Gas kinetic flux solver based finite volume weighted essentially non-oscillatory scheme for inviscid compressible flows

A high-order gas kinetic flux solver(GKFS)is presented for simulating inviscid compressible flows.The weighted essentially non-oscillatory(WENO)scheme on a uniform mesh in the finite volume formulation is combined with the circular function-based GKFS(C-GKFS)to capture more details of the flow fields with fewer grids.Different from most of the current GKFSs,which are constructed based on the Maxwellian distribution function or its equivalent form,the C-GKFS simplifies the Maxwellian distribution function into the circular function,which ensures that the Euler or Navier-Stokes equations can be recovered correctly.This improves the efficiency of the GKFS and reduces its complexity to facilitate the practical application of engineering.Several benchmark cases are simulated,and good agreement can be obtained in comparison with the references,which demonstrates that the high-order C-GKFS can achieve the desired accuracy.

Adaptive partitioning-based discrete unified gas kinetic scheme for flows in all flow regimes

To improve the efficiency of the discrete unified gas kinetic scheme(DUGKS)in capturing cross-scale flow physics,an adaptive partitioning-based discrete unified gas kinetic scheme(ADUGKS)is developed in this work.The ADUGKS is designed from the discrete characteristic solution to the Boltzmann-BGK equation,which contains the initial distribution function and the local equilibrium state.The initial distribution function contributes to the calculation of free streaming fluxes and the local equilibrium state contributes to the calculation of equilibrium fluxes.When the contribution of the initial distribution function is negative,the local flow field can be regarded as the continuous flow and the Navier-Stokes(N-S)equations can be used to obtain the solution directly.Otherwise,the discrete distribution functions should be updated by the Boltzmann equation to capture the rarefaction effect.Given this,in the ADUGKS,the computational domain is divided into the DUGKS cell and the N-S cell based on the contribu-tion of the initial distribution function to the calculation of free streaming fluxes.In the N-S cell,the local flow field is evolved by solving the N-S equations,while in the DUGKS cell,both the discrete velocity Boltzmann equation and the correspond-ing macroscopic governing equations are solved by a modified DUGKS.Since more and more cells turn into the N-S cell with the decrease of the Knudsen number,a significant acceleration can be achieved for the ADUGKS in the continuum flow regime as compared with the DUGKS.

Kinetic Model of Gaseous Alkanes Formed from Coal in a Confined System and Its Application to Gas Filling History in Kuqa Depression,Tarim Basin,Northwest China

Based on the pyrolysis products for the Jurassic low-mature coal under programmed temperature,and chemical and carbon isotopic compositions of natural gas from the Kuqa Depression, the genetic origin of natural gas was determined,and then a gas filling model was established,in combination with the geological background of the Kuqa Depression.The active energy of CH_4,C_2H_6 and C_3H_8 was gotten after the data of pyrolysis gas products under different heating rates（2℃/h and 20℃/h）were fitted by the Gas Oil Ratio（GOR）Isotope Model soft.When the frequency factor（Af）was chosen as 1×10^（14）,the active energy of CH_4,C_2H_6 and C_3H_8 was 58 kcal/mol,57 kcal/mol and 54 kcal/ mol,respectively.The distributive ranges of theδ^（13）C_1,δ^（13）C_2 andδ^（13）C_3 values for the pyrolysis gas products are-35.9‰to-30.7‰,-26.2‰to-21.3‰and-26.4‰to-22.7‰,respectively.All of the natural gases from the Kuqa Depression are dominated by hydrocarbon gases,with the high gas dryness（C_1/C_（1-4））at the middle and northern parts of the depression and the low values at both east and west sides and the southern part.The carbon isotopes of methane and its homologs as a typical coal-type gas are enriched in ^（13）C,and the distributive range of theδ^（13）C_1,δ^（13）C_2 andδ^（13）C_3 value is-32‰to -38‰,-22‰to-24‰and-20‰to-22‰,respectively,with the carbon isotopes of gaseous alkanes being less negative with the carbon number.With the ethane being enriched in ^（13）C the increasing tendency of the geological reserve of natural gas in the Kuqa Depression is observed.This observed change is consistent with the results of pyrolysate gas yield of coal as a potential gas source in the Kuqa Depression,suggesting natural gas was thermally derived from the humic organic matters and the carbon isotopes of gaseous alkanes would coarsely predict the geological reserve of gas in the Kuqa Depression.Through the simulation of kinetic processes of gas generation for the Jurassic coal in the Kuqa Depression,the gas in the Kela 2 gas field would get the threshold of gas expulsion after 27 Ma,be expelled out of source rocks as＂pulse action＂,and then filled in the gas reservoir.The peak gas-filling history took place during the past 2 Ma.

