Direct Simulation Monte Carlo Method Research Articles

A discrete unified gas kinetic scheme with sparse velocity grid for rarefied gas flows

In this paper, a discrete unified gas kinetic scheme (DUGKS) with a sparse grid method applied in velocity space (DUGKS-SG) is proposed for simulating rarefied gas flows. The DUGKS-SG decomposes the computationally demanding problem into smaller and independent subproblems, thereby reducing the computational costs and exhibiting good parallelism. Several numerical tests, including the two-dimensional Riemann problem and the lid-driven microcavity flow, have been conducted to validate the performance of the DUGKS-SG. Comparisons with the original DUGKS and the Direct Simulation Monte Carlo (DSMC) method demonstrate that DUGKS-SG can provide satisfactory results with improved efficiency. Specifically, a maximum speedup of 9.486 for a 2D case with 7 CPU cores and 13.035 for a 3D case with 8 CPU cores can be achieved. These results suggest that the proposed DUGKS-SG can serve as an efficient numerical method for rarefied gas flow simulations.

A second-order particle Fokker-Planck model for rarefied gas flows

The direct simulation Monte Carlo (DSMC) method has become a powerful tool for studying rarefied gas flows. However, for the DSMC method to be effective, the cell size must be smaller than the mean free path, and the time step smaller than the mean collision time. These constraints make it difficult to use the DSMC method in multiscale rarefied gas flows. Over the past decade, the particle Fokker-Planck (FP) method has been studied to address computational cost issues in the near-continuum regime. To capture the main features of the Boltzmann equation, various FP models have been proposed, such as the quadratic entropic FP (Quad-EFP) and the ellipsoidal statistical FP (ESFP). Nevertheless, few studies have clearly demonstrated that the FP method offers a computational advantage over the DSMC method without sacrificing accuracy. This is because conventional particle FP methods have employed first-order accuracy schemes. The present study proposes a unified stochastic particle ESFP (USP-ESFP) model. This model improves the accuracy of shear stress and heat flux predictions. Additionally, a spatial interpolation scheme is introduced to the particle FP method. The numerical test cases include relaxation problem, Couette flows, Poiseuille flows, velocity perturbation, and hypersonic flows around a cylinder. The results show that the USP-ESFP model agrees well with both analytical and DSMC results. Furthermore, the USP-ESFP model is found to be less sensitive to cell size and time step than the DSMC method, resulting in a factor of four speed-up for the considered hypersonic flow around a cylinder.

Improving computational efficiency in DSMC simulations of vacuum gas dynamics with a fixed number of particles per cell

The present study addresses the challenge of enhancing computational efficiency without compromising accuracy in numerical simulations of vacuum gas dynamics using the direct simulation Monte Carlo (DSMC) method. A technique termed ‘fixed particle per cell (FPPC)’ was employed, which enforces a fixed number of simulator particles across all computational cells. The proposed technique eliminates the need for real-time adjustment of particle weights during simulation, reducing calculation time. Using the SPARTA solver, simulations of rarefied gas flow in a micromixer and rarefied supersonic airflow around a cylinder were conducted to validate the proposed technique. Results demonstrate that applying the FPPC technique effectively reduces computational costs while yielding results comparable to conventional DSMC implementations. Additionally, the application of local grid refinement coupled with the FPPC technique was investigated. The results show that integrating local grid refinement with the FPPC technique enables accurate prediction of flow behaviour in regions with significant gradients. These findings highlight the efficacy of the proposed technique in improving the accuracy and efficiency of numerical simulations of complex vacuum gas dynamics at a reduced computational cost.

The effects of energy accommodation of reflected gas molecules on flow structures during expired spacecraft reentry

To study the influence of energy accommodation of scattering gas molecules on flow fields during large expired spacecraft reentry, a more elaborated gas-surface interaction model, compared with full Maxwellian diffuse model, is employed in implicit algorithms based on Boltzmann model equation. The characteristic distributions around cylinder at different fluid regimes are accordingly obtained by implicit algorithms, Navier-Stokes solver and DSMC ((Direct Simulation Monte Carlo) method. And the consistency of these results is verified. It is confirmed that present algorithms are capable of solving external flow problems covering various fluid regimes. Then the simulation results see that under current conditions set in the paper, pressure and temperature are proportional to wall activation (ω=Tw/T∞, Tw is surface temperature, T∞ denotes as free stream temperature), but their amplitudes alter with ω at different fluid regimes. As for the effects of energy accommodation coefficients (αe), both pressure and temperature profiles vary in a linear way with αe. However, the variation ranges of these parameters are diverse with regard to different fluid regimes. These observations are favor to the construction of efficient forecasting software, which could predict the flight path of large defunct spacecraft. In this forecasting software, the external ballistics computations and aerothermodynamic simulations are synchronously carried out.

