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A numerical simulation of a weakly ionized air flow around the OREX re-entry capsule is performed, aiming at the comparison of the electron density predicted by DSMC and NS computations to the flight data. The NS computations are performed for two approximations: one-temperature and multi-temperature. The one-temperature and multi-temperature electron density profiles are close to each other; however, the other macroparameters are different. The NS electron density profiles agree well with the profile computed by Gupta et al. (1997) using the Viscous Shock Layer model. The computed number density of electrons is consistent with the flight data. The DSMC prediction is closer to the OREX data than the NS results.

The effects of surface chemical processes on the aerothermodynamics of a blunted body are numerically studied by the Direct Simulation Monte Carlo method under typical conditions of spacecraft re-entry into the upper layers of the atmosphere (Knudsen number 0.01). A recently developed model of surface physical and chemical processes with allowance for multiple re- action channels is used in computations. The results of the present study demonstrate a significant contribution of surface chemistry to the heat flux toward the body surface. If the surface reactions between non-identical species leading to nitrogen monoxide for- mation are taken into account, the gas composition near the surface is significantly changed and the heat flux noticeably increases.

Cross sections of oxygen dissociation were calculated by solving an inverse problem by the Tikhonov regularization method. The approach employs generalized Treanor-Marrone model state-specific rate constants fitted to ab initio data as a source of input macroscopic information. The cross section set predicts state-specific rates that agree with the original Treanor-Marrone rates in the temperature range of 5000-20000 K for the entire range of vibrational states.

Navier–Stokes computations of a high-enthalpy (~ 22 MJ/kg) air flow around a double cone are performed for conditions of experimental studies carried out at the Calspan University of Buffalo Research Center (CUBRC). The aim of this work is to use the experimental data in order to assess CFD capabilities. The present computations are based on one-temperature and multi-temperature approaches. The computations based on the multi-temperature approach employ recent (December, 2018) QCT-based models of dissociation of N2 and O2. Numerical results are in good agreement with the experimental measurements of the heat flux and pressure on the double cone surface. Our computational results are also compared to the computational results of other authors (Kianvashrad et al., 2018 and Hao et al. 2017), and reasonable agreement is observed.

Using the GPU calculation, the integral aerothermodynamics of the Federation crew module in a wide range of altitudes, Mach numbers and the angle of attack were obtained by the Direct Simulation Monte Carlo (DSMC) method. A technique for calculating the radiative heat flux onto the surface of the capsule has been developed. With the help of the created technique and data of the DSMC simulation of the structure of an ionized shock layer, estimates of the spectral and total radiative flux to the surface were made.Using the GPU calculation, the integral aerothermodynamics of the Federation crew module in a wide range of altitudes, Mach numbers and the angle of attack were obtained by the Direct Simulation Monte Carlo (DSMC) method. A technique for calculating the radiative heat flux onto the surface of the capsule has been developed. With the help of the created technique and data of the DSMC simulation of the structure of an ionized shock layer, estimates of the spectral and total radiative flux to the surface were made.

An ionized flow around the RAM C-II space vehicle is studied by the direct simulation Monte Carlo method in the range of altitudes of 73 to 81 km. It is shown that the predicted value of the plasma density in the shock layer essentially depends on the approach to simulation of high-temperature nonequilibrium dissociation. Good agreement of the results of numerical simulation with flight experiment data is obtained.

Various issues of numerical simulation of supersonic gas flows with allowance for thermochemical nonequilibrium on the basis of fluid dynamic equations in the two-temperature approximation are discussed. The computational tool for modeling flows with thermochemical nonequilibrium is the commercial software package ANSYS Fluent with an additional userdefined open-code module. A comparative analysis of results obtained by various models of vibration-dissociation coupling in binary gas mixtures of nitrogen and oxygen is performed. Results of numerical simulations are compared with available experimental data.

