1. Mathematical modeling of flows with detonation waves. Studies of nonlinear dynamics of one-dimensional pulsating detonation. Investigation of the mechanisms of initiation and propagation of gas detonation waves in areas of complex shape.
2. Cartesian grid methods for numerical simulation of gas flows in areas with varying boundary geometry. Numerical study of the dynamics of motion of several bodies (in general, bodies of complex shape and interact with each other) in the flow of a compressible medium.
3. Numerical simulation of flows of two-phase compressible media within the framework of models of mechanics of heterogeneous media. The Baer-Nunziato equations. The interaction of shock waves with dust layers and clouds.
Main publications:
P. S. Utkin, A. I. Lopato, A. A. Vasilev, “Mechanisms of detonation initiation in multi-focusing systems”, Shock Waves, 30:7-8 (2020), 741–753, (JCR 2020 Q3, SJR 2020 Q2)
Ya. E. Poroshyna, A. I. Lopato, P. S. Utkin, “Nonlinear dynamics of pulsating detonation wave with two-stage chemical kinetics in the shock-attached frame”, Journal of Inverse and Ill-Posed Problems, 29:4 (2021), 557–576, (JCR 2020 Q1)
Ya. E. Poroshyna, P. S. Utkin, “Numerical simulation of a normally incident shock wave – dense particles layer interaction using the Godunov solver for the Baer–Nunziato equations”, International Journal of Multiphase Flow, 142 (2021), 103718, (JCR 2020 Q2, SJR 2020 Q1)
P. S. Utkin, D. A. Sidorenko, V. M. Boiko, “Dynamics of motion of a pair of particles in a supersonic flow”, Shock Waves, 31:6 (2021), 571–582, (JCR 2020 Q3, SJR 2020 Q2)
P. S. Utkin, P. A. Chuprov, “Numerical simulation of shock wave propagation over a dense particle layer using the Baer-Nunziato model”, Physics of Fluids, 35:11 (2023), 113313, (JCR 2022 Q1, SJR 2022 Q1)
