Direct Simulation Monte Carlo Results Research Articles

An improved analytical method for rarefied aerothermodynamics on a complex geometry in free-molecular flows

A numerical method for high altitude aerothermodynamic analysis code for Very Low Earth Orbit (VLEO) satellite and spacecraft, named as HACS, is presented in this article. HACS is a computational tool that addresses the challenges by integrating the free-molecular gas kinetic model with novel particle sampling method and robust particle tracing algorithm to predict the shadow region on surfaces. To ensure the reliability and accuracy of the HACS, a rigorous verification and validation process has been systematically conducted by comparing the aerothermodynamic properties of forces, moments, and heat flux with the direct simulation Monte-Carlo (DSMC) results. The HACS is applied to the realistic geometries of VLEO satellite, the Apollo re-entry module, and spacecraft including fin and wing shapes. Results demonstrate that HACS provides the aerothermodynamic properties within the time frame of 60 seconds for the complex geometries and the accuracy of the HACS is guaranteed above 120 km altitude. The maximum relative error of the aerothermodynamic properties is less than 5% compared to the DSMC results at the lowest altitude of about 120 km, and has smaller relative errors as the altitude increases.

Effects of the chirp rate on single-shot coherent Rayleigh-Brillouin scattering

Single-shot coherent Rayleigh-Brillouin scattering (CRBS) is modeled using direct simulation Monte Carlo (DSMC). In CRBS, an optical lattice generated by the interference of two pump lasers traps the neutral particles via the dipole force. The gradient of refractive index due to the trapped particles of the gaseous media leads to coherent scattering of a probe beam, resulting in the CRBS signal. Additionally, using a chirped laser beam, CRBS signals can be obtained in a single laser shot, shortening the measurement time of the gas flow (on the order of 100 ns). The DSMC results of single-shot CRBS assuming Maxwellian velocity distribution functions (VDFs) show good agreement with experimental data, including argon, carbon dioxide, and xenon, for different gas pressures. One of the key observations obtained from the present simulations is that the CRBS signals become asymmetric when using a fast chirp rate due to finite time for collisionless trapping and collisional thermalization. Published by the American Physical Society 2024

Magnetohydrodynamic and Aerodynamic Assessment of a 70° Spherecone at Mars and Venus

An electrical conductivity database for continuum flow in a CO2 atmosphere over a 70° spherecone was created using the Data Parallel Line Relaxation Code computational fluid dynamics software to inform development of future magnetohydrodynamic subsystems at Venus and Mars. Sixteen freestream conditions were considered at Mars with atmospheric relative velocities from 5 to 8 km/s and altitudes between 20 and 80 km. Sixteen freestream conditions were considered at Venus with atmospheric relative velocities from 9 to 12 km/s and altitudes between 85 and 115 km. Results indicate that the total electrical conductivity in the flow volume always increases as velocity increases. At low velocities, the electrical conductivity is higher at high altitudes whereas, at high velocities, the electrical conductivity is higher at low altitudes. Three of the 80 km altitude computational fluid dynamics solutions show good agreement with direct simulation Monte Carlo results. In general, computational fluid dynamics predicts thinner shocks, higher electron number density, and similar vibrational temperatures to direct simulation Monte Carlo. The magnetohydrodynamic force was calculated at both Mars and Venus. Results indicate there may not be sufficient control authority to use magnetohydrodynamics as a trajectory control mechanism at Mars without artificially increasing the electrical conductivity of the flow, but there may be appreciable control authority for a drag-modulated aerocapture at Venus.

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.

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.

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.

Regular reflection of shock waves in steady flows: viscous and non-equilibrium effects

Numerical analysis of a steady monatomic gas flow about the point of the regular reflection of a strong oblique shock wave from the symmetry plane is conducted with the Navier–Stokes–Fourier (NSF) equations, the regularized Grad 13-moment (R13) equations and the direct simulation Monte Carlo (DSMC) method. In contrast to the inviscid solution to this problem completely defined by the Rankine–Hugoniot (RH) relations, all three models predict a complicated flow structure with strong thermal non-equilibrium and a long wake with flow parameters not predicted by the RH relations. The temperature $T_y$ related to thermal motion of molecules in the direction normal to the symmetry plane has a maximum inside the reflection zone while in a planar shock wave the maximum is observed for the $T_x$ temperature. The R13 equations predict these features much better than the NSF equations and are in good agreement with the benchmark DSMC results. An analysis of the flow with the conservation equations was conducted in order to evaluate the effects of various processes on a fluid element moving along the symmetry plane. In contrast to the shock wave where effects of viscosity and heat conduction are one-dimensional with zeroth net contribution to the fluid-element energy across the shock, the flow across the zone of the shock reflection is dominated by two-dimensional effects with positive net contribution of viscosity and negative contribution of heat conduction to the fluid-element energy. These effects are believed to be the main source of the wake with parameters deviating from the RH values.