The paper is devoted to the comparative study of Shakhov model kinetic equation and Direct Simulation Monte Carlo (DSMC) solutions as applied to high-speed flow of a monatomic gas over generic three-dimensional space vehicle under angle of attack. The corresponding calculations are carried out using Nesvetay and SMILE software packages, developed by the authors. Satisfactory agreement is shown for surface distribution of pressure, friction and heat transfer coefficients despite very different modeling approaches and computational meshes employed. It is thus shown that the use of the model kinetic equations with approximate collision integrals provides accurate results for high-speed external monatomic gas flows over complex three-dimensional geometries at acceptable computational cost.

A numerical and experimental analysis is performed to study specific features of shock wave formation near a wedge with the leading edge having a bluntness radius that is small as compared to the wedge size and commensurable with the mean free path of molecules in the free stream. Numerical solutions are compared with the shock polar that describes the pressure and angle of flow deflection behind the shock in the inviscid formulation Based on numerical simulations with allowance for viscosity, the internal structure of the shock wave predicted by the two-dimensional computation is compared with that of the one-dimensional shock wave. Comparisons are performed at the stagnation line and further downstream. The results of these comparisons are explained with the use of total enthalpy fields. Comparisons of density distributions inside the shock wave for different bluntness radii are used to explain the Schlieren visualization patterns observed in experiments. It is shown that reduction of the bluntness radi...

A new deterministic method of solving the Boltzmann equation has been proposed. The method has been employed in numerical studies of the plane shock wave structure in a hard sphere gas. Results for Mach numbers $$M=4$$ and $$M=8$$ have been compared with predictions of the direct simulation Monte Carlo (DSMC) method, which has been used to obtain the reference solution. Particular attention in estimating the solution accuracy has been paid to a fine structural effect: the presence of a total temperature peak exceeding the temperature value further downstream. The results of solving the Boltzmann equation for the shock wave structure are in excellent agreement with the DSMC predictions.

In this work, collisional schemes of the direct simulation Monte Carlo (DSMC) method are compared. The sensitivity of the schemes to the number of simulated particles is investigated. The original No-Time-Counter (NTC) scheme, proposed by G.A. Bird, its modification NTC-2007 and majorant collision frequency (MCF) scheme, proposed by M. S. Ivanov and S.V. Rogasinsky are considered. For the high-speed Couette flow with parameters corresponding to a near-continuum regime (speed ratio S is equal to 10, Knudsen number Kn is equal to 0.01) the convergence of shear stress component is analysed. Calculations with different total number of the simulated particles (in the range from 500 to 106) were performed. It was shown, that the deviation of NTC-2007 scheme from the reference solution is about four times larger as compared to the MCF scheme. The original NTC scheme exhibits much higher sensitivity to the number of simulated particles.

Various chemical dissociation reactions models (Total collision energy model – TCE, Quantum Kinetic model – QK and Extended vibrational bias model – EVB) were implemented in the direct simulation Monte Carlo code SMILE++. It was shown that the dissociation models considered predict the same reaction rate over a wide range of temperatures in thermal equilibrium case. The analysis for the nonequilibrium case was carried out on the basis of dissociating nitrogen gas flow modelling around the wedge for the Hornung and Smith experiments conditions. All dissociation models proposed predict various results both in the standoff distance of the bow shock wave and in the temperature values behind it. It was generally shown, that taking into account the vibrational favoring (during dissociation) results in decreasing the reaction rate, which can be manifested in increasing the shock wave standoff distance.

A novel approach to modeling high-temperature nonequilibrium dissociation in air at a level of molecular collisions is proposed. Information on the energy dependence of the specific reaction cross sections, which is necessary for such modeling, is determined numerically from available macroscopic information on the dependence of the reaction rate constant on translational and vibrational temperatures. The results of Direct Simulation Monte Carlo (DSMC) computations show that the proposed model yields a correct reaction rate in vibrational-translational nonequilibrium. The use of the new model in DSMC computations of high-altitude aerothermodynamics results in obtaining a noticeably different flow structure and a higher heat flux, as compared to that predicted by standard DSMC models (such as the total collision energy model).

