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Empirical gas–surface interaction models, such as the Maxwell model and the Cercignani–Lampis model, are widely used as the boundary condition in rarefied gas flow simulations. The accuracy of these models in the prediction of macroscopic behavior of rarefied gas flows is less satisfactory in some cases especially the highly non-equilibrium ones. Molecular dynamics simulation can accurately resolve the gas–surface interaction process at atomic scale, and hence can predict accurate macroscopic behavior. They are however too computationally expensive to be applied in real problems. In this work, a statistical physical-based gas–surface interaction model, which complies with the basic relations of boundary condition, is developed based on the framework of the washboard model. In virtue of its physical basis, this new model is capable of capturing some important relations/trends for which the classic empirical models fail to model correctly. As such, the new model is much more accurate than the classic models, and in the meantime is more efficient than MD simulations. Therefore, it can serve as a more accurate and efficient boundary condition for rarefied gas flow simulations. [ABSTRACT FROM AUTHOR]

A major challenge for the conventional Direct Simulation Monte Carlo ( DSMC ) technique lies in the fact that its computational cost becomes prohibitive in the near continuum regime, where the Knudsen number ( Kn )—characterizing the degree of rarefaction—becomes small. In contrast, the Fokker–Planck ( FP ) based particle Monte Carlo scheme allows for computationally efficient simulations of rarefied gas flows in the low and intermediate Kn regime. The Fokker–Planck collision operator—instead of performing binary collisions employed by the DSMC method—integrates continuous stochastic processes for the phase space evolution in time. This allows for time step and grid cell sizes larger than the respective collisional scales required by DSMC . Dynamically switching between the FP and the DSMC collision operators in each computational cell is the basis of the combined FP-DSMC method, which has been proven successful in simulating flows covering the whole Kn range. Until recently, this algorithm had only been applied to two-dimensional test cases. In this contribution, we present the first general purpose implementation of the combined FP-DSMC method. Utilizing both shared- and distributed-memory parallelization, this implementation provides the capability for simulations involving many particles and complex geometries by exploiting state of the art computer cluster technologies. [ABSTRACT FROM AUTHOR]

A new numerical methodology associated with a unified treatment is presented to solve the Boltzmann–BGK equation of gas dynamics for the classical and quantum gases described by the Bose–Einstein and Fermi–Dirac statistics. Utilizing a class of globally-stiffly-accurate implicit–explicit Runge–Kutta scheme for the temporal evolution, associated with the discrete ordinate method for the quadratures in the momentum space and the weighted essentially non-oscillatory method for the spatial discretization, the proposed scheme is asymptotic-preserving and imposes no non-linear solver or requires the knowledge of fugacity and temperature to capture the flow structures in the hydrodynamic (Euler) limit. The proposed treatment overcomes the limitations found in the work by Yang and Muljadi (2011) [33] due to the non-linear nature of quantum relations, and can be applied in studying the dynamics of a gas with internal degrees of freedom with correct values of the ratio of specific heat for the flow regimes for all Knudsen numbers and energy wave lengths. The present methodology is numerically validated with the unified treatment by the one-dimensional shock tube problem and the two-dimensional Riemann problems for gases of arbitrary statistics. Descriptions of ideal quantum gases including rotational degrees of freedom have been successfully achieved under the proposed methodology. [ABSTRACT FROM AUTHOR]

Recently, Fokker–Planck based particle Monte Carlo schemes have been proposed and evaluated for simulations of rarefied gas flows [1–3] . In this paper, the variance reduction for particle Monte Carlo simulations based on the Fokker–Planck model is considered. First, deviational based schemes were derived and reviewed, and it is shown that these deviational methods are not appropriate for practical Fokker–Planck based rarefied gas flow simulations. This is due to the fact that the deviational schemes considered in this study lead either to instabilities in the case of two-weight methods or to large statistical errors if the direct sampling method is applied. Motivated by this conclusion, we developed a novel scheme based on correlated stochastic processes. The main idea here is to synthesize an additional stochastic process with a known solution, which is simultaneously solved together with the main one. By correlating the two processes, the statistical errors can dramatically be reduced; especially for low Mach numbers. To assess the methods, homogeneous relaxation, planar Couette and lid-driven cavity flows were considered. For these test cases, it could be demonstrated that variance reduction based on parallel processes is very robust and effective. [ABSTRACT FROM AUTHOR]

A Fokker–Planck based particle Monte Carlo algorithm was devised recently for simulations of rarefied gas flows by the authors [1–3] . The main motivation behind the Fokker–Planck (FP) model is computational efficiency, which could be gained due to the fact that the resulting stochastic processes are continuous in velocity space. This property of the model leads to simulations where the computational cost becomes independent of the Knudsen number (Kn) [3] . However, the Fokker–Planck model which can be seen as a diffusion approximation of the Boltzmann equation, becomes less accurate as Kn increases. In this study we propose a hybrid Fokker–Planck–Direct Simulation Monte Carlo (FP–DSMC) solution method, which is applicable for the whole range of Kn. The objective of this algorithm is to retain the efficiency of the FP scheme at low Kn ( Kn ≪ 1 ) and to employ conventional DSMC at high Kn ( Kn ≫ 1 ). Since the computational particles employed by the FP model represent the same data as in DSMC, the coupling between the two methods is straightforward. The new ingredient is a switching criterion which would ideally result in a hybrid scheme with the efficiency of the FP method and the accuracy of DSMC for the whole Kn-range. Here, we adopt the number of collisions in a given computational cell and for a given time step size as a decision criterion in order to switch between the FP model and DSMC. For assessment of the hybrid algorithm, different test cases including flow impingement and flow expansion through a slit were studied. Both accuracy and efficiency of the model are shown to be excellent for the presented test cases. [ABSTRACT FROM AUTHOR]

Abstract: A unified gas-kinetic scheme (UGKS) is constructed for both continuum and rarefied flow computations. The underlying principle for the development of UGKS is the direct modeling for the gas evolution process from the kinetic to the hydrodynamic scale, which is used in the flux construction across a cell interface. More specifically, the physical process from the kinetic particle free transport to the hydrodynamic pressure wave propagation is recovered in the flux function. In the previous study, the UGKS has been developed mainly for monatomic gas with particle translational motion only. The construction of time evolution solution is based on the BGK, Shakhov, and ES–BGK models. The UGKS has been validated through extensive numerical tests. In this paper, a UGKS for diatomic gas will be constructed, where the gas-kinetic Rykov model with a Landau–Teller–Jeans-type rotational energy relaxation is used in the numerical scheme. The new scheme will be tested in many cases, such as homogeneous flow relaxation, shock structure calculations, hypersonic flow passing a flat plate, and the flow around a blunt circular cylinder. The analytic, DSMC, and experimental measurements will be used for validating the solutions of UGKS. [Copyright &y& Elsevier]

Abstract: The paper is devoted to the further development and systematic performance evaluation of a recent deterministic framework Nesvetay-3D for modelling three-dimensional rarefied gas flows. Firstly, a review of the existing discretization and parallelization strategies for solving numerically the Boltzmann kinetic equation with various model collision integrals is carried out. Secondly, a new parallelization strategy for the implicit time evolution method is implemented which improves scaling on large CPU clusters. Accuracy and scalability of the methods are demonstrated on a pressure-driven rarefied gas flow through a finite-length circular pipe as well as an external supersonic flow over a three-dimensional re-entry geometry of complicated aerodynamic shape. [Copyright &y& Elsevier]