Moving of surfaces method which preserves spherical parts

It is necessary to find the location of boundaries for every time when one is computing a nonsteady problem of mathematical physics with moving boundaries. The boundaries are surfaces if solution depends on three space variables. Assume that a plot of one boundary is a part of sphere and all points of this plot move with identical velocities when $t=0$. Then during some time the plot will be a part of sphere. In this paper an algorithm is suggested of moving surfaces preserving spherical plots under indicated conditions.