A state-to-state model for internal energy exchange and molecular dissociation allows for high-fidelity DSMC simulations. Elementary reaction cross sections for the N2 (v, J)+ N system were previously extracted from a quantum-chemical database, originally compiled at NASA Ames Research Center. Due to the high computational cost of simulating the full range of inelastic collision processes (approx. 23 million reactions), a coarse-grain model, called the Uniform RoVibrational Collisional (URVC) bin model can be used instead. This allows to reduce the original 9390 rovibrational levels of N2 to 10 energy bins. In the present work, this reduced model is used to simulate a 2D flow configuration, which more closely reproduces the conditions of high-speed entry into Earth’s atmosphere. For this purpose, the URVC bin model had to be adapted for integration into the “Rarefied Gas Dynamics Analysis System” (RGDAS), a separate high-performance DSMC code capable of handling complex geometries and parallel computation...

Self-consistent interaction of a non-resonant optical lattice with a gas of polarizable particles is considered. We investigate periodic modulations of gas density in the field of high-intensity laser radiation from two opposing sources and potential’s evolution due to intense Bragg reflection. The self-consistent model of laser field and gas interaction is developed and implemented into the SMILE++ software system based on the Direct Simulation Monte Carlo method. We observed noticeable variation of the force acting on the particles in the interaction region, especially in its central part. Taking into account the arising spatial inhomogeneity of the optical potential we demonstrated noticeable effects on the evolution of the self-consistent system if the interaction region has a macroscopic size.

Non-resonant interaction of polarized gas molecules with optical lattices is studied. Transient processes of gas particle optical trapping and wave propagation and refraction are considered, with the impact of gas density inhomogeneity on laser radiation taken into account. The computations are performed using SMILE++ Direct Simulation Monte Carlo code modified to incorporate lattice-gas interaction and a thin layer model. The influence of the size of the interaction region on the evolution of the optical field to steady state is demonstrated for a self-consistent interaction between the optical lattice and the gas. The proposed method will be useful for studying gas - laser field interaction under realistic experimental conditions.Non-resonant interaction of polarized gas molecules with optical lattices is studied. Transient processes of gas particle optical trapping and wave propagation and refraction are considered, with the impact of gas density inhomogeneity on laser radiation taken into account. The computations are performed using SMILE++ Direct Simulation Monte Carlo code modified to incorporate lattice-gas interaction and a thin layer model. The influence of the size of the interaction region on the evolution of the optical field to steady state is demonstrated for a self-consistent interaction between the optical lattice and the gas. The proposed method will be useful for studying gas - laser field interaction under realistic experimental conditions.

This paper studies the applicability of various versions of the regularized 13-moment system (R13) as applied to the problem of the shock wave structure in a monatomic Maxwell gas in a wide range of Mach numbers (1.0

This work is aimed at the development of surface chemistry models for the Direct Simulation Monte Carlo (DSMC) method applicable to non-equilibrium high-temperature flows about reentry vehicles. Probabilities of the surface processes dependent on individual properties of each particular molecule are determined from the macroscopic reaction rate data. Two different macroscopic finite rate sets are used for construction of DSMC surface recombination models. The models are implemented in the SMILE++ software system for DSMC computations. A comparison with available experimental data is performed. Effects of surface recombination on the aerothermodynamics of a blunt body at high-altitude reentry conditions are numerically studied with the DSMC method.

The mechanism of internal energy exchange in CO2 including vibration-translation and different types of vibration-vibration exchange applicable for DSMC calculations is proposed. The microscopic probabilities of internal energy exchange processes transitions are obtained in the analytical form on the basis of known reaction rate coefficients using the inverse Laplace transform.

