The possibility of initiating detonation in a closed field due to motion of its boundaries for a one-step kinetic model is studied by numerical simulation of the problems of flow of a propane-air mixture inside and outside a rotating elliptic cylinder enclosed in a circular cylinder; in rotation of a circular cylinder with parabolic blades uniformly distributed along its boundary, or in rotation of a starshaped figure with parabolic rays originating from the center of rotation; and in a plane chamber with deformable walls. Critical parameter values for which detonation occurs are determined. A method of approximate description of the processes occurring in three-dimensional helical channels is considered. In the numerical study of these processes, software based on the Godunov scheme was used.Introduction. Among the problems of wave processes in reactive gas mixtures, self-sustained detonation propagation holds a special place. Continuing attention to this problem is due, in particular, to the use of detonations in various human activities. Increased interest in detonation in the last decade has been motivated by attempts to use detonation in propulsion units. Estimates show that the thermal efficiency of engines using detonation combustion is much higher than the efficiency of conventional combustion devices. In this case, the main problem is detonation initiation. Traditionally, there are two approaches to solving this problem. The first involves the ignition of a mixture by a weak energy source with subsequent deflagration-to-detonation transition implemented by special devices boosting combustion. This leads to transition from normal combustion to a detonation mode. The second approach, called direct initiation of detonation, consists of detonation initiation by a shock wave propagating from an external energy source, for example, igniting of an explosive or electrical or laser breakdown. Detonation can be initiated by a shock wave propagating ahead of a body moving at hypersonic velocity in a combustible mixture or ahead of an immovable body in hypersonic flow. In the late 1990s, a new method of initiation using the cumulation effect of an initially weak shock wave near the axis or center of symmetry [1, 2] was studied in a one-dimensional approach. An extension of this approach to two-dimensional plane and axisymmetric flows is the original method of contoured tubes [3,4], according to which a weak shock wave moving in a channel interacts with the walls, resulting in cumulation near the axis creation of favorable conditions for ignition and transformation of the shock to a detonation wave. According to the hypersonic analogy [5,6], the tube flow is similar to the axisymmetric one-dimensional unsteady flow produced by a piston whose radius varies with time according to the shape of the tube contour. Investigations of the detonation initiation by a piston have led to the conclusion that it is effective from the point of view of minimization of both power inputs and the time required for detonation initiation ...