Benchmarking, development and applications of an open source DSMC solver

Several important engineering gas flow problems fall within the transition Knudsen number regime, e.g. re-entry of spacecraft, or gas flows in micro-scale geometries. The transition regime remains the most difficult to obtain reliable analytical or numerical results for, but the most successful method has been the direct simulation Monte Carlo (DSMC) numerical technique. Due to the nature of high temperature, hypersonic flows, and equipment limitations at the micro-scale, there is a scarcity of reliable experimental data for transition regime flows; numerical experiments using DSMC are an essential tool for the design of engineering systems that encounter these kinds of flows. We benchmark a recently developed open-source DSMC solver against existing DSMC solvers, analytical solutions, and experimental data. The solver is then extended to include some important features that enable it to be applied to a larger range of engineering problems. Vibrational energy and the quantum-kinetic chemical reaction model are implemented in our DSMC solver, preparing it for use with hypersonic flow problems with shockwaves and local regions of very high temperature. Low speed fixed pressure boundary conditions are also implemented, for use with simulations of gas flows in micro-channels. The extended solver is then used to investigate two different engineering problems. Firstly, simulations of gas flows in micro-channels with bends are performed. We find that the inclusion of a sharp ninety degree bend does not lead to significant losses, and can even lead to a small increase in mass flow rate within a limited range of Knudsen number. Adding a second bend is found to increase this mass flow rate enhancement. Finally, we investigate rarefied gas effects on high area-to-mass ratio spacecraft in low Earth orbit, taking inspiration from the Crookes radiometer. We find that the ii non-equilibrium gas effects can be exploited for use as propellant-free inter-spacecraft position control within a swarm, by altering the temperature of one spacecraft relative to another. A small degree of attitude control can be exercised in a similar manner, through non-uniform heating of an individual spacecraft.Several important engineering gas flow problems fall within the transition Knudsen number regime, e.g. re-entry of spacecraft, or gas flows in micro-scale geometries. The transition regime remains the most difficult to obtain reliable analytical or numerical results for, but the most successful method has been the direct simulation Monte Carlo (DSMC) numerical technique. Due to the nature of high temperature, hypersonic flows, and equipment limitations at the micro-scale, there is a scarcity of reliable experimental data for transition regime flows; numerical experiments using DSMC are an essential tool for the design of engineering systems that encounter these kinds of flows. We benchmark a recently developed open-source DSMC solver against existing DSMC solvers, analytical solutions, and experimental data. The solver is then extended to include some important features that enable it to be applied to a larger range of engineering problems. Vibrational energy and the quantum-kinetic chemical reaction model are implemented in our DSMC solver, preparing it for use with hypersonic flow problems with shockwaves and local regions of very high temperature. Low speed fixed pressure boundary conditions are also implemented, for use with simulations of gas flows in micro-channels. The extended solver is then used to investigate two different engineering problems. Firstly, simulations of gas flows in micro-channels with bends are performed. We find that the inclusion of a sharp ninety degree bend does not lead to significant losses, and can even lead to a small increase in mass flow rate within a limited range of Knudsen number. Adding a second bend is found to increase this mass flow rate enhancement. Finally, we investigate rarefied gas effects on high area-to-mass ratio spacecraft in low Earth orbit, taking inspiration from the Crookes radiometer. We find that the ii non-equilibrium gas effects can be exploited for use as propellant-free inter-spacecraft position control within a swarm, by altering the temperature of one spacecraft relative to another. A small degree of attitude control can be exercised in a similar manner, through non-uniform heating of an individual spacecraft

Coupling of state-resolved rovibrational coarse-grain model for nitrogen to stochastic particle method for simulating internal energy excitation and dissociation

