare reasonably well with those extracted from real data (e.g., Georgobiani et al., 2007; Couvidat and Birch, 2009). Another important point on the topic of “virtual observations” is that large-scale simulations have helped validate granule-tracking techniques to reconstruct velocity fields at the solar surface (Rieutord et al., 2001).
On the specific problem of the origin of supergranulation, an important result is that the supergranulation scale does not seem to emerge as a particular scale in purely hydrodynamic simulations incorporating the ionisation of Hydrogen and Helium, which tends to disprove the “classical” Simon and Leighton (1964) supergranulation theory. Finally, it is encouraging for the future that the most recent MHD simulations to date (Ustyugov, 2009; Stein et al., 2009b) start to be large enough for meaningful numerical studies of the process of network formation and supergranulation-scale MHD to be possible.
It is fair to say, however, that even the most advanced and impressive numerical efforts to date can only be considered as preliminary with respect to the supergranulation puzzle. As shown in Section 4.2, recent observations indicate that the supergranulation scale is an undeniable feature of the horizontal velocity power spectrum of solar surface convection, whatever method is used to compute the spectrum. This observation has not been reproduced by any numerical simulation so far. The superrotation rate of supergranules is another open question that no simulation can address at the moment. Finally, the interactions between supergranulation, the magnetic network, and internetwork fields are still poorly understood.
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