The entry of a shock wave with the Mach number Mis = 2.03 into a microchannel and its further propagation is numerically studied with the use of kinetic and continuum approaches. Numerical simulations on the basis of the Navier — Stokes equations and the Direct Simulation Monte Carlo method are performed for different Knudsen numbers Kn = 8·10−3 and 8·10−2 based on the microchannel half-height. At the Knudsen number Kn = 8·10−3, amplification of the shock wave after its entry into the microchannel is observed. Further downstream, the shock wave is attenuated, which is in qualitative agreement with experimental data. It is demonstrated that results predicted by a quasi-one-dimensional model (which ignores viscosity and heat conduction) of shock wave propagation over a channel with an abrupt change in the area agrees with results of numerical simulations on the basis of the Euler equations. In both cases, shock wave acceleration (amplification) after its entry into the microchannel is observed. At the Knudsen number Kn = 8·10−2, the influence of the entrance shape on shock wave propagation over the microchannel is examined. Intense attenuation of the shock wave is observed in three cases: channel with sudden contraction, junction of two channels with an additional thin separating plate, and rounded junction in the form of a sector with an angle of 90° (quarter of a circumference). It is shown that the microchannel entrance shape can affect further propagation of the shock wave. The wave has the highest velocity in the case with a rounded entrance.

The rarefaction effects in the problem of hypersonic flow around a profile with blunted leading edge are studied in the flow regimes when the edge bluntness radius is comparable with the mean free path in the free stream. The flow around a cylindrically blunted thick plate at zero incidence was modelled numerically in the transitional regime by using the direct simulation Monte Carlo method, the finite-difference solution of the kinetic equation of the relaxation type (the ellipsoidal statistical model), and the solution of the Navier — Stokes equations. It is shown that for the Knudsen numbers in terms of the bluntness radius below 0.1, the Navier — Stokes equations can be applied successfully for viscous flow description behind the shock wave provided that the initial rarefaction effects are taken into account via the slip and temperature jump boundary conditions on the plate surface. For Knudsen number of about 0.5, the rarefaction effects are more appreciable; in particular, a substantial anisotropy of the distribution function takes place, but the Navier — Stokes equations yield, as before, a qualitatively correct result. The initial stage of the boundary layer development in the edge vicinity has been studied. In the considered range of Knudsen numbers, the entropy layer near the edge is comparable with the boundary layer thickness. As the distance from the leading edge increases one observes the absorption of the entropy layer by the boundary layer. In the studied parameter range, the interaction between the boundary and entropy layers leads to a flow stability increase.

The applicability of a new model in terms of the description of real gas effects in the Direct Simulation Monte Carlo method is analysed. The model is used in a numerical study of the internal structure of the front of a strong shock wave and relaxation zone behind the front for conditions corresponding to spacecraft entry into the Martian atmosphere. The influence of the free-stream parameters on relaxation of various energy modes of molecules in the wave front and in the relaxation region is considered. The effect of chemical reactions on the flow structure is studied. A detailed analysis of flow nonequilibrium is performed at the level of the velocity distribution function and population of rotational and vibrational levels of molecules.

Various versions of the regularized 13-moment system (R13) are applied to the problem of the shock wave structure in a monatomic Maxwell gas for Mach numbers up to M = 10. Numerical solutions are compared to direct simulation Monte Carlo results computed by the SMILE++ software system, in order to identify applicability and limitations of the variants. Over time, several versions of the R13 equations were presented, which differ in non-linear contributions for high-order moments but agree in asymptotic expansion to the third order in the Knudsen number. All variants describe typical subsonic microflows well, for which the non-linear contributions only play a minor role. The challenge of the present study is to determine the real boundaries of applicability of each variant of the moment equations as applied to non-equilibrium supersonic flows, depending on the Mach number and local Knudsen number.