We propose to couple a state-resolved rovibrational coarse-grain model to a stochastic particle method for simulating internal energy excitation and dissociation of a molecular gas. An existing coarse-grain model based on the NASA Ames ab initio database for the N2-N system is modified using variably-spaced energy bins. Thermodynamic properties of the new coarse-grained model closely match those of the full set of rovibrational levels over a wide temperature range, using a number of bins much smaller than the complete mechanism. The chemical-kinetic behavior of the original equally -- and new variably -- spaced bin formulations is compared by simulating excitation and dissociation of N2 in an adiabatic, isochoric reactor. The variably-spaced formulation is better suited for reproducing the dynamics of the full database at conditions of interest in Earth reentry. Furthermore, we discuss details of our Direct Simulation Monte Carlo (DSMC) implementation for the coarse-grain model and describe changes to the collision algorithm necessary to accommodate our state-resolved reaction mechanism. The DSMC code is then verified against equivalent master equation (ME) calculations. In these simulations, state-resolved cross sections are used in analytical form. They verify micro-reversibility for the bins and allow for faster execution of the code. In our verification, we obtain very close agreement for the N and N2 concentrations, as well as the translational and rovibrational mode temperatures obtained independently using both methods. In addition to macroscopic moments, we compare internal energy populations predicted at selected time steps via DSMC and ME. We observe good agreement between both methods within the statistical scatter limits imposed by DSMC. In future work, the rovibrational coarse-grain model coupled to the particle method will allow us to study 3D reentry flow configurations.Comment: 40 pages, 19 figure

Investigation of volume diffusion hydrodynamics : application to tight porous media

Various engineering problems imply rarefied gas flows that rely in the transition and free molecular regimes, e.g., micro and nano devices. The recent expansion of shale gas production where rarefied conditions are found in reservoirs exposed another area of application with a major importance. Continuum based methods like standard Navier- Stokes equations break down in the transition regime and free molecular regime. In order to model such flows discrete methods are usually adopted. Boltzmann equation can theoretically be used to simulate rarefied gas flows. However, complexity of its collision integral limits its applications mostly to simple cases (i.e., one dimension problems). The direct simulation Monte Carlo method which mimics the Boltzmann equation is the dominant method for simulating rarefied gas flows. It has been tested in several engineering problems, ranging from nano scale flow to re-entry vehicles with very consistent results in comparison with experimental data and analytical solutions. Its computational cost is, however, enormous for complex cases. Observations from Crookes radiometer inspired extending the continuum methods so that they could capture non-equilibrium phenomena in small scales. In the present thesis two different hydrodynamic model are presented. The first one is based on the Korteweg expression and the second one is called “Bi-velocity”. Firstly, the two models are presented in their mathematical forms. The proposed models are then developed in open-source computational fluid dynamics solvers. The models are tested and benchmarked in different rarefied gas flows problems in the whole range of Knudsen number. We used problems that are found in micro and nano systems and tight porous media. Results from the hydrodynamic models are compared against experimental data where available and the direct simulation Monte Carlo method. The two extended hydrodynamic models show improved results in comparison with standard Navier-Stokes

Investigation of flow-flow, flow-surface, and multiphase interaction problems in rarefied gas dynamics

