Numerical solution of the kinematics of the stream interface. Top left: temporal velocity profile of the driving HSS plasma. The HSS is assumed to have a longitudinal width of 22°, and the slices are set at 0°, 4°, 6°, 8°, and 10° to the HSS center. Top right: resulting velocity of the stream interface versus its distance from the Sun. Bottom left: total mass of the stream interface per solid angle, dependent on its distance from the Sun. Bottom right: numerical arrival time of the stream interface at 1 AU versus the analytically approximated arrival time derived by Eq. (28).