Investigation on a coupled Navier–Stokes–Direct Simulation Monte Carlo method for the simulation of plume flowfield of a conical nozzle

To assess the plume effects of space thrusters, the accurate plume flowfield is indispensable. The plume flow of thrusters involves both continuum and rarefied flow regimes. Coupled Navier–Stokes–Direct Simulation Monte Carlo (NS–DSMC) method is a major approach to the simulation of continuum‐rarefied flows. An axisymmetric coupled NS–DSMC solver, possessing adaptive‐interface and two‐way coupling features, is investigated in this paper for the simulation of the nozzle and plume flows of thrusters. The state‐based coupling scheme is adopted, and the gradient local Knudsen number is used to indicate the breakdown of continuum solver. The nitrogen flows in a conical nozzle and its plume are chosen as the reference case to test the coupled solver. The threshold value of the continuum breakdown parameter is studied based on both theoretical kinetic velocity sampling and coupled numerical tests. Succeeding comparisons between coupled and full DSMC results demonstrate their conformities, meanwhile, the former saves 58.8% computational time. The pitot pressure evaluated from the coupled simulation result is compared with the experimental data proposed in literatures, revealing that the coupled method makes precise predictions on the experimental pitot pressure. Copyright © 2014 John Wiley & Sons, Ltd.     

Simulations for gas flows in microgeometries using the direct simulation Monte Carlo method

Micro gas flows are often encountered in MEMS devices and classical CFD could not accurately predict the flow and thermal behavior due to the high Knudsen number. Therefore, the gas flow in microgeometries was investigated using the direct simulation Monte Carlo (DSMC) method. New treatments for boundary conditions are verified by simulations of micro-Poiseuille flow, compared with the previous boundary treatments, and slip analytical solutions of the continuum theory. The orifice flow and the corner flow in microchannels are simulated using the modified DSMC codes. The predictions were compared with existing experimental phenomena as well as predictions using continuum theory. The results showed that the channel geometry significantly affects the microgas flow. In the orifice flow, the flow separation occurred at very small Reynolds numbers. In the corner flow, no flow separation occurred even with a high driving pressure. The DSMC results agreed well with existing experimental information.     

The direct simulation Monte Carlo method using unstructured adaptive mesh and its application

The implementation of an adaptive mesh‐embedding (h‐refinement) scheme using unstructured grid in two‐dimensional direct simulation Monte Carlo (DSMC) method is reported. In this technique, local isotropic refinement is used to introduce new mesh where the local cell Knudsen number is less than some preset value. This simple scheme, however, has several severe consequences affecting the performance of the DSMC method. Thus, we have applied a technique to remove the hanging node, by introducing the an‐isotropic refinement in the interfacial cells between refined and non‐refined cells. Not only does this remedy increase a negligible amount of work, but it also removes all the difficulties presented in the originals scheme. We have tested the proposed scheme for argon gas in a high‐speed driven cavity flow. The results show an improved flow resolution as compared with that of un‐adaptive mesh. Finally, we have used triangular adaptive mesh to compute a near‐continuum gas flow, a hypersonic flow over a cylinder. The results show fairly good agreement with previous studies. In summary, the proposed simple mesh adaptation is very useful in computing rarefied gas flows, which involve both complicated geometry and highly non‐uniform density variations throughout the flow field. Copyright © 2002 John Wiley & Sons, Ltd.     

Molecular models for simulation of rarefied gas flows using direct simulation Monte Carlo method

The direct simulation Monte Carlo (DSMC) method is a technique for the numerical simulation of the rarefied gas flows by employing simulated molecules in simulated physical spaces. In the procedures involved in DSMC, the accuracy of the simulation of intermolecular collisions depends on the collision model adopted in the collision routine. The simplest molecular model is the hard-sphere model. In order to improve the accuracy of the simulations, more and more refined collision models were introduced for the use in DSMC. Thus, the variable hard-sphere, the variable soft-sphere, the generalised hard-sphere, the generalised soft-sphere and the variable sphere models were put forward by various researchers. And, all these models have met with varying degrees of success. Meanwhile, the Borgnakke-Larsen model, statistical inelastic cross-section models for both continuous and discrete internal energy and the dynamic molecular collision model were proposed for the treatment of polyatomic molecules in which transfer of energy among translational, rotational and vibrational degrees of freedom is possible. This paper gives a brief introduction to the intermolecular potentials based on which the molecular models have been constructed. Then the various models are introduced in the chronological sequence; finally concluding with a brief summary of the progress that has been made so far in this area.     