Presently, with the development of technology, the need to study and understand high-speed rarefied gas flows has become an impending reality in terms of its potential assets to a wide spectrum of industries, ranging from interplanetary travel to coating technology. This study addresses the interactions of high-speed rariefied gas flows with one another, surfaces, and solid particles in order to ascertain high-speed rarefied gas behaviours in various applications. Three different interaction scenarios -two of which rely on numerical analysis and one which is based on the development of a novel solver- are investigated, where computations are conducted with a direct simulation Monte Carlo (DSMC) solver, dsmcFoam+, and a particle laden rarefied gas multiphase flow solver, rarefiedMultiphaseFoam, within the framework of an open-source tool, OpenFOAM. Rarefied shock-shock interactions have a crucial impact on aerodynamic performance and aero-heating characteristics in supersonic and hypersonic flight platforms. A shock-shock interaction problem can arise in high-speed vehicles, where an oblique shock on one part of the body impinges on a bow shock from a different part of the body and the nature of the interaction can change as the vehicle increases in altitude to a more rarefied environment. Part of this research examines the outcomes of a numerical study investigating the formation of Edney shock patterns from type-I to type-VI as a result of shock-shock interactions at different rarefaction levels. The free-stream flow is at a Mach number of 10. Both geometrical and rarefaction parameters in shock-shock interaction problems determine what type of Edney pattern is formed. As the flow becomes more rarefied, the regions of enhanced thermo mechanical loading spread further over the surface but their peak values decrease. It is known that these shock interactions can have unsteady behaviour in the continuum regime; current works show that although increasing rarefaction tends to move the flow towards steady behaviour, it still possible to have unsteady flow behaviour under more rarefied conditions. In another case, the interactions of high-speed rarefied flows with one another and a surface are analysed. The canting axis of thrusters on space platforms, which likely operate in a vacuum environment with a high degree of flow rarefaction, is significant in order to create the desired torque for manoeuvring, maintaining orbit, eliminating perturbation forces, docking, etc. Therefore, the interactions of expanding plumes with one another and with solid surfaces in multi-nozzle arrays are inevitable. In order to gain a better understanding of the effect of nozzle configurations and conditions on the plume-plume and plume-surface interactions, a simulation matrix is carried out for a sonic nozzle. As nozzle arrays are packed more tightly together, the plume-plume interactions become stronger, which has an influence on the stagnation line density and temperature profiles. For a given stagnation temperature, the spacing between nozzles in the array does not have a strong influence on the normalised surface pressure, but there is an increase in the maximum normalised shear stress as the distance between the nozzles increases. There is a significant difference in the results for double and quadruple nozzle arrays, with greater normalised stagnation pressures and shear stresses found as the number of nozzles in the array is increased. For a single nozzle, increasing the stagnation temperature does not have a significant effect on the normalised surface pressures, but does increase the maximum normalised shear stress and the measured heat flux on the surface. For arrays of double and quadruple nozzles, the number of nozzles has a much greater influence on the measured surface pressure, surface shear stress, and surface heat transfer than the stagnation temperature. In the last case, the effect of the impingement height on the plume and surface parameters is discussed while maintaining all the parameters of the 1000 K single plume case but with varying impingement heights. It is found that the smaller impingement height results in a denser plume, and a greater impact on the surface. However, higher impingement heights result in a wider distribution on the surface as the plume can expand more. With the awareness of a lack of a solver for rarefied gas flows-solid particle interactions, the final case in this thesis focuses on the development, benchmarking and testing of a multiphase open-source code, rarefiedMultiphaseFoam. Such a solver provides applicable benefits such as modelling of the transport of unburnt solid propellant in rocket a plume, and simulating of the impingement of two-phase plume on a surface in a vacuum environment, as well as providing numerical solutions in terms of surface coating technology, where multiphase gas and solid flows are employed, etc. This dsmcFoam+ based solver is capable of simulating one-way coupling interactions. This type of particle-laden rarefied gas flow has two components: the rarefied gas flow itself and the solid particles transported by the gas flow. The main restriction is that the solid phase surrounded by the gas phase is assumed to be in the free-molecular regime with respect to the solid particle diameters and that it is a one-way coupling, so that only the effect of gas particles on the solid particles is considered. rarefiedMultiphaseFoam can produce results for steady and transient one-way coupling problems in zero-dimensional (0D), one-dimesion (1D), two-dimensions (2D) (both planar and maxisymmetric), and three-dimensions (3D). Two benchmarking cases on momentum and energy transfer from gas molecules to solid particles, and free expansion of a two-phase jet flow are presented. The reliability of the solver is further demonstrated through a test case on surface coating using the Aerosol Deposition Method. The benchmarking cases yield results that are in good agreement with theoretical, experimental, and numerical data in the literature

A hybrid Gaussian mixture/DSMC approach to study the Fourier thermal problem

In rarefied gas dynamics scattering kernels deserve special attention since they contain all the essential information about the effects of physical and chemical properties of the gas–solid surface interface on the gas scattering process. However, to study the impact of the gas–surface interactions on the large-scale behavior of fluid flows, these scattering kernels need to be integrated in larger-scale models like Direct Simulation Monte Carlo (DSMC). In this work, the Gaussian mixture (GM) model, an unsupervised machine learning approach, is utilized to establish a scattering kernel for monoatomic (Ar) and diatomic (H2) gases directly from Molecular Dynamics (MD) simulations data. The GM scattering kernel is coupled to a pure DSMC solver to study isothermal and non-isothermal rarefied gas flows in a system with two parallel walls. To fully examine the coupling mechanism between the GM scattering kernel and the DSMC approach, a one-to-one correspondence between MD and DSMC particles is considered here. Benchmarked by MD results, the performance of the GM-DSMC is assessed against the Cercignani–Lampis–Lord (CLL) kernel incorporated into DSMC simulation (CLL-DSMC). The comparison of various physical and stochastic parameters shows the better performance of the GM-DSMC approach. Especially for the diatomic system, the GM-DSMC outperforms the CLL-DSMC approach. The fundamental superiority of the GM-DSMC approach confirms its potential as a multi-scale simulation approach for accurately measuring flow field properties in systems with highly nonequilibrium conditions.</p