Gas-kinetic numerical method for solving mesoscopic velocity distribution function equation

A gas-kinetic numerical method for directly solving the mesoscopic velocity distribution function equation is presented and applied to the study of three-dimensional complex flows and micro-channel flows covering various flow regimes. The unified velocity distribution function equation describing gas transport phenomena from rarefied transition to continuum flow regimes can be presented on the basis of the kinetic Boltzmann-Shakhov model equation. The gas-kinetic finite-difference schemes for the velocity distribution function are constructed by developing a discrete velocity ordinate method of gas kinetic theory and an unsteady time-splitting technique from computational fluid dynamics. Gas-kinetic boundary conditions and numerical modeling can be established by directly manipulating on the mesoscopic velocity distribution function. A new Gauss-type discrete velocity numerical integra- tion method can be developed and adopted to attack complex flows with different Mach numbers. HPF paral- lel strategy suitable for the gas-kinetic numerical method is investigated and adopted to solve three-dimensional complex problems. High Mach number flows around three-dimensional bodies are computed preliminarilywith massive scale parallel. It is noteworthy and of practical importance that the HPF parallel algorithm for solving three-dimensional complex problems can be effectively developed to cover various flow regimes. On the other hand, the gas-kinetic numerical method is extended and used to study micro-channel gas flows including the classical Couette flow, the Poiseuillechannel flow and pressure-driven gas flows in twodimensional short micro-channels. The numerical experience shows that the gas-kinetic algorithm may be a powerful tool in the numerical simulation of microscale gas flows occuring in the Micro-Electro-Mechanical System （MEMS）.

THE ASYMPTOTIC PRESERVING UNIFIED GAS KINETIC SCHEME FOR GRAY RADIATIVE TRANSFER EQUATIONS ON DISTORTED QUADRILATERAL MESHES

In this paper,we consider the multi-dimensional asymptotic preserving unified gas kinetic scheme for gray radiative transfer equations on distorted quadrilateral meshes.Different from the former scheme [J.Comput.Phys.285（2015）,265-279] on uniform meshes,in this paper,in order to obtain the boundary fluxes based on the framework of unified gas kinetic scheme（UGKS）,we use the real multi-dimensional reconstruction for the initial data and the macro-terms in the equation of the gray transfer equations.We can prove that the scheme is asymptotic preserving,and especially for the distorted quadrilateral meshes,a nine-point scheme [SIAM J.SCI.COMPUT.30（2008）,1341-1361] for the diffusion limit equations is obtained,which is naturally reduced to standard five-point scheme for the orthogonal meshes.The numerical examples on distorted meshes are included to validate the current approach.

Pseudopotential-based discrete unified gas kinetic scheme for modeling multiphase fluid flows

To directly incorporate the intermolecular interaction effects into the discrete unified gas-kinetic scheme(DUGKS)for simulations of multiphase fluid flow,we developed a pseudopotential-based DUGKS by coupling the pseudopotential model that mimics the intermolecular interaction into DUGKS.Due to the flux reconstruction procedure,additional terms that break the isotropic requirements of the pseudopotential model will be introduced.To eliminate the influences of nonisotropic terms,the expression of equilibrium distribution functions is reformulated in a moment-based form.With the isotropy-preserving parameter appropriately tuned,the nonisotropic effects can be properly canceled out.The fundamental capabilities are validated by the flat interface test and the quiescent droplet test.It has been proved that the proposed pseudopotential-based DUGKS managed to produce and maintain isotropic interfaces.The isotropy-preserving property of pseudopotential-based DUGKS in transient conditions is further confirmed by the spinodal decomposition.Stability superiority of the pseudopotential-based DUGKS over the lattice Boltzmann method is also demonstrated by predicting the coexistence densities complying with the van der Waals equation of state.By directly incorporating the intermolecular interactions,the pseudopotential-based DUGKS offers a mesoscopic perspective of understanding multiphase behaviors,which could help gain fresh insights into multiphase fluid flow.

A Gas Kinetic Scheme for the Simulation of Compressible Multicomponent Flows

In this paper,a gas kinetic scheme for the compressible multicomponent flows is presented by making use of two-species BGK model in[A.D.Kotelnikov and D.C.Montgomery,A Kinetic Method for Computing Inhomogeneous Fluid Behavior,J.Comput.Phys.134(1997)364-388].Different from the conventional BGK model,the collisions between different species are taken into consideration.Based on the Chapman-Enskog expansion,the corresponding macroscopic equations are derived from this two-species model.Because of the relaxation terms in the governing equations,the method of operator splitting is applied.In the hyperbolic part,the integral solutions of the BGK equations are used to construct the numerical fluxes at the cell interface in the framework of finite volume method.Numerical tests are presented in this paper to validate the current approach for the compressible multicomponent flows.The theoretical analysis on the spurious oscillations at the interface is also presented.