Design and Evaluation of a Hypersonic Waverider Vehicle Using DSMC

This work investigates the aerodynamic performance of a hypersonic waverider designed to operate at Mach 7, focusing on optimizing its design through advanced computational methods. Utilizing the Direct Simulation Monte Carlo (DSMC) method, the three-dimensional flow field around the specifically designed waverider was simulated to understand the shock wave interactions and thermal dynamics at an altitude of 90 km. The computational approach included detailed meshing around the vehicle’s critical leading edges and the use of three-dimensional iso-surfaces of the Q-criterion to map out the shock and vortex structures accurately. Additional simulation results demonstrate that the waverider achieved a lift–drag ratio of 2.18, confirming efficient aerodynamic performance at a zero-degree angle of attack. The study’s findings contribute to the broader understanding of hypersonic flight dynamics, highlighting the importance of precise computational modeling in developing vehicles capable of operating effectively in near-space environments.

Development of convolutional neural network-based surrogate model for three-dimensional vacuum plume prediction via direct simulation Monte Carlo method

The vacuum plume phenomenon encountered during lunar exploration missions poses significant challenges, such as impingement forces, heat fluxes, and spacecraft contamination. Numerical simulation represents the predominant method for evaluating the impacts of vacuum plumes. However, the conventional direct simulation Monte Carlo (DSMC) method, despite being the standard, is notably time-consuming and impractical for real-time analysis. Addressing this limitation, our research explores deep learning, specifically convolutional neural networks (CNN), for the efficient prediction of vacuum plume dynamics. We introduce a novel CNN-based DSMC method (CNN-DSMC-3D), leveraging a dataset obtained from three-dimensional DSMC simulations. This approach translates the spacecraft's shape and boundary conditions into a signed distance function and an identifier matrix. The CNN-DSMC-3D method effectively predicts the vacuum plume field, aligning closely with DSMC results across various lunar surface conditions. Crucially, the CNN-DSMC-3D method achieves a speed increase in four to six orders of magnitude over the conventional DSMC method, demonstrating substantial potential for real-time aerospace applications and offering a paradigm shift in the simulation of lunar landing scenarios.

Real-time vacuum plume flow field reconstruction during lunar landings based on deep learning

In space missions, the vacuum plume generated by rocket engines can negatively impact spacecraft. Therefore, researching the vacuum plume is crucial to guarantee the regular operation of spacecraft. The conventional numerical simulation methodology, the direct simulation Monte Carlo (DSMC) method, is time-consuming and lacks real-time calculation capabilities. Recently, deep learning (DL) methods have emerged in the field of fluid dynamics. In this study, a DL model trained by a convolutional neural network with multiple decoders is introduced to predict the vacuum plume flow field during lunar landings. The network processes shape topology information and boundary conditions as inputs, yielding flow field data including velocity and pressure fields as outputs. Meanwhile, the flow field prediction results under different conditions and training methods are discussed. The results show that the predicted flow field under different lunar surface conditions is in accord with the DSMC results. The maximum mean and standard deviation errors of the data distribution of each flow field do not exceed 9.72% and 9.07%, respectively. Different training methods with flat and inclined lunar surfaces also have an impact on the prediction results. Compared with the DSMC method, the DL method exhibits higher efficiency with a speedup of about four orders of magnitude, indicating that the DL-based flow field reconstruction method has strong application prospects in the real-time computation of vacuum plume flow fields.

Numerical simulation of plume–surface interaction and lunar dust dispersion during lunar landing using four engines

As the lander approaches the lunar surface, the engine plumes impinge on the lunar regolith and entrain lunar dust from the surface. This plume–surface interaction and the resulting dispersion of lunar dust form a multi-physics, multi-scale problem, which becomes even more complex under multi-engine conditions. This study employed the direct simulation Monte Carlo method to simulate the plume–surface interaction flow field of a four-engine lunar lander at various landing altitudes and lunar surface angles. Flow characteristics were analyzed, and the impact of the plume and backflow on the lander was assessed. Subsequently, lunar dust simulation was conducted using the plume field as a basis. The study determined the spatial distribution of particles with different diameters at various landing altitudes and surface angles, as well as their impact velocities on the lander. Furthermore, taking into account the variations in the lander's altitude and attitude, a dynamic simulation of lunar dust during the landing process was conducted. This process resulted in the dynamic distribution of lunar dust during landing, laying the groundwork for real-time simulation of lunar dust distribution and reliable visualization during landing simulations. These findings are valuable for assessing and mitigating the hazards posed by lunar dust.