This work is aimed at development of detailed molecular surface chemistry models for DSMC method, their implementation into the SMILE++ software system, verification and validation. An approach to construction of DSMC suface chemistry models based on macroscopic reaction rate data was proposed. The approach was applied to macroscopic data for the air mixture of Deutschmann et al. The resulting DSMC surface chemistry model was implemented into SMILE++ software system and verified for thermal equilibrium conditions.

The effects of viscosity and heat conduction, heat losses due to the wall heat transfer, as well as nonequilibrium phenomena can play an important role in microflows. Recent numerical investigations [1] of shock wave propagation in a microchannel with allowance for viscosity and rarefaction effects revealed significant differences from the inviscid theory, which ensures a correct description of the majority of specific features of macroflows. In that work, the shock wave was generated by breakdown of a diaphragm separating high-pressure and low-pressure domains.

This study is devoted to the analysis of applicability of moment equations to the shock wave structure problem in a wide range of Mach numbers. A modification of original Grad's 13-moment set of equations, so-called regularized Grad's set of equations (R13), is taken as a mathematical model. The numerical method for this set is formulated as a variant of the explicit high-order Godunov scheme with linear reconstruction of flow parameters. The degree of applicability of moment equations is determined by comparisons with Direct Simulation Monte Carlo (DSMC) predictions. Numerical results for hard sphere molecules show that the R13 set of equations describes well the internal structure of the shock wave in a wide range of Mach numbers. Nevertheless, R13 set significantly overpredicts the overall temperature overshoot (about 3 times for M=8), which is apparently related to nonlinearity of the dependence of the product of the transverse temperature component and density on normalized density.

Owing to their high lift-to-drag ratio, space and hypersonic flying vehicles with slightly blunted leading edges offer a large lateral range, which substantially expands their capabilities as promising transportation systems. A specific feature of high-velocity flows around leading edges of small bluntness is significant influence of rarefaction, even on those segments of the flight trajectory where the vehicle as a whole is in a continuum flow. As it is rather difficult to model such flows experimentally, an urgent task is to develop effective numerical methods for calculating high-velocity flows in the vicinity of slightly blunted leading edges.

The problem of the detonation-wave front structure can be considered as an object to be studied within the kinetic theory of gases by analogy with the classical problem of the shock-wave structure [1]. The molecular kinetic description of the gas based on the solution of the Boltzmann kinetic equation is usually used for flows of a rather dilute gas, in particular, in problems of high-altitude aerothermodynamics of space vehicles and vacuum gas dynamics, though it is also applicable for values of pressure typical for detonation processes (close to ground-level atmospheric pressure). The most effective numerical method for solving the Boltzmann equation is currently the Direct Simulation Monte Carlo (DSMC) method [2].

Entry of a shock wave into a microchannel and its propagation in the channel are studied numerically by the continuum and kinetic approaches. It is shown that the shock wave is amplified immediately after it enters the microchannel. After that, the shock wave in an inviscid computation propagates over the microchannel with a constant velocity. In a viscous computation, the shock wave velocity decreases and the wave attenuates. Qualitative agreement between experimental data and viscous computations is demonstrated.

The supersonic flow past a finite flat plate at zero angle of attack is considered. The Navier‐Stokes equations, Direct Simulation Monte Carlo (DSMC) statistical method and deterministic solving relaxation‐type model kinetic equations using a high‐order shock capturing scheme are used for numerical simulation of the problem. The results obtained with different approaches are compared and analyzed. The limits of continuum approach applicability as well as the accuracy of description based on model kinetic equations are studied.

The viscosity effects on strong and weak shock wave reflection are investigated with the Navier‐Stokes and DSMC flow solvers. It is shown that the viscosity plays a crucial role in the vicinity of three‐shock intersection. Instead of a singular triple point, in viscous flow there is a smooth three shock transition zone, where one‐dimensional shock jump relations cannot be applied. At the flow parameters corresponding to the von Neumann reflection, when no inviscid three‐shock solution exists, the computations predict an irregular shock‐wave configuration similar to that observed previously in experiments. The existence of a viscous zone in the region of shock‐wave interaction allows a continuous transition from the parameters behind the Mach stem to the parameters behind the reflected shock, which is impossible in the inviscid three‐shock theory.