Nonequilibrium Flow Simulations Using Unified Gas-Kinetic Wave-Particle Method

Nonequilibrium flows are commonly encountered in aerospace engineering applications such as spacecraft reentry, rocket launch, and satellite attitude control. Numerical simulations help greatly in the understanding of nonequilibrium flow, multiscale effects, and the dynamics in these applications. Coupling particle transport and collision within the gas evolution process, the unified gas-kinetic wave-particle (UGKWP) method has been developed for multiscale flow simulation, offering a strategy that strikes a balance between accuracy and efficiency. In the present study, the UGKWP method simulates challenging flow problems with large Knudsen number variations, including supersonic flow around a sphere, hypersonic flow around a space vehicle, nozzle plume into vacuum, and side-jet impingement on the hypersonic flow. The UGKWP accurately captures complex flow structures and has been verified through experimental data or direct simulation Monte Carlo results. Regarding computational cost, the UGKWP method requires only 60 GiB of memory to simulate the three-dimensional space vehicle with 560,593 cells under various flow conditions, which is manageable even on personal workstations. Given its excellent efficiency and accuracy, the UGKWP method shows its substantial benefits in simulating multiscale flow for aerospace engineering applications.

Design and optimisation of a passive Atmosphere-Breathing Electric Propulsion (ABEP) intake

In order to extend the orbital lifetime of spacecraft operating in Very-Low Earth Orbit (VLEO), Atmosphere-Breathing Electric Propulsion (ABEP) can be employed for atmospheric drag compensation. The concept is based on the ingestion of rarefied atmospheric particles to be used as propellant for an electric thruster, thereby removing the need for onboard propellant. The present paper aims to design and analyse a passive ABEP intake optimised for the RF Helicon-based Plasma Thruster (IPT), which is selected as the most promising system due to its electrodeless design, as it removes the issue of thruster corrosion, and reduced susceptibility to atmospheric variations. This is achieved by implementing the analytical model, referred to as the Balancing Model (BM), along with its main performance parameters. The Direct Simulation Monte Carlo (DSMC) solver dsmcFoam+ is thus employed to simulate the transmission probability of cylinders and hexagonal prisms with non-zero entrance velocity, yielding a mean percentage error of 2% when compared to independent DSMC results. In addition, a novel DSMC transmittance investigation of square prisms is performed. Various design configurations are optimised for circular and hexagonal intakes based on the functional requirements of the thruster, leading to a maximum collection efficiency of 45% for a cylindrical intake with a hexagonal honeycomb. The optimal intake is hence simulated via DSMC, showing a good accuracy with the BM with or without intermolecular collisions, yielding a percentage error of 0.22% in the former case and 5.53% in the latter one. The variation of incidence flow angle, accommodation coefficient and thruster transmission probability is finally investigated, and the results are validated by the agreement shown with values retrieved from the literature.

Fast vacuum plume prediction using a convolutional neural networks-based direct simulation Monte Carlo method

The vacuum plume, which can incur impingement forces, heat fluxes, and contaminations on the spacecraft, has been a vital issue in space missions such as lunar landings. The direct simulation Monte Carlo (DSMC) method is generally used to simulate the vacuum plume. However, DSMC is a particle simulation, and thus, it is very time-consuming, making it impossible to achieve real-time analysis during lunar landings. Motivated by this tricky issue, we explore the feasibility of deep learning to predict the vacuum plume using convolutional neural networks (CNN). In the study, a CNN-based DSMC method (CNN-DSMC) is proposed. The dataset is obtained by the DSMC simulation. The inputs of CNN-DSMC are the shape information and the boundary conditions, which are transformed into the signed distance function (SDF) and identifier matrix (IM), respectively. In particular, a shock-based partitioned method is developed to construct IM to suit the complex flow field with the shock wave. Finally, a vacuum plume velocity field is predicted using the proposed CNN-DSMC, and the prediction of CNN-DSMC is well consistent with DSMC results. Most importantly, compared with the traditional DSMC, the speedup of CNN-DSMC can be up to 4 orders of magnitude, suggesting that CNN-DSMC is a promising method for real-time analysis during lunar landings.