Study of supersonic nozzle flows in low-pressure environments: starting jets and lunar plume-surface interactions

Supersonic nozzle flows play an important role in aerospace engineering, e.g. controlling motions, attitudes, and orbits of space vehicles using various propulsion systems. Supersonic nozzle flows include free nozzle flows and restricted nozzle flows, such as plume-surface interactions if a surface obstructs the flow propagation. When compressed gas is discharged from a nozzle into a low-pressure environment in the case of free nozzle flows, the shock wave diffracts around the nozzle lip and a vortex loop forms. These phenomena have attracted much attention in the continuum flow regime, but how the shock diffraction and vortex behave under rarefied flow conditions has received less attention. Understanding transient flow in rarefied conditions is helpful for increasing thrust vector control and avoiding potential contamination and erosion of spacecraft surfaces. Furthermore, comprehending plume-surface interactions is critical for the design of lander modules and future bases on bodies such as the moon, as it is necessary to anticipate surface erosion patterns and the transport of displaced regolith material. Extraterrestrial conditions are difficult to recreate experimentally (e.g. the effects of low gravity, strong radiation and extreme temperature difference). Available numerical techniques for modelling regolith entrainment and subsequent movement suffer from limited accessibility and different levels of sophistication. In this thesis, a design for an open-ended shock tube connected to a vacuum chamber is presented. This is used to release a shockwave into a low-pressure environment and study the subsequent vortex ring formation as the gas diffracts around the shocktube exit. Schlieren visualisation and pressure measurements of the vortex ring formation are conducted. The flow structure degenerates through a decrease in the strength of the embedded shock waves and an increase in their thickness, and the counter-rotating vortex ring when the environmental pressure decreases. The existence of the vortex ring is confirmed through spectral analysis when the environmental pressure is as low as 1.0kPa. Due to limitations with experimental measurement equipment and techniques, the shock wave diffraction problem should be complemented with numerical techniques. A program to generate ensemble-averaged direct simulation Monte Carlo (DSMC) results is designed. Computational fluid dynamics (CFD) and ensemble-averaged DSMC methods are implemented to simulate the formation of a two-dimensional vortex loop due to shock wave diffraction around a 90◦ corner. The influence of the Mach number and rarefaction on the development and growth of the vortex loop are studied. A concept, called rorticity, was used to investigate the transient structures of vortex loops. The simplification of the internal structure of vortex loops and postponement of the vortex loop formation due to the increase of the rarefaction level are confirmed. Two properties from the decomposition equation of vorticity to quantify the vortex strength; rorticity flux (i.e. representing the vortex rotational strength), and the shear vector flux (i.e. representing the vortex shear movement strength), are derived. A mutual transformation relationship between the rorticity and shear vectors has been identified, suggesting that this concept can be employed to better explain vortex flow phenomena. It is found that the increase of the Knudsen number thickens the Knudsen layer, causing the failure of the generation of the vortex sheet and the subsequent formation of vortex loops. A new solver based on dsmcFoamPlus – rarefiedMultiphaseFoam, is developed for solving rarefied multiphase flows. The solver is extended to include a two-way coupling model and a particle phase change model. Additionally, the solid stochastic collison model and the multiphase nparticle-in-cell (MPPIC) method for solving dilute and dense granular flows, respectively, have been implemented in the new solver. The models mentioned are rigorously benchmarked against analytical solutions and previous results in the literature. The benchmarking results of the two-way coupling method show excellent agreement with analytical results. The results of a reproduced uniform gas-solid flow and a purely gravity-controlled granular flow sedimentation agree well with previous numerical results in the literature. A solid particle is allowed to experience a physical and continuous phase change and diameter variation using the updated phase change model. Finally, the rarefiedMultiphaseFoam solver is used to simulate two lunar plume-surface interaction (PSI) cases using the stochastic collision model and the MPPIC method, respectively. Both methods are applied to a scaled down version of the Apollo era lunar module descent engine and comparisons are made between the two simulation results. The results show that the transient effects are essential to both the gas and solid phase evolution and the entrained dust particles significantly influence the evolution of the gas flow. In the PSI simulations, the MPPIC method is more reliable than the stochastic collision method because it takes enduring contacts and the close-packing limit into account. Furthermore, it is identified that the breakdown of the locally free-molecular flow assumption has a significant impact on the solid particle temperatures