Rarefied cylindrical Couette problem: Effect of a very sharp transition from weakly rarefied flow near the inner cylinder to free molecular flow at very low average Knudsen numbers

We consider the rarefied cylindrical Couette flow. The outer cylinder rotates at a constant angular velocity, and the inner one is at rest. The Knudsen number, calculated from the average gas density, is much less than one. To find the fluid dynamic variables and fluxes, the direct simulation Monte Carlo method (DSMC) is used. We find the effect of a very sharp decrease in shear stress and energy fluxes transferred to the cylinders if the Knudsen number is sufficiently low and the rotation speed of the outer cylinder is sufficiently high. We show that when the average Knudsen number is sufficiently low, if the velocity is initially high and increases slightly further, the weakly rarefied flow regime near the inner cylinder transitions abruptly to a free molecular flow regime. Thus, the flow abruptly separates from the inner cylinder. We compare the fluxes obtained by solving the Navier–Stokes equations and by the DSMC method. It turns out that the solutions of the Navier–Stokes equations with slip boundary conditions also change abruptly at certain critical values, and these critical values are close to the appropriate DSMC values.

Multi-species modeling in the particle-based ellipsoidal statistical Bhatnagar-Gross-Krook method including internal degrees of freedom

The implementation of the ellipsoidal statistical Bhatnagar-Gross-Krook (ESBGK) method in the open-source particle code PICLas is extended for multi-species modeling of polyatomic molecules, including internal energies with multiple vibrational degrees of freedom. For this, the models of Mathiaud et al. [1], Pfeiffer [2] and Brull [3,4] are combined. In order to determine the transport coefficients of the gas mixture, Wilke's mixing rules and collision integrals are compared. The implementation is verified with simulation test cases of a supersonic Couette flow as well as a hypersonic flow around a 70° blunted cone. The solutions of the ESBGK method are compared to the Direct Simulation Monte Carlo (DSMC) method to assess the accuracy, where overall good agreement is achieved. In general, collision integrals should be preferred for the determination of the transport coefficients, since the results using Wilke's mixing rules show larger deviations in particular for large mass ratios. Considering the computational efficiency of the methods, a considerable reduction in computational time is possible with the ESBGK model.

A general drag coefficient model for a spherical particle incorporating rarefaction and particle-to-gas temperature ratio effects

A concept and model of two critical Reynolds numbers Rep,cr1 and Rep,cr2 corresponding respectively to onsets of drag crisis and recovery are proposed. A drag model at limits of zero particle Mach and Knudsen numbers is constructed. On this basis, we develop a general drag coefficient model applicable for a spherical particle traveling in a gas by using a large number of available data derived from the previous experiments, direct numerical simulations and direct simulation Monte-Carlo methods. The scope of applicability of the proposed drag model covers all flow regimes relative to the particle characterized by particle Reynolds and Mach (or Knudsen) numbers and different particle-to-gas temperature ratios. Its comparison with two latest general drag models shows the significantly smaller relative error. Furthermore, quasi-one dimensional simulations against two supersonic nozzle gas-particle flow experiments are conducted with an in-house code to validate its accuracy in comparison with the two drag models.

A statistical boundary for 3D rarefied flows through meshes: implementation to a new version of dsmcFoam+ and wind tunnel validation

AbstractThe Direct Simulation Monte Carlo (DSMC) method has become a standard tool for rarefied aerodynamics and microchannel flows. However, the performance benefits of DSMC, such as adaptive grid sizes and number of particles, are constrained by the need to resolve small geometric details of mesh applications within relatively large simulation volumes. The requirement for a sufficient number of particles in even the smallest cells imposes a significant computational burden. A novel set of cyclic statistical boundary conditions is proposed to address the computational bottleneck associated with simulating micrometre-scale structures prevalent in atmospheric and space research under rarefied flow conditions. These conditions account for the geometric parameters of a geometric mesh and the angular dependency of impacting particles, aiming to alleviate the computational challenges posed by conventional approaches. Validation against wind tunnel measurements demonstrates excellent agreement for one of the implemented boundaries, able to simulate fine meshes for conditions of rocket soundings in the Mesosphere. The newly developed boundary conditions are implemented within the advanced DSMC solver, dsmcFoam+ framework. For this study, the solver is ported from OpenFOAM® version 2.4.0 to the OpenFOAM® version v2306 to leverage recent code developments, particularly in dynamic meshes, load balancing, and barycentric particle tracking. This advancement enhances the capabilities of DSMC simulations, offering improved fidelity and accuracy in capturing rarefied flow phenomena.

