Numerical simulation plays a key role in modeling and understanding highly nonlinear two- and three-dimensional plasma processes. A typical process of this type is represented by magnetic reconnection At the Earth's magnetopause magnetic reconnection is believed to be the cause of magnetic flux transfer events or structures which are interpreted in terms of rotational discontinuities. For both observations a clear correlation to a southward interplanetary magnetic field (i.e. large magnetic shear across the magnetopause) is a typical property. From theory and computer simulation it is known that a large magnetic shear is also a requirement for magnetic reconnection. In terms of MHD simulations two major approaches may be distinguished. One of these approaches considers the interaction of the total (dayside) magnetospheric system with the solar wind plasma. These simulations may provide qualitative insight into how the three-dimensional structure of the dayside magnetosphere controls dynamical processes at the magnetopause. Another class of simulations considers a local approximation of the magnetopause i.e. length scales which are small compared with the radius of curvature. The better spatial resolution of these simulations allows us to study basic processes in more detail. Here we will review main results of both kinds of three-dimensional MHD simulations. Using the local approximation we will also present some new results which might be relevant to the formation of boundary layers at the magnetopause.
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A. Otto (1991) studied this question.