## 1 Introduction  
The problem of controlling high-speed flows by non-mechanical means, namely, remote energy input, is currently at the forefront in the field of flow/flight control research. [1]. Recently, the use of electric discharges, microwaves, and laser energy deposition to control supersonic flows are quite developed areas of research in aerospace technology [1, 2, 3]. Historical analysis of breakthrough results obtained several decades ago, indicating the possibility of controlling supersonic flows by supplying energy to various parts of the flow and the surface of an aerodynamic (AD) body, is presented in [4]. In [5], the study is conducted on a sonic boom effect using continuous energy deposition consisting of two and three longitudinal heated filaments. The flow case was considered when one of the filaments was located upper to the pointed AD body. Due to the impact of such an energy deposition on the flow, a decrease in the perceived loudness in decibels (PLdB) on the ground was obtained, although this was shown to require significant energy consumption. An overview of studies of noise generation (the Sonic Boom problem) in the field of supersonic flows/flights is presented in [6], where a summary is provided of the research conducted in the framework of the Second AIAA Sonic Boom Workshop. Previously, the efficiency of energy supply in the form of longitudinal filaments for the reduction of aerodynamic drag was established theoretically and experimentally [7; 8; 9]. At present, researchers are paying attention to the influence of spatially inhomogeneous plasma structures on the flow. In a supersonic flow, it was obtained that the reflected SW was suppressed in the region of a multifilament plasma generated by Quasi-DC electric discharges [10]. In [11], an array of surface plasma actuators was used to control the interaction of a shock wave (SW) with a boundary layer in a flow. As a result, the disappearance of a SW fragment inside the inhomogeneous area was established. In experiments [12], thermal and density inhomogeneities were generated using a discharge plasma formed by a number of the heated wires, which, when interacting with SW, was a reason for the RMI manifestation and the vortex lines origination. The influence of the region of ionization instability of a glow gas discharge, which is accompanied by the formation of a layered structure of the ionization strata, on an initially flat plane SW was studied in [13]. In these experiments, it was shown that the stratification of the electron temperature field leads to the stratification of the gas temperature, and the impact of an inhomogeneous plasma medium caused distortion and partial SW vanishing. The calculations performed showed the manifestation of the RMI at many points, leading to SW smearing, which was consistent with the experimental results [13]. In [14], the effect of a combined energy deposition in the supersonic flow is considered, and a double-vortex mechanism influencing the AD body was suggested. Besides, it was shown that the generation of double vortices is the result of the RMIs manifestation at two points in the flow. A natural continuation of this idea was the study of the effect of a TSS on the supersonic flow past an AD body [15], where a new multi-vortex mechanism of the TSS action on the surface of an AD body connected with multiple manifestations of the RMIs was established. Basic principles for non-stationary and stationary control of a high-speed flow using TSSs were obtained [16; 17]. A possibility of controlling the bow shock wave (BSW) and the aerodynamic characteristics of a streamlined body, such as parameters at the stagnation point, drag and lift forces, location, and shape of the BSW, etc., by using a TSS in front of the BSW has been shown. In [18], the complex conservative difference schemes are presented, which have the second order of space-time approximation on a minimal stencil, which is the stencil of [PERSON]'s scheme.