The paper describes a new effective software system SMILE++ for comprehensive studying of rarefied gas flows by the DSMC method. The system design is based on the principles of Object‐Oriented Programming, which makes it readily modifiable in order to add new capabilities. Examples of SMILE++ application to various problems of rarefied gas dynamics are presented.

The simulation of stationary plasma thruster plume is important for spacecraft design due to possible interaction plume with spacecraft surface. Such simulations are successfully performed using the particle‐in‐cell technique for describing the motion of charged particles, namely the propellant ions. In conventional plume models the electrons are treated using various fluid approaches. In this work, we suggest an alternative approach, where the electron kinetics is considered ‘ab initio’, using the particle‐in‐cell—Monte Carlo collision method. To avoid the large computational expenses due to small time steps, the relaxation of simulated plume plasma is split into the fast relaxation of the electrons distribution function and the slow one of the ions. The model is self‐consistent but hybrid, since the simultaneous electron and ion motion is not really modeled. The obtained electron temperature profile is in good agreement with experiment.

Numerical simulations of shock wave propagation in microchannels and microtubes (viscous shock tube problem) have been performed using three different approaches: the Navier‐Stokes equations with the velocity slip and temperature jump boundary conditions, the statistical Direct Simulation Monte Carlo method for the Boltzmann equation, and the model kinetic Bhatnagar‐Gross‐Krook equation with the Shakhov equilibrium distribution function. Effects of flow rarefaction and dissipation are investigated and the results obtained with different approaches are compared. A parametric study of the problem for different Knudsen numbers and initial shock strengths is carried out using the Navier‐Stokes computations.

Larsen‐Borgnakke model, widely used in the DSMC method to simulate rotation‐translation and vibration‐translation exchanges in molecular collisions, is applied for the first time to resonant exchange between the vibrational modes of diatomic molecules (VV exchange). The validation of the model is performed through comparisons with experimental data on VV exchange in nitrogen.

In this work, we continue to study the possibility of applying moment equations for strongly nonequilibrium flows by an example of the problem of the shock wave structure in a monatomic gas in a wide range of Mach numbers for various models of molecular interaction. The object of the study is the so-called regularized 13-moment Grad’s system (R13). First time, both linear and nonlinear versions of this system of equations were considered for the problem at such wide range of parameters. The Godunov method with increased accuracy is used as a numerical tool for solving the R13 system. The numerical results for the R13 system are analyzed by using data obtained by the Direct Simulation Monte Carlo (DSMC) method, experimental data, and analytical results. As a whole, the R13 system provides an adequate description of the shock wave structure in a wide range of Mach numbers. For Mach numbers around 2, good agreement with experimental and DSMC results is observed for both linear and nonlinear versions of the system. For high Mach numbers, the result strongly depends on the molecular interaction model used: shock wave structure predictions of the nonlinear R13 system are better for Maxwell molecules and worse for hard spheres as compared to the linear version. Particular attention in this work is paid to studying nonmonotonicity of the total temperature profile (temperature overshoot) in the structure of a strong shock wave. It is shown that the moment equations correctly predict the existence of the temperature overshoot. At the same time, the solution of the moment equations overpredicts the temperature overshoot at least two-fold for Mach number M = 8, and the nonlinear version of the R13 system yields a better result for this parameter than the linear version.

Recently a new class of schemes, called Time Relaxed Monte Carlo (TRMC) has been introduced for the numerical solution of the Boltzmann equation of gas dynamics. The motivation is to propose a systematic framework to derive Monte Carlo methods effective near the fluid dynamic regime. Before the methods can be accepted as alternative tools to other methods, they have to show that they are able to reproduce results obtainable by well established reliable methods. In this paper a detailed comparison is performed between TRMC methods and the Majorant Frequency Scheme in the case of the space‐homogeneous Boltzmann equation. In particular, the effect of finite number of particles is considered.

