  Computational heliophysics has shed light on the fundamental physical
processes inside the Sun, such as the differential rotation, meridional
circulation, and dynamo-generation of magnetic fields. However, despite the
substantial advances, the current results of 3D MHD simulations are still far
from reproducing helioseismic inferences and surface observations. The reason
is the multi-scale nature of the solar dynamics, covering a vast range of
scales, which cannot be solved with the current computational resources. In
such a situation, significant progress has been achieved by the mean-field
approach, based on the separation of small-scale turbulence and large-scale
dynamics. The mean-field simulations can reproduce solar observations,
qualitatively and quantitatively, and uncover new phenomena. However, they do
not reveal the complex physics of large-scale convection, solar magnetic
cycles, and the magnetic self-organization that causes sunspots and solar
eruptions. Thus, developing a synergy of these approaches seems to be a
necessary but very challenging task.