气体化学反应流动的DSMC／EPSM混合算法研究

发展了平衡粒子模拟方法(EPSM)，建立了与高温气体化学反应动力学理论相匹配的：EPSM耦合模型，并通过混合参数进行流区的自动识别，将：EPSM方法与蒙特卡罗直接模拟方法(OSMC)结合，构造了可模拟化学反应流动的DSMC／EPSM混合算法。应用该算法对汲及化学反应的二维高超音速竖板绕流流场进行模拟，将结果与DSMC方法的结果进行比较，验证了新算法对求解化学反应流动的可行性。将混合算法的计算效率与DSMC方法的计算效率进行比较，发现混合算法能够大大提高计算效率。     

DSMC／EPSM混合算法研究

将EPSM算法与DSMC方法结合，构造了可模拟含近连续流区及过渡流区的DSMC/EPSM混合算法。运用混合算法模拟了马赫数等于5时超音速竖板绕流及马赫数等于4时超音速平板绕流，并将结果与DSMC算法的结果进行比较，证明了DSMC／EPSM混合算法的有效性，同时将EPSM算法与DSMC算法的效率进行了比较。     

Variance‐reduced Monte Carlo solutions of the Boltzmann equation for low‐speed gas flows: A discontinuous Galerkin formulation

We present and discuss an efficient, high‐order numerical solution method for solving the Boltzmann equation for low‐speed dilute gas flows. The method's major ingredient is a new Monte Carlo technique for evaluating the weak form of the collision integral necessary for the discontinuous Galerkin formulation used here. The Monte Carlo technique extends the variance reduction ideas first presented in Baker and Hadjiconstantinou (Phys. Fluids 2005; 17 , art. no. 051703) and makes evaluation of the weak form of the collision integral not only tractable but also very efficient. The variance reduction, achieved by evaluating only the deviation from equilibrium, results in very low statistical uncertainty and the ability to capture arbitrarily small deviations from equilibrium (e.g. low‐flow speed) at a computational cost that is independent of the magnitude of this deviation. As a result, for low‐signal flows the proposed method holds a significant computational advantage compared with traditional particle methods such as direct simulation Monte Carlo (DSMC). Copyright © 2008 John Wiley & Sons, Ltd.     

Direct numerical test of the B-G-K model equation by the DSMC method

In the present paper the rarefied gas flow caused by the sudden change of the wall temperature and the Rayleigh problem are simulated by the DSMC method which has been validated by experiments both in global flow field and velocity distribution function level. The comparison of the simulated results with the accurate numerical solution of the B-G-K model equation shows that near equilibrium the B-G-K equation with corrected collision frequency can give accurate result but as farther away from equilibrium the B-G-K equation is not accurate. This is for the first time that the error caused by the B-G-K model equation has been revealed. The project supported by the National Natural Science Foundation of China (19772059, 19889209)     

Spacecraft aerodynamics and trajectory simulation during aerobraking

This paper uses a direct simulation Monte Carlo （DSMC） approach to simulate rarefied aerodynamic characteristics during the aerobraking process of the NASA Mars Global Surveyor （MGS） spacecraft. The research focuses on the flowfield and aerodynamic characteristics distribution under various free stream densities. The vari- ation regularity of aerodynamic coefficients is analyzed. The paper also develops an aerodynamics-aeroheating-trajectory integrative simulation model to preliminarily calculate the aerobraking orbit transfer by combining the DSMC technique and the classical kinematics theory. The results show that the effect of the planetary atmospheric density, the spacecraft yaw, and the pitch attitudes on the spacecraft aerodynamics is significant. The numerical results are in good agreement with the existing results reported in the literature. The aerodynamics-aeroheating-trajectory integrative simulation model can simulate the orbit transfer in the complete aerobraking mission. The current results of the spacecraft trajectory show that the aerobraking maneuvers have good performance of attitude control.     

大尺度网格下DSMC仿真碰撞概率的修正方法

从DSMC碰撞概率的实现途径出发,通过引入最小二乘法及亚松弛的思想给出一种大尺度网格下分子仿真碰撞概率的修正方法,将该方法应用于非结构四面体网格下的DSMC模拟中,计算分析了文献中钝锥模型的绕流结果,数值结果初步验证了本文方法的合理性和有效性。     

Multi‐resolution analysis for high accuracy and efficiency of Euler computation

A multi‐resolution analysis (MRA) is proposed for efficient flow computation with preserving the high‐order numerical accuracy of a conventional solver. In the MRA process, the smoothness of a flow pattern is assessed by the difference between original flow property values, and the values approximated by high‐order interpolating polynomial in decomposition. Insignificant data in smooth region are discarded, and flux computation is performed only where crucial features of a solution exist. The reduction of expensive flow computation improves the overall computational efficiency. In order to maintain the high‐order accuracy, modified thresholding procedure restricts the additional error introduced by the thresholding below the order of accuracy of a conventional solver. The practical applicability of the MRA method is validated in various continuous and discontinuous flow problems. The MRA stably computes the Euler equations for continuous and discontinuous flow problems and maintains the accuracy of a conventional solver. Overall, it substantially enhances the computational efficiency of the conventional third‐order accurate solver. Copyright © 2014 John Wiley & Sons, Ltd.     