Kinetics and model of gas generation of source rocks in the deepwater area, Qiongdongnan Basin

In order to investigate the hydrocarbon generation process and gas potentials of source rocks in deepwater area of the Qiongdongnan Basin, kinetic parameters of gas generation （activation energy distribution and frequency factor） of the Yacheng Formation source rocks （coal and neritic mudstones） was determined by thermal simulation experiments in the closed system and the specific KINETICS Software. The results show that the activation energy （Ea） distribution of C1–C5 generation ranges from 50 to 74 kcal/mol with a frequency factor of 2.4×1015 s–1 for the neritic mudstone and the Ea distribution of C1–C5 generation ranges from 49 to 73 kcal/mol with a frequency factor of 8.92×1013 s–1 for the coal. On the basis of these kinetic parameters and combined with the data of sedimentary burial and paleothermal histories, the gas generation model of the Yacheng Formation source rocks closer to geological condition was worked out, indicating its main gas generation stage at Ro （vitrinite reflectance） of 1.25%–2.8%. Meanwhile, the gas generation process of the source rocks of different structural locations （central part, southern slope and south low uplift） in the Lingshui Sag was simulated. Among them, the gas generation of the Yacheng Formation source rocks in the central part and the southern slope of the sag entered the main gas window at 10 and 5 Ma respectively and the peak gas generation in the southern slope occurred at 3 Ma. The very late peak gas generation and the relatively large gas potential indices （GPI：20×10^8–60×10^8 m^3/km^2） would provide favorable conditions for the accumulation of large natural gas reserves in the deepwater area.

Synthesis of Gas Transport through Nano Composite Ceramic Membrane for Esterification and Volatile Organic Compound Separations

The transport behaviour of carrier gases with inorganic catalytic ceramic membrane used for ethyl lactate production and VOC （volatile organic compound） recovery in the gauge pressure range of 0.10-1.00 bar and temperature range of 333 K was investigated. The gases include Ar （argon）, N2 （nitrogen） and CO2 （carbon dioxide）. The gas kinetic diameter with respect to permenace was found to occur in the order of At 〉 CO2 〉 N2, which was not in agreement with molecular sieving mechanism of transport after the first dip-coating of the support. However, gas flow rate was found to increase with gauge pressure in the order of Ar 〉 CO2 〉 N2, indicating Knudsen mechanism of transport. The porous ceramic support showed a higher flux indicating Knudsen transport. The surface image of the dip-coated porous ceramic membrane was characterised using SEM （scanning electron microscopy） to determine the surface morphology of the porous support at 333 K.

Direct modeling for computational fluid dynamics

All fluid dynamic equations are valid under their modeling scales, such as the particle mean free path and mean collision time scale of the Boltzmann equation and the hydrodynamic scale of the Navier-Stokes （NS） equations. The current computational fluid dynamics （CFD） focuses on the numerical solution of partial differential equations （PDEs）, and its aim is to get the accurate solution of these governing equations. Under such a CFD practice, it is hard to develop a unified scheme that covers flow physics from kinetic to hydrodynamic scales continuously because there is no such governing equation which could make a smooth transition from the Boltzmann to the NS modeling. The study of fluid dynamics needs to go beyond the traditional numer- ical partial differential equations. The emerging engineering applications, such as air-vehicle design for near-space flight and flow and heat transfer in micro-devices, do require fur- ther expansion of the concept of gas dynamics to a larger domain of physical reality, rather than the traditional dis- tinguishable governing equations. At the current stage, the non-equilibrium flow physics has not yet been well explored or clearly understood due to the lack of appropriate tools. Unfortunately, under the current numerical PDE approach, it is hard to develop such a meaningful tool due to the absence of valid PDEs. In order to construct multiscale and multiphysics simulation methods similar to the modeling process of con- structing the Boltzmann or the NS governing equations, the development of a numerical algorithm should be based on the first principle of physical modeling. In this paper, instead of following the traditional numerical PDE path, we introduce direct modeling as a principle for CFD algorithm develop- ment. Since all computations are conducted in a discretized space with limited cell resolution, the flow physics to be mod- eled has to be done in the mesh size and time step scales. Here, the CFD is more or less a direct construction of dis- crete numerical evolution equations, where the mesh size and time step will play dynamic roles in the modeling process. With the variation of the ratio between mesh size and local particle mean free path, the scheme will capture flow physics from the kinetic particle transport and collision to the hydro- dynamic wave propagation. Based on the direct modeling, a continuous dynamics of flow motion will be captured in the unified gas-kinetic scheme. This scheme can be faithfully used to study the unexplored non-equilibrium flow physics in the transition regime.