uniGasFoam: a particle-based OpenFOAM solver for multiscale rarefied gas flows

This paper presents uniGasFoam, an open-source particle-based solver for multiscale rarefied gas flow simulations, which has been developed within the well-established OpenFOAM framework, and is an extension of the direct simulation Monte Carlo (DSMC) solver dsmcFoam+. The developed solver addresses the coupling challenges inherent in hybrid continuum-particle methods, originating from the disparate nature of finite-volume (FV) solvers found in computational fluid dynamics (CFD) software and DSMC particle solvers. This is achieved by employing alternative stochastic particle methods, resembling DSMC, to tackle the continuum limit. The uniGasFoam particle-particle coupling produces a numerical implementation that is simpler and more robust, faster in many steady-state flows, and more scalable for transient flows compared to conventional continuum-particle coupling. The presented framework is unified and generic, and can couple DSMC with stochastic particle (SP) and unified stochastic particle (USP) methods, or be employed for pure DSMC, SP, and USP gas simulations. To enhance user experience, reduce required computational resources and minimise user error, advanced adaptive algorithms such as transient adaptive sub-cells, non-uniform cell weighting, and adaptive global time stepping have been integrated into uniGasFoam. In this paper, the hybrid USP-DSMC module of uniGasFoam is rigorously validated through multiple benchmark cases, consistently showing excellent agreement with pure DSMC, hybrid CFD-DSMC, and literature results. Notably, uniGasFoam achieves significant computational gains compared to pure dsmcFoam+ simulations, rendering it a robust computational tool well-suited for addressing multiscale rarefied gas flows of engineering importance

A Two-dimensional Hybrid-Direct Kinetic Model of a Hall Thruster

The goal of this dissertation is to improve the state-of-the art modeling approaches available for simulating the discharge plasma in a Hall effect thruster (HET). A HET is a space propulsion device that utilizes electrical energy to ionize and accelerate propellant, generating thrust. The device features a cross-field configuration, whereby the transverse magnetic field traps electrons, and the axial electric field electrostatically accelerates ions out of the thruster channel. This configuration enables desirable thruster performance characteristics typically characterized by a relatively high specific impulse (1000-3000 s) and a high thrust density (a few Newtons per square meter). High fidelity computational models are useful to investigate the physical processes that govern the HET's performance, efficiency, and lifetime limitations. The non-equilibrium nature of the plasma transport should be resolved so that the flow can be accurately characterized. A grid-based direct kinetic (DK) simulation is capable of modeling the non-equilibrium state of plasma without the numerical noise that is inherent to particle-based methods since the velocity distribution functions (VDFs) are obtained in a deterministic manner. As the primary objective of this work, a two-dimensional, hybrid-DK simulation of the discharge plasma in a HET is developed. As a secondary objective, a plasma sheath, one of the important physical structures that form in the discharge plasma of a HET near the channel walls, is examined via a two-dimensional full DK simulation that highlights slight spatial differences in the sheath as a result of electrically disparate, adjacent wall materials. The memory storage requirements and computational load for the parallelized DK simulation grow with additional species, physical space dimensions, and velocity space dimensions. Some of these numerical limitations are encountered within this work. The hybrid-DK HET model utilizes a quasi-one-dimensional fluid electron algorithm in conjunction with a two-dimensional DK method to simulate the motion of neutral atoms and ions in a HET channel and near-field plume. Upon its development, the hybrid-DK simulation is benchmarked against results obtained from a two-dimensional hybrid-particle-in-cell (PIC) simulation with an identical fluid electron algorithm. To achieve agreement between the simulation results, a boundary condition for the DK model that satisfies particle conservation at the wall boundaries is developed, and electron model boundary conditions that provide solution stability are sought and utilized. For both high-frequency and low-frequency oscillations, the two simulations show good agreement for both time-averaged and dynamic plasma properties. Statistical noise tends to randomize plasma oscillations in the PIC simulation results, whereas the DK results exhibit coherent oscillatory behavior. Furthermore, results indicate that the DK simulation is capable of responding to small changes in electron dynamics, which is promising for future work. The DK plasma sheath simulation models a two-dimensional plasma sheath that highlights slight spatial differences inside the sheath as a result of electrically disparate, adjacent materials. To accomplish this goal, a quasi-one-dimensional sheath model is first built in a two-dimensional framework, boundary conditions are developed, and results are verified against theoretical expectations. Then, the full two-dimensional plasma sheath is modeled. The proof-of-concept model shows that two-dimensional effects are present in the vicinity of the discontinuous plasma potential at the wall, and electron and ion VDFs both clearly exhibit changes due to these effects.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/162983/1/astridr_1.pd