Data-driven nonlinear constitutive relations for rarefied flow computations

To overcome the defects of traditional rarefied numerical methods such as the Direct Simulation Monte Carlo (DSMC) method and unified Boltzmann equation schemes and extend the covering range of macroscopic equations in high Knudsen number flows, data-driven nonlinear constitutive relations (DNCR) are proposed first through the machine learning method. Based on the training data from both Navier-Stokes (NS) solver and unified gas kinetic scheme (UGKS) solver, the map between responses of stress tensors and heat flux and feature vectors is established after the training phase. Through the obtained off-line training model, new test cases excluded from training data set could be predicated rapidly and accurately by solving conventional equations with modified stress tensor and heat flux. Finally, conventional one-dimensional shock wave cases and two-dimensional hypersonic flows around a blunt circular cylinder are presented to assess the capability of the developed method through various comparisons between DNCR, NS, UGKS, DSMC and experimental results. The improvement of the predictive capability of the coarse-graining model could make the DNCR method to be an effective tool in the rarefied gas community, especially for hypersonic engineering applications.

High order finite volume schemes with IMEX time stepping for the Boltzmann model on unstructured meshes

In this work, we present a family of time and space high order finite volume schemes for the solution of the full Boltzmann equation. The velocity space is approximated by using a discrete ordinate approach while the collisional integral is approximated by spectral methods. The space reconstruction is implemented by integrating the distribution function, which describes the state of the system, over arbitrarily shaped and closed control volumes using a Central Weighted ENO (CWENO) technique. Compared to other reconstruction methods, this approach permits to keep compact stencil sizes which is a remarkable property in the context of kinetic equations due to the considerable demand of computational resources. The full discretization is then obtained by combining the previous phase-space approximation with high order Implicit–Explicit (IMEX) Runge–Kutta schemes. These methods guarantee stability, accuracy and preservation of the asymptotic state. Comparisons of the Boltzmann model with simpler relaxation type kinetic models (like BGK) are proposed showing the capability of the Boltzmann equation to capture different physical solutions. The theoretical order of convergence is numerically measured in different regimes and the methods are tested on several standard two-dimensional benchmark problems in comparison with Direct Simulation Monte Carlo results. The article ends with a prototype engineering problem consisting of a subsonic and a supersonic flow around a NACA 0012 airfoil. All test cases are run with MPI parallelization on several cores, thus making the proposed methods suitable for parallel distributed memory supercomputers.

Time-dependent homogeneous states of binary granular suspensions

The time evolution of a homogeneous bidisperse granular suspension is studied in the context of the Enskog kinetic equation. The influence of the surrounding viscous gas on the solid particles is modeled via a deterministic viscous drag force plus a stochastic Langevin-like term. It is found first that, regardless of the initial conditions, the system reaches (after a transient period lasting a few collisions per particle) a universal unsteady hydrodynamic regime where the distribution function of each species not only depends on the dimensionless velocity (as in the homogeneous cooling state) but also on the instantaneous temperature scaled with respect to the background temperature. To confirm this result, theoretical predictions for the time-dependent partial temperatures are compared against direct simulation Monte Carlo (DSMC) results; the comparison shows an excellent agreement confirming the applicability of hydrodynamics in granular suspensions. Also, in the transient regime, the so-called Mpemba-like effect (namely, when an initially hotter sample cools sooner than the colder one) is analyzed for inelastic collisions. The theoretical analysis of the Mpemba effect is performed for initial states close to and far away from the asymptotic steady state. In both cases, good agreement is found again between theory and DSMC results. As a complement to the previous studies, we determine in this paper the dependence of the steady values of the dynamic properties of the suspension on the parameter space of the system. More specifically, we focus our attention on the temperature ratio T1/T2 and the fourth degree cumulants c1 and c2 (measuring the departure of the velocity distributions f1 and f2 from their Maxwellian forms). While our approximate theoretical expression for T1/T2 agrees very well with computer simulations, some discrepancies are found for the cumulants. Finally, a linear stability analysis of the steady state solution is also carried out showing that the steady state is always linearly stable.

Propagation of two-dimensional vibroacoustic disturbances in a rarefied gas

The effect of gas rarefaction on the propagation of two-dimensional vibroacoustic disturbances generated by a nonuniformly oscillating plane is studied. Closed-form descriptions are obtained in the free-molecular (left panel of the figure) and continuum (right panel) limits and complemented by direct simulation Monte Carlo results. The impacts of gas rarefaction on signal decay rate and directivity pattern are highlighted and rationalized.