Monte Carlo simulations on the thermodynamic properties of high‐density gases

The thermodynamic properties of Ar, H₂ and CH₄ at high‐density conditions are studied using Monte Carlo simulations. The isotherms of Ar at 500K, H₂ at 1000K and CH₄ at 500K are obtained respectively. To validate the accuracy of the simulation results, the thermodynamic properties of these gases are also studied with van der Waals equation and compared with the reference data. The agreement with reference shows that Monte Carlo method can produce reliable thermodynamic properties of high‐density gases based on the accurate intermolecular potential model. Therefore, the accuracy of the simulations depends primarily on the accuracy of the potential model, and this dependence is also discussed. Copyright © 2012 John Wiley & Sons, Ltd.     

Numerical Analysis of the Influence of Thermal Stresses on the Nonlinear Thermomolecular Pressure Difference Effect

On the basis of a numerical analysis of the non-Navier-Stokes gas-dynamic equations for slow non-isothermal gas flows, the nonlinear thermomolecular pressure difference effect due to a large temperature gradient along the lateral surface of a capillary is investigated. It is shown that the magnitude of the effect is substantially different from the values calculated using the Navier-Stokes equations. For two models of molecular interaction (Maxwell molecules and hard spheres), the possibility of a quasi-one-dimensional interpretation of the effect for experimental estimation purposes is demonstrated. The solutions of the relaxation kinetic equation for flow in a plane capillary at small Knudsen numbers and the gas-dynamic equations for slow non-isothermal flows are compared and the range of their applicability is estimated.     

An attempt to improve accuracy of higher‐order statistics and spectra in direct numerical simulation of incompressible wall turbulence by using the compact schemes for viscous terms

We attempt to improve accuracy in the high‐wavenumber region in DNS of incompressible wall turbulence such as found in fully developed turbulent channel flow. In particular, it is shown that the improvement of accuracy of viscous terms in the Navier–Stokes equations leads to the improvement of accuracy of higher‐order statistics and various spectra. It is emphasized that increase in required computational cost will not be crucial when incompressible flow is simulated, because the introduction of a higher‐order scheme into the viscous terms does not increase computational cost for solving the Poisson equation. We introduced fourth‐order and eighth‐order central compact schemes for discretizing the viscous terms in DNS of a fully developed turbulent channel flow. The results are compared with those using second‐order and fourth‐order central‐difference schemes applied to the viscous terms and those obtained by the spectral method. The results show that accuracy improvement of the viscous terms improve accuracy of higher‐order statistics (i.e., skewness and flatness factors of streamwise velocity fluctuation) and various spectra of velocity and pressure fluctuations in the high‐wavenumber region. Copyright © 2013 John Wiley & Sons, Ltd.     

Evaluation of some high‐order shock capturing schemes for direct numerical simulation of unsteady two‐dimensional free flows

The present study addresses the capability of a large set of shock‐capturing schemes to recover the basic interactions between acoustic, vorticity and entropy in a direct numerical simulation (DNS) framework. The basic dispersive and dissipative errors are first evaluated by considering the advection of a Taylor vortex in a uniform flow. Two transonic cases are also considered. The first one consists of the interaction between a temperature spot and a weak shock. This test emphasizes the capability of the schemes to recover the production of vorticity through the baroclinic process. The second one consists of the interaction of a Taylor vortex with a weak shock, corresponding to the framework of the linear theory of Ribner. The main process in play here is the production of an acoustic wave. The results obtained by using essentially non‐oscillatory (ENO), total variation diminishing (TVD), compact‐TVD and MUSCL schemes are compared with those obtained by means of a sixth‐order accurate Hermitian scheme, considered as reference. The results are as follows; the ENO schemes agree pretty well with the reference scheme. The second‐order accurate Upwind‐TVD scheme exhibits a strong numerical diffusion, while the MUSCL scheme behavior is very sensitive to the value on the parameter β in the limiter function minmod. The compact‐TVD schemes do not yield improvement over the standard TVD schemes. Copyright © 2000 John Wiley & Sons, Ltd.     