Open Source Toolkit for Reentry Object Modeling

Predicting the mass, position, and velocity of an object during its reentry are critical to satisfy NASA and ESA requirements. This thesis outlines a 3-D orbit and mass determination system for use on low earth orbit as applicable to general objects, of various material and size. The solution uses analytical models to calculate heat flux and aerodynamic drag, with some basic numerical models for simple orbit propagation and mass flow rate due to ablation. The system outlined in this thesis currently provides a framework for rough estimates of demise altitude and final mass, but also allows for many potential accuracy and speed improvements. 77 aerospace materials were tested, in solid spheres, cubes, and cylinders; it was found that materials with low latent heat of fusion (less than 10 kJ/kgK) demise before reaching the ground, while materials with higher melting point temperatures (over 1200K), high specific heats, and high latent heat of fusion (over 30 kJ/kgK) lose small amounts of mass before hitting the ground at speeds of 200-300m/s . The results of this thesis code are validated against NASA\u27s Debris Assessment System (DAS), specifically the test cases of Acrylic, Molybdenum, and Silver

On the connection of probabilistic model checking, planning, and learning for system verification

This thesis presents approaches using techniques from the model checking, planning, and learning community to make systems more reliable and perspicuous. First, two heuristic search and dynamic programming algorithms are adapted to be able to check extremal reachability probabilities, expected accumulated rewards, and their bounded versions, on general Markov decision processes (MDPs). Thereby, the problem space originally solvable by these algorithms is enlarged considerably. Correctness and optimality proofs for the adapted algorithms are given, and in a comprehensive case study on established benchmarks it is shown that the implementation, called Modysh, is competitive with state-of-the-art model checkers and even outperforms them on very large state spaces. Second, Deep Statistical Model Checking (DSMC) is introduced, usable for quality assessment and learning pipeline analysis of systems incorporating trained decision-making agents, like neural networks (NNs). The idea of DSMC is to use statistical model checking to assess NNs resolving nondeterminism in systems modeled as MDPs. The versatility of DSMC is exemplified in a number of case studies on Racetrack, an MDP benchmark designed for this purpose, flexibly modeling the autonomous driving challenge. In a comprehensive scalability study it is demonstrated that DSMC is a lightweight technique tackling the complexity of NN analysis in combination with the state space explosion problem.Diese Arbeit präsentiert Ansätze, die Techniken aus dem Model Checking, Planning und Learning Bereich verwenden, um Systeme verlässlicher und klarer verständlich zu machen. Zuerst werden zwei Algorithmen für heuristische Suche und dynamisches Programmieren angepasst, um Extremwerte für Erreichbarkeitswahrscheinlichkeiten, Erwartungswerte für Kosten und beschränkte Varianten davon, auf generellen Markov Entscheidungsprozessen (MDPs) zu untersuchen. Damit wird der Problemraum, der ursprünglich mit diesen Algorithmen gelöst wurde, deutlich erweitert. Korrektheits- und Optimalitätsbeweise für die angepassten Algorithmen werden gegeben und in einer umfassenden Fallstudie wird gezeigt, dass die Implementierung, namens Modysh, konkurrenzfähig mit den modernsten Model Checkern ist und deren Leistung auf sehr großen Zustandsräumen sogar übertrifft. Als Zweites wird Deep Statistical Model Checking (DSMC) für die Qualitätsbewertung und Lernanalyse von Systemen mit integrierten trainierten Entscheidungsgenten, wie z.B. neuronalen Netzen (NN), eingeführt. Die Idee von DSMC ist es, statistisches Model Checking zur Bewertung von NNs zu nutzen, die Nichtdeterminismus in Systemen, die als MDPs modelliert sind, auflösen. Die Vielseitigkeit des Ansatzes wird in mehreren Fallbeispielen auf Racetrack gezeigt, einer MDP Benchmark, die zu diesem Zweck entwickelt wurde und die Herausforderung des autonomen Fahrens flexibel modelliert. In einer umfassenden Skalierbarkeitsstudie wird demonstriert, dass DSMC eine leichtgewichtige Technik ist, die die Komplexität der NN-Analyse in Kombination mit dem State Space Explosion Problem bewältigt