Forces acting on near-wall spherical particles in shear flows of diluted gases

In the present paper, we studied the forces on a spherical particle of radius R moving in the vicinity of the plane wall in a shear flow of free molecular regime. We consider that the distance ratio between the plane wall and the particle (L) and the particle radius (R) is large (e.g., L/R > 5), and the gas molecular mean free path (λ) is much higher than the particle size (λ/R ≫1). An analytical formula for the forces is obtained based on gas kinetic theory and certain simplifying assumptions, and is verified by using Direct Simulation Monte Carlo Method. It is found that the forces acting on the particle can be affected by the momentum accommodation coefficients (σ) of the wall and particle surfaces, the wall/gas temperature ratios (Tw/T), and the velocity gradient (G) of the gas flow. In the cases of specular reflections (σ = 0), the near-wall effect can be neglected. With the increase of the momentum accommodation coefficients, the near-wall effect can be enhanced. When near-wall particles move in the direction parallel to the plane wall, there is a lift force which is perpendicular to the wall due to the near-wall effect and the shear flow. For Tw/T < 1, the lift force for the near-wall particles is in the direction against the wall. While for Tw/T > 1, the force is in the direction away from the plane wall. The findings presented in this paper can provide theoretical guidance for the application of near-wall particles in shear flows.

Effects of geometrical parameters on rarefied gas flows and Knudsen force in the system of triangular-rectangular beams with different temperatures

In the rarefied gas, the gas flows induced by the inhomogeneous temperature fields and the Knudsen force exerting on the immersed structure are potentially applicable to the micro/nano-electromechanical systems (MEMS/NEMS) and aerospace. The system composed of a series of triangle cold beams and rectangle hot beams is proposed, and the effects of the beam geometry, dimensions, and positions for different pressures on rarefied gas flows and Knudsen force are researched based on the direct simulation Monte Carlo (DSMC) method. The results reveal that both the gas flows and Knudsen force are highly sensitive to these factors. Particularly, the applications of triangular cross-section cold beams and large height-to-width ratios are necessary for a larger Knudsen force. Compared to the rectangle cold beam, when the triangle cold beam has an inclination of approximately 20°, the peak value of Knudsen force can increase by 142%. Moreover, Knudsen force monotonically reduces with the distance between the cold and hot beams increasing. However, the effects of the distance between the cold beam and substrate (substrate proximity) on Knudsen force depend on the ambient pressure. In general, an appropriate increase in substrate proximity appears to be a smart way to practically enhance the Knudsen force.

Accuracy and performance evaluation of low density internal and external flow predictions using CFD and DSMC

The Direct Simulation Monte Carlo (DSMC) method was widely used to simulate low density gas flows with large Knudsen numbers. However, DSMC encounters limitations in the regime of lower Knudsen numbers (Kn<0.05). In such cases, approaches from classical computational fluid dynamics (CFD) relying on the continuum assumption are preferred, offering accurate solutions at acceptable computational costs. In experiments aimed at imaging aerosolized nanoparticles in vacuo a wide range of Knudsen numbers occur, which motivated the present study on the analysis of the advantages and drawbacks of DSMC and CFD simulations of rarefied flows in terms of accuracy and computational effort. Furthermore, the potential of hybrid methods is evaluated. For this purpose, DSMC and CFD simulations of the flow inside a convergent–divergent nozzle (internal expanding flow) and the flow around a conical body (external shock generating flow) were carried out. CFD simulations utilize the software OpenFOAM and the DSMC solution is obtained using the software SPARTA. The results of these simulation techniques are evaluated by comparing them with experimental data (1), evaluating the time-to-solution (2) and the energy consumption (3), and assessing the feasibility of hybrid CFD-DSMC approaches (4).