Correlations for aerodynamic coefficients for prolate spheroids in the free molecular regime

A new set of aerodynamic correlations are proposed for an ellipsoidal particle in the free molecular regime by carrying out flow simulations using the Direct Simulation Monte Carlo (DSMC) method. The in-house DSMC solver is modified to be consistent with free molecular flow assumptions as well as to reduce computational cost. The solver is validated against an open-source DSMC solver, viz., SPARTA, the free molecular theory and experimental data for flow over a sphere and right circular cylinder in the free molecular regime. The flow is simulated over ellipsoidal particles at different aspect ratios, angles of attack and speed ratios to estimate the aerodynamic properties. Regression analysis is performed to give correlations for the variation of aerodynamic properties such as drag, lift and torque coefficients. The correlations are rigorously tested against the DSMC results, obtained from our in-house solver as well as those obtained from SPARTA, over a wide range of parameters.

Molecular level simulations of combustion processes using the DSMC method

A technique called the Direct Simulation Monte Carlo (DSMC) method is used for simulating laminar one-dimensional hydrogen-air flames with an aim to establish the feasibility of molecular-level simulations for combustion using the Quantum-Kinetic (QK) reaction model. In DSMC, simulation particles are employed which represent many molecules with similar properties. The DSMC method effectively solves the Boltzmann equation by decoupling the motion of molecules into two phases: a Move phase and a Collision phase. Chemistry is treated using the Quantum-Kinetic model in which the total energy exchange resulting from molecular collision determines the outcome of the chemical reactions. A major advantage of DSMC is that it avoids using continuum Arrhenius reaction rates or simplified gradient laws for the diffusivities of mass, momentum and heat. Instead, any such laws and their parameters emerge naturally from the DSMC results. Simulations of one-dimensional hydrogen-air flames using the DSMC method with a detailed chemical scheme show promising results for molecular-level simulations of combustion. An adjustment to the activation energy of a key reaction is made in order to achieve the correct flame speed. The species and temperature profiles from DSMC show reasonable agreement with those obtained from Direct Numerical Simulation (DNS) using a conventional continuum approach. Likewise, the molecular diffusivity of hydrogen and oxygen also show reasonable agreement with the DNS results, although differences in the results still exist, especially for oxygen diffusivity. These are expected to improve with further development in the DSMC method for combustion.

The effect of a solid boundary on the propagation of thermodynamic disturbances in a rarefied gas

We study the effect of a rigid boundary on the propagation of thermodynamic disturbances in a gas under non-continuum conditions. We consider a semi-infinite setup confined by an infinite planar wall and introduce initial gas disturbances in the form of density and temperature inhomogeneities. The problem is formulated for arbitrary small-amplitude perturbations and analyzed in the entire range of gas rarefaction rates, governed by the Knudsen (Kn) number. Our results describe the system relaxation to equilibrium, with specific emphasis on the effect of the solid surface. Analytical solutions are obtained in the free-molecular and near-continuum (based on the Navier–Stokes–Fourier and regularized 13 moment equations) regimes and compared with direct simulation Monte Carlo results. The impact of the solid wall is highlighted by comparing between diffuse (adiabatic or isothermal) and specular boundary reflections. Focusing on a case of an initial temperature disturbance, the results indicate that the system relaxation time shortens with increasing Kn. The isothermal boundary consistently reverberates the weakest acoustic disturbance, as the energy carried by the impinging wave is partially absorbed by the surface. The specular and adiabatic wall systems exhibit identical responses in the continuum limit while departing with increasing Kn due to higher-order moment effects. The unsteady normal force exerted by the gas on the surface is quantified and analyzed.