The DSMC method is currently one of the main tools for studying the hypersonic chemically reacting rarefied flows. New models of the DSMC method are permanently developed for a more detailed description of physical and chemical processes in gases. Their implementation into the existing DSMC codes, however, is rather difficult. The promising way of overcoming these difficulties is to develop object‐oriented DSMC codes that can be readily modified to include the new models. The present paper deals with the development of the structure of objects of a new object‐oriented DSMC code including a database of physicochemical properties of gases.

By the example of one‐dimensional problems of heat transfer and Couette flow, the influence of the statistical dependence between the simulated molecules on the deviation of the numerical solution obtained by the Direct Simulation Monte Carlo method from the solution of the Boltzmann equation is considered. The fraction of repeated collisions is used as the measure of the statistical dependence. The relation between the statistical dependence and the deviation of the numerical solution caused by a finite number of simulated molecules and by spatial and temporal discretization is examined.

A new class of schemes of the DSMC type for computing near‐continuum flows has been recently suggested: the time‐relaxed Monte Carlo (TRMC) methods. An important step preceding the wide use of these schemes is their validation by classical homogeneous and one‐dimensional problems of gas dynamics. For this purpose, a plane Couette flow is considered in the present paper. A comparison of TRMC results with the data obtained by time‐proved schemes of the DSMC method (here we used the Majorant Frequency Scheme) in a wide range of Knudsen numbers and for different values of wall velocity is presented.

The applicability analysis of DSMC models of real gas effects, namely, translational‐internal energy transfer and chemical reactions, is performed. Three models are considered: conventional Larsen‐Borgnakke/Total Collision Energy model for continuous internal energies, modified Larsen‐Borgnakke/Total Collision Energy model for discrete internal energies, and new vibrationally favored model for discrete internal energies, which is proposed in the present paper. The detailed comparison of the DSMC results, obtained using all the three models, with the Jeans, Landau‐Teller and Arrhenius rates is given for diatomic and polyatomic molecules.

Hypersonic chemically reacting flow around a wedge in the near‐continuum regime was numerically studied by the DSMC method with the main goal of validation of real gas effect models. The influence of vibration‐dissociation coupling on the results of numerical simulations was analyzed. To this end, two models of chemical reactions were used in the computations, the total collisional energy model and a vibrationally favored model. The numerical results were compared with the experimental data of Hornung and Smith on the shock‐wave stand‐off distance in a hypersonic flow around the wedge. Sensitivity of simulation results to chemical reaction rate constants was also estimated.

The flow structure along the stagnation line for a blunted body descending in the Martian atmosphere was simulated by the DSMC method for Knudsen numbers ranging from 10−2 to 10−3. Along with the conventional continuous approach for translational‐internal energy transfer and chemical reactions, the new discrete internal energy model with corrected reaction rates was used in the computations. The impact of chemical reactions on the structure of the shock‐wave front was examined. The nonequilibrium inside the bow shock was studied both in terms of macroparameters and distribution functions of translational, rotational, and vibrational energy modes. It is shown that vibrational relaxation and chemical reactions have a significant effect on the structure of the shock‐wave front.

A combined particle method was applied to simulate numerically the ATON Hall‐effect thruster plume. This method employs the Particle‐in‐Cell / Monte Carlo collisions technique for modeling the plume ions and the Direct Simulation Monte Carlo method for modeling the neutral species. ATON thruster plume expansion into the vacuum chamber was simulated, and a comparison with experimental data was performed. The back‐pressure effects of the facility were assessed using two different methods of modeling plume‐background interactions. The importance of accurate modeling of this interactions was demonstrated through a comparison with total ion current measurements. ATON thruster plume expansion under space vacuum conditions was also simulated, and the structure of slow ion back flow was studied.