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

Acta Mechanica Sinica 2007年第2期23卷 121-132页

作者： Zhihui Li hanxin zhang National Laboratory for Computational Fluid Dynamics Beijing 100083 China Hypervelocity Aerodynamics Institute.Mianyang 621000 China

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）.

关键词： Gas kinetic theory . Velocity distributionfunction . Boltzmann model equation .Spacecraft flows . Micro-scale gas flows

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A Lagrangian criterion of unsteady flow separation for two-dimensional periodic flows

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Applied Mathematics and Mechanics(English Edition) 2018年第7期39卷 1007-1018页

作者： Shuaibin HAN Shuhai zhang hanxin zhang State Key Laboratory of Aerodynamics China Aerodynamics Research and Development Center Mianyang 621000 Sichuan Province China China Aerodynamics Research and Development Center Mianyang 621000 Sichuan Province China

The present paper proposes a Lagrangian criterion of unsteady flow separation for two-dimensional periodic flows based on the principle of weighted averaging zero skin-friction given by Haller （HALLER, G. Exact theory of unsteady separation for two-dimensional flows. Journal of Fluid Mechanics, 512, 257-311 （2004））. By analyzing the distribution of the finite-time Lyapunov exponent （FTLE） along the no-slip wall, it can be found that the periodic separation takes place at the point of the zero FTLE. This new criterion is verified with an analytical solution of the separation bubble and a numerical simulation of lid-driven cavity flows.

关键词： Lagrangian criterion unsteady flow separation finite-time Lyapunov ex-ponent(FTLE) two-dimensional periodic flow

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Detached-eddy simulations and analyses on new vortical flows over a 76/40° double delta wing

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Science China(Physics,Mechanics & Astronomy) 2013年第6期56卷 1062-1073页

作者： LI Qin SUN Dong zhang hanxin State Key Laboratory of Aerodynamics China and National Laboratory of CFD Beijing University of Aeronautics and Astronautics

Numerical simulations were performed on the massively separated flows of a 76/40° double delta wing using detached-eddy simulation(DES).A new type of cross-flow vortex is suggested.A vortex was initially generated near the junction of the strake and wing,which then moved towards the wing tip at certain wavelength and *** were made in detail on the mechanism of the generation of the cross-flow vortex,that is,the inviscid cross-flow instability which differs from that of the swept blunt ***-section topology of the cross-flow vortex is also investigated,and the wavelength of the vortex array and the characteristic frequency are *** analyses showed that the cross-flow vortices have an influence on the pressure distribution,which can cause a 10%-20% deviation from the averaged distribution.

关键词： double delta wing massively separated flows cross-flow instability vortex substructures DES

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A class of fully third-order accurate projection methods for solving the incompressible Navier-Stokes equations

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Acta Mechanica Sinica 2005年第6期21卷 542-549页

作者： Yuxin Ren Yuxi Jiang Miao'er Liu hanxin zhang Department of Engineering Mechanics Tsinghua University Beijing 100084 China CNOOC Research Center Beijing China National Key Laboratory for CFD Beijing China

In this paper, a fully third-order accurate projection method for solving the incompressible Navier-Stokes equations is proposed. To construct the scheme, a continuous projection procedure is firstly presented. We then derive a sufficient condition for the continuous projection equations to be temporally third-order accurate approximations of the original Navier-Stokes equations by means of the localtruncation-error-analysis technique. The continuous projection equations are discretized temporally and spatially to third-order accuracy on the staggered grids, resulting in a fully third-order discrete projection scheme. The possibility to design higher-order projection methods is thus demonstrated in the present paper. A heuristic stability analysis is performed on this projection method showing the probability of its being stable. The stability of the present scheme is further verified through numerical tests. The third-order accuracy of the present projection method is validated by several numerical test cases.