Monte Carlo simulation in the stochastic analysis of non-linear systems under external stationary Poisson white noise input

A method for the evaluation of the probability density function (p.d.f.) of the response process of non-linear systems under external stationary Poisson white noise excitation is presented. The method takes advantage of the great accuracy of the Monte Carlo simulation (MCS) in evaluating the first two moments of the response process by considering just few samples. The quasi-moment neglect closure is used to close the infinite hierarchy of the moment differential equations of the response process. Moreover, in order to determine the higher order statistical moments of the response, the second-order probabilistic information given by MCS in conjunction with the quasi-moment neglect closure leads to a set of linear differential equations. The quasi-moments up to a given order are used as partial probabilistic information on the response process in order to find the p.d.f. by means of the C-type Gram-Charlier series expansion.     

Enhancement of the accuracy of the finite volume particle method for the simulation of incompressible flows

A finite volume particle (FVP) method for simulation of incompressible flows that provides enhanced accuracy is proposed. In this enhanced FVP method, a dummy neighbor particle is introduced for each particle in the calculation and used for the discretization of the gradient model and Laplacian model. The error‐compensating term produced by introducing the dummy neighbor particle enables higher order terms to be calculated. The proposed gradient model and Laplacian model are applied in both pressure and pressure gradient calculations. This enhanced FVP scheme provides more accurate simulations of incompressible flows. Several 2‐dimensional numerical simulations are given to confirm its enhanced performance.     

Positive‐definite q‐families of continuous subcell Darcy‐flux CVD(MPFA) finite‐volume schemes and the mixed finite element method

A new family of locally conservative cell‐centred flux‐continuous schemes is presented for solving the porous media general‐tensor pressure equation. A general geometry‐permeability tensor approximation is introduced that is piecewise constant over the subcells of the control volumes and ensures that the local discrete general tensor is elliptic. A family of control‐volume distributed subcell flux‐continuous schemes are defined in terms of the quadrature parametrization q (Multigrid Methods. Birkhauser: Basel, 1993; Proceedings of the 4th European Conference on the Mathematics of Oil Recovery, Norway, June 1994; Comput. Geosci. 1998; 2 :259–290), where the local position of flux continuity defines the quadrature point and each particular scheme. The subcell tensor approximation ensures that a symmetric positive‐definite (SPD) discretization matrix is obtained for the base member (q=1) of the formulation. The physical‐space schemes are shown to be non‐symmetric for general quadrilateral cells. Conditions for discrete ellipticity of the non‐symmetric schemes are derived with respect to the local symmetric part of the tensor. The relationship with the mixed finite element method is given for both the physical‐space and subcell‐space q‐families of schemes. M‐matrix monotonicity conditions for these schemes are summarized. A numerical convergence study of the schemes shows that while the physical‐space schemes are the most accurate, the subcell tensor approximation reduces solution errors when compared with earlier cell‐wise constant tensor schemes and that subcell tensor approximation using the control‐volume face geometry yields the best SPD scheme results. A particular quadrature point is found to improve numerical convergence of the subcell schemes for the cases tested. Copyright © 2007 John Wiley & Sons, Ltd.     

Finite‐difference 4th‐order compact scheme for the direct numerical simulation of instabilities of shear layers

An algorithm based on the 4th‐order finite‐difference compact scheme is developed and applied in the direct numerical simulations of instabilities of channel flow. The algorithm is illustrated in the context of stream function formulation that leads to field equation involving 4th‐order spatial derivatives. The finite‐difference discretization in the wall‐normal direction uses five arbitrarily spaced points. The discretization coefficients are determined numerically, providing a large degree of flexibility for grid selection. The Fourier expansions are used in the streamwise direction. A hybrid Runge–Kutta/Crank–Nicholson low‐storage scheme is applied for the time discretization. Accuracy tests demonstrate that the algorithm does deliver the 4th‐order accuracy. The algorithm has been used to simulate the natural instability processes in channel flow as well as processes occurring when the flow is spatially modulated using wall transpiration. Extensions to three‐dimensional situations are suggested. Copyright © 2005 John Wiley & Sons, Ltd.     

Assessment of WENO schemes for multi‐dimensional Euler equations using GPU

This paper presents a detailed study on the implementation of Weighted Essentially Non‐Oscillatory (WENO) schemes on GPU. GPU implementation of up to ninth‐order accurate WENO schemes for the multi‐dimensional Euler equations of gas dynamics is presented. The implementation detail is discussed in the paper. The computational times of different schemes are obtained and the speedups are reported for different number of grid points. Furthermore, the execution times for the main kernels of the code are given and compared with each other. The numerical experiments show the speedups for the WENO schemes are very promising especially for fine grids. Copyright © 2014 John Wiley & Sons, Ltd.