Grad's Second Problem and Its Solution Within the Framework of Burnett Hydrodynamics

Abstract In his seminal work, Grad not only derived 13 moment equations but also suggested two problems to check his derived equations. These problems are highly instructive as they bring out the character of the equations by examining their solutions to these problems. In this work, we propose Grad's second problem as the potential benchmark problem for checking the accuracy of different sets of higher-order transport equations. The problem definition can be stated as: examination of steady-state solution for a gas at rest in infinite domain upon application of a one-dimensional heat flux. With gas at rest (no bulk velocity), the interest lies in obtaining the solution for pressure and temperature. The problem is particularly interesting with respect to the solution for pressure when Maxwell and hard-sphere molecules are considered. For Maxwell molecules, it is well known that the exact normal solution of Boltzmann equation gives uniform pressure with no stresses in the flow domain. In the case of hard-sphere molecules, direct simulation Monte Carlo (DSMC) results predict nonuniform pressure field giving rise to stresses in the flow domain. The simplistic nature of the problem and interesting results for pressure for different interaction potentials makes it an ideal test problem for examining the accuracy of higher-order transport equations. The proposed problem is solved within the framework of Burnett hydrodynamics for hard-sphere and Maxwell molecules. For hard-sphere molecules, it is observed that the Burnett order stresses do not become zero; they rather give rise to a pressure gradient in a direction opposite to that of temperature gradient, consistent with the DSMC results. For Maxwell molecules, the numerical solution of Burnett equations predicts uniform pressure field and one-dimensional temperature field, consistent with the exact normal solution of the Boltzmann equation.

Investigation of non-equilibrium boundary conditions considering sliding friction for micro/nano flows

Purpose Accurate prediction of temperature and heat is crucial for the design of various nano/micro devices in engineering. Recently, investigation has been carried out for calculating the heat flux of gas flow using the concept of sliding friction because of the slip velocity at the surface. The purpose of this study is to exetend the concept of sliding friction for various types of nano/micro flows. Design/methodology/approach A new type of Smoluchowski temperature jump considering the viscous heat generation (sliding friction) has recently been proposed (Le and Vu, 2016b) as an alternative jump condition for the prediction of the surface gas temperature at solid interfaces for high-speed non-equilibrium gas flows. This paper investigated the proposed jump condition for the nano/microflows which has not been done earlier using four cases: 90° bend microchannel pressure-driven flow, nanochannel backward facing step with a pressure-driven flow, nanoscale flat plate and NACA 0012 micro-airfoil. The results are compared with the available direct simulation Monte Carlo results. Also, this paper has demonstrated low-speed preconditioned density-based algorithm for the rarefied gas flows. The algorithm captured even very low Mach numbers of 2.12 × 10−5. Findings Based on this study, this paper concludes that the effect of inclusion of sliding friction in improving the thermodynamic prediction is case-dependent. It is shown that its performance depends not only on the slip velocity at the surface but also on the mean free path of the gas molecule and the shear stress at the surface. A pressure jump condition was used along with the new temperature jump condition and it has been found to often improve the prediction of surface flow properties significantly. Originality/value This paper extends the concept of using sliding friction at the wall for micro/nano flows. The pressure jump condition was used which has been generally ignored by researchers and has been found to often improve the prediction of surface flow properties. Different flow properties have been studied at the wall apart from only temperature and heat flux, which was not done earlier.

Quantification of thermally-driven flows in microsystems using Boltzmann equation in deterministic and stochastic contexts

When the flow is sufficiently rarefied, a temperature gradient, for example, between two walls separated by a few mean free paths, induces a gas flow—an observation attributed to the thermostress convection effects at the microscale. The dynamics of the overall thermostress convection process is governed by the Boltzmann equation—an integrodifferential equation describing the evolution of the molecular distribution function in six-dimensional phase space—which models dilute gas behavior at the molecular level to accurately describe a wide range of flow phenomena. Approaches for solving the full Boltzmann equation with general intermolecular interactions rely on two perspectives: one stochastic in nature often delegated to the direct simulation Monte Carlo (DSMC) method and the others deterministic by virtue. Among the deterministic approaches, the discontinuous Galerkin fast spectral (DGFS) method has been recently introduced for solving the full Boltzmann equation with general collision kernels, including the variable hard/soft sphere models—necessary for simulating flows involving diffusive transport. In this work, the deterministic DGFS method, Bhatnagar-Gross-Krook (BGK), Ellipsoidal statistical BGK (ESBGK), and Shakhov kinetic models, and the widely used stochastic DSMC method, are utilized to assess the thermostress convection process in micro in-plane Knudsen radiometric actuator—a microscale compact low-power pressure sensor utilizing the Knudsen forces. The BGK model underpredicts the heat-flux, shear-stress, and flow speed; the S-model overpredicts; whereas, ESBGK comes close to the DSMC results. On the other hand, both the statistical/DSMC and deterministic/DGFS methods, segregated in perspectives, yet, yield inextricable results, bespeaking the ingenuity of Graeme Bird who laid down the foundation of practical rarefied gas dynamics for microsystems.