关键词： Incompressible Navier-Stokes equations Projection methods - Third-order scheme - Local truncation error

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Analyses of the Dispersion Overshoot and Inverse Dissipation of the High-Order Finite Difference Scheme

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Advances in Applied Mathematics and Mechanics 2013年第6期5卷 809-824页

作者： Qin Li Qilong Guo hanxin zhang State Key Laboratory of Aerodynamics Mianyang 621000SichuanChina National Laboratory of Computational Fluid Dynamics Beijing University of Aeronautics and AstronauticsBeijing 100191China

Analyses were performed on the dispersion overshoot and inverse dissipation of the high-order finite difference scheme using Fourier and precision *** under discussion included the pointwise-and staggered-grid type,and were presented in weighted form using candidate schemes with third-order accuracy and three-point *** of these were commonly used in the construction of difference *** for the dispersion overshoot were presented and their critical states were *** kinds of instabilities were studied due to inverse dissipation,especially those that occur at lower wave *** for the occurrence were presented and the relationship of the two instabilities was *** were made between the analytical results and the dispersion/dissipation relations by Fourier transformation of typical *** an example,an application of the criteria was given for the remedy of inverse dissipation in Weirs&Mart´ın’s third-order scheme.

关键词： High-order difference scheme dispersion overshoot inverse dissipation

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A Numerical Study on Supersonic Combustion Optimization Based on the Streamwise Vortex-Couple Method

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Fluid Dynamics & Materials Processing 2023年第1期19卷 207-222页

作者： Hao Tian Yongkang Zheng hanxin zhang China Aerodynamics Research and Development Center Mianyang621000China

In this paper,some typical methods to promote mixing in supersonic combustion are reviewed,and the fluid-dynamic mechanism underpinning the development of the supersonic shear layer in the presence of a streamwise vortex is analyzed through computational fluid *** is proven that the streamwise vortex-couple method is an excellent approach to enhance mixing.A specific combustor design is proposed accordingly.

关键词： Supersonic combustion streamwise vortex numerical simulation

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Numerical study on the gas-kinetic high-order schemes for solving Boltzmann model equation

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Science China(Physics,Mechanics & Astronomy) 2011年第9期54卷 1687-1701页

作者： LI ZhiHui PENG AoPing zhang hanxin DENG XiaoGang National Laboratory for Computational Fluid Dynamics Beifing 100191 China China Aerodynamics Research and Development Center Mianyang 621000 China

The high-order compact finite difference technique is introduced to solve the Boltzmann model equation, and the gas-kinetic high-order schemes are developed to simulate the different kinetic model equations such as the BGK model, the Shakhov model and the Ellipsoidal Statistical (ES) model in this paper. The methods are tested for the one-dimensional unsteady shock-tube problems with various Knudsen numbers, the inner flows of normal shock wave for different Mach numbers, and the two-dimensional flows past a circular cylinder and a NACA 002 airfoil to verify the reliability of the present high-order algorithm and simulate gas transport phenomena covering various flow regimes. The computed results are found in good agreement both with the theoretical prediction from continuum to rarefied gas dynamics, the related DSMC solutions, and with the experimental results. The numerical effect of the schemes with the different precision and the different types of Boltzmann collision models on the computational efficiency and computed results is investigated and analyzed. The numerical experience indicates that an approach developing and applying the gas-kinetic high-order algorithm is feasible for directly solving the Boltzmann model equation.

关键词： Boltzmann model equation velocity distribution function high-order compact scheme discrete velocity ordinate method gas-kinetic high order accurate algorithm

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Hypersonic Shock Wave/Boundary Layer Interactions by a Third-Order Optimized Symmetric WENO Scheme

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Transactions of Nanjing University of Aeronautics and Astronautics 2017年第5期34卷 524-534页

作者： Li Chen Guo Qilong Li Qin zhang hanxin State Key Laboratory of Aerodynamics China Aerodynamics Research and Development Center Mianyang 621000 P. R. China Computational Aerodynamics Institute China Aerodynamics Research and Development Center Mianyang 621000 P. R. China

A novel third-order optimized symmetric weighted essentially non-oscillatory(WENO-OