A new three-dimensional magnetohydrodynamic (MHD) simulation code based on the fourth-order Runge-Kutte-Gill time advance and the direct finite space difference is applied to the detailed study of the solar wind interaction with the Earth's dipole field with special emphasis on its numerical soundness. The dynamic formation processes of the bow shock and the magnetopause are revealed, where the transient propagation characteristic of fast waves play the leading role. The plasma sheet formation process is also revealed. The high temperature, high density, and hence high pressure in the plasma sheet are caused by the fast waves which compress the dipole field. The study of the effects of the interplanetary magnetic field (IMF) on the plasma sheet finds that when the IMF is directed south, the plasma sheet is strongly compressed by the reconnected magnetic flux which is carried from the dayside. The peak plasma sheet pressure that appears around 8 RE (RE: Earth's radius) on the nightside is almost exactly as large as the solar wind dynamic pressure in the absence of the IMF. When the IMF is north, the nightside lobe magnetic field is peeled off, so that the plasma sheet pressure becomes weakly depressed in comparison with the no-IMF case.

This indicates that the direction of the IMF largely influences the pressure of the plasma sheet. More interestingly and importantly, no Kelvin--Helmholtz instability occurs along the magnetopause in an ideal MHD, contrary to the conventional understanding. Furthermore, no entry of mass, momentum, and energy through the magnetopause is observed at all in our simulation. This strongly ensures enough numerical accuracy and validity of the present work. Thus the simulation results of earlier works where a considerable amount of solar wind momentum is transported into the magnetosphere must be due to a numerical inaccuracy. As further evidence showing the numerical validity of the present code, the relationship between the standoff distance and the adiabatic constant is compared with the strong shock theory, and a fairly good agreement is obtained. On the other hand, the standoff distance is found to be weakly dependent upon the dynamic pressure of the solar wind in the realistic parameter range. ¿ American Geophysical Union 1990