Development of Compressible Mixing Layer Instability Simulated Using the Direct Simulation Monte Carlo Method

Development of Compressible Mixing Layer Instability Simulated Using the Direct Simulation Monte Carlo Method

Numerical and experimental study of supersonically expanding argon plasma using a micrometer hollow cathode discharge

Pulsed discharge nozzles (PDNs) have been successfully used for decades to produce rotationally cold (Trot ∼ 20 K) radicals and ions of astrophysical interest and to characterize these species spectroscopically. In this work, an evolution of the PDN, the piezostack pulsed discharge nozzle (P2DN), is used for the first time to investigate the characteristics of the still poorly understood supersonic plasma expansion. The P2DN allows for a better control of the reservoir pressure of which an accurate measurement is required to characterize the plasma expansion. This new source, thus, gives the opportunity to further optimize the plasma conditions and extend its use to new target species. The spatial distribution of an argon plasma and the effect of the supersonic flow for different pressures are studied by combining a two-dimensional extended fluid model (extFM) and a direct simulation Monte Carlo (DSMC) method. The combined simulation is validated with experimental results obtained through emission spectroscopy associated with a group-code collisional-radiative model to retrieve the plasma parameters. The validated numerical approach (DSMC-extFM) allows for an accurate characterization of the plasma structure in our typical experimental conditions (a reservoir pressure ranging from 90 to 905 mbar). Thus, this simulation will be used in future studies to improve the plasma conditions to favor the synthesis of (transient) hydrocarbon species as found in space, by seeding the argon gas with a suitable precursor, such as acetylene.

Investigation of local Nusselt number in a rarefied microchannel gas flow using Direct Simulation Monte Carlo method

Heat transfer in microscale and rarefied gaseous flows has been investigated for high Knudsen number (Kn) flows using the Direct Simulation Monte Carlo (DSMC) method. A wide range of Kn [0.05 – 5], pressure ratio [1.2 – 4] and wall temperature [323 K – 723 K] is studied. The heat flux and local Nusselt number (Nu) are found to exhibit three distinct sections along the length of the microchannel – heat transfer-dominated section, constant heat transfer section and exit section. The defining roles of different effects such as non-equilibrium conditions at the wall, viscous dissipation, axial conduction, pressure work, and shear work have been considered implicitly in the DSMC method. These parameters are seen to influence the heat transfer differently at lower and higher Kn. These results help to quantify the fraction of total heat exchange and reveals the complex interplay of various terms of the energy equation in gas flow in microchannels.

Zero-dimensional analysis of the effect of water vapor on reducing electrons in the plasma sheath

In this study, an air-water vapor ionization reaction model is developed within the quantum-kinetic (Q–K) model of the direct simulation Monte Carlo method to investigate the detailed mechanism of how water vapor reduces electrons. The zero-dimensional simulations of a typical non-equilibrium flow field downstream of a normal shock are designed, where the electron number density decreases by two orders of magnitude due to water vapor. We conclude that the introduction of water vapor reduces the mole fractions of oxygen atoms and nitrogen atoms through five pairs of reactions and enhances the reverse nitric oxide associative ionization reaction, leading to electron consumption. The phenomena and corresponding mechanisms under varying mole fractions of water vapor, air temperatures, and water vapor temperatures are investigated. Based on the mechanisms, we propose that the addition of hydrogen ions could improve the water's mitigation effect, which is then proven to be able to reduce the electron number density by another two orders of magnitude, not only at high air temperatures but also at lower air temperatures or lower mass injection rates.

An improved continuum model for hypersonic thermal nonequilibrium flow in the near-continuum regime

In this work, the rarefied Couette flow of diatomic gases with thermal nonequilibrium effects is investigated by the direct simulation Monte Carlo (DSMC) method, and a macroscopic computational model is developed to consider the local rarefaction effects for diatomic gases in the near-continuum regime. The nonlinear transport properties of the diatomic gases are studied, indicating that effective viscosity and effective translational thermal conductivity in the shear nonequilibrium state are affected by translational nonequilibrium effects, which obey the same laws for both monatomic and diatomic gases. The transport coefficients of internal energy modes are affected by both translational nonequilibrium and internal energy relaxation, therefore, the effective rotational and vibrational thermal conductivities are related to the effective viscosity through a modified Eucken relation that accounts for internal energy relaxation. Conclusively, effective constitutive relations are newly established as a function of the shear nonequilibrium parameter and the modified Eucken factors for thermal nonequilibrium flows, and these are integrated into the macroscopic two-temperature model. Subsequently, it is assessed in the simulation of hypersonic flows over flat plates and cylinders at various Knudsen numbers. The results show that the surface shear stress and heat flux obtained by the proposed model agree well with the DSMC results, indicating significantly improved performance compared to the conventional Navier–Stokes two-temperature model for hypersonic flows in the near-continuum regime.