Effect of the particle temperature on lift force of nanoparticle in a shear rarefied flow

The nanoparticles suspended in a shear flow are subjected to a shear lift force,which is of great importance for the nanoparticle transport.In previous theoretical analysis on the shear lift,it is usually assumed that the particle temperature is equal to the temperature of the surrounding gas media.However,in some particular applications,the particle temperature can significantly differ from the gas temperature.In the present study,the effect of particle temperature on the shear lift of nanoparticles is investigated and the corresponding formulas of shear lift force are derived based on the gas kinetic theory.For extremely small nanoparticles(with radius R<2 nm)or large nanoparticles(R>20 nm),the influence of the particle temperature can be neglected.For the intermediate particle size,the relative error induced by the equal gas–particle temperature can be significant.Our findings can bring an insight into accurate evaluation of the nanoparticle transport properties.

A Modified Gas-Kinetic Scheme for Turbulent Flow

The implementation of a turbulent gas-kinetic scheme into a finite-volume RANS solver is put forward,with two turbulent quantities,kinetic energy and dissipation,supplied by an allied turbulence model.This paper shows a number of numerical simulations of flow cases including an interaction between a shock wave and a turbulent boundary layer,where the shock-turbulent boundary layer is captured in a much more convincing way than it normally is by conventional schemes based on the Navier-Stokes equations.In the gas-kinetic scheme,the modeling of turbulence is part of the numerical scheme,which adjusts as a function of the ratio of resolved to unresolved scales of motion.In so doing,the turbulent stress tensor is not constrained into a linear relation with the strain rate.Instead it is modeled on the basis of the analogy between particles and eddies,without any assumptions on the type of turbulence or flow class.Conventional schemes lack multiscale mechanisms:the ratio of unresolved to resolved scales–very much like a degree of rarefaction–is not taken into account even if it may grow to non-negligible values in flow regions such as shocklayers.It is precisely in these flow regions,that the turbulent gas-kinetic scheme seems to provide more accurate predictions than conventional schemes.

Hyperbolic Moment Equations in Kinetic Gas Theory Based on Multi-Variate Pearson-IV-Distributions

In this paper we develop a new closure theory for moment approximationsin kinetic gas theory and derive hyperbolic moment equations for 13 fluid variablesincluding stress and heat flux. Classical equations have either restricted hyperbolicity regions like Grad’s moment equations or fail to include higher moments in apractical way like the entropy maximization approach. The new closure is based onPearson-Type-IV distributions which reduce to Maxwellians in equilibrium, but allowanisotropies and skewness in non-equilibrium. The closure relations are essentiallyexplicit and easy to evaluate. Hyperbolicity is shown numerically for a large range ofvalues. Numerical solutions of Riemann problems demonstrate the capability of thenew equations to handle strong non-equilibrium.

An implicit parallel UGKS solver for flows covering various regimes

This paper presents an engineering-oriented UGKS solver package developed in China Aerodynamics Research and Development Center(CARDC).The solver is programmed in Fortran language and uses structured body-fitted mesh,aiming for predicting aerodynamic and aerothermodynamics characteristics in flows covering various regimes on complex three-dimensional configurations.The conservative discrete ordinate method and implicit implementation are incorporated.Meanwhile,a local mesh refinement technique in the velocity space is developed.The parallel strategies include MPI and OpenMP.Test cases include a wedge,a cylinder,a 2D blunt cone,a sphere,and a X38-like vehicle.Good agreements with experimental or DSMC results have been achieved.

A Comparison and Unification of Ellipsoidal Statistical and Shakhov BGK Models

The Ellipsoidal Statistical model(ES-model)and the Shakhov model(S-model)were constructed to correct the Prandtl number of the original BGK model through the modification of stress and heatflux.With the introduction of a new pa-rameter to combine the ES-model and S-model,a generalized kinetic model can be developed.This new model can give the correct Navier-Stokes equations in the con-tinuumflow regime.Through the adjustment of the new parameter,it provides abun-dant dynamic effect beyond the ES-model and S-model.Changing the free parameter,the physical performance of the new model has been tested numerically.The unified gas kinetic scheme(UGKS)is employed for the study of the new model.In transitionflow regime,many physical problems,i.e.,the shock structure and micro-flows,have been studied using the generalized model.With a careful choice of the free parameter,good results can be achieved for most test cases.Due to the property of the Boltz-mann collision integral,the new parameter in the generalized kinetic model cannot be fully determined.It depends on the specific problem.Generally speaking,the S-model predicts more accurate numerical solutions in most test cases presented in this paper than the ES-model,while ES-model performs better in the cases where theflow is mostly driven by temperature gradient,such as a channelflow with large boundary temperature variation at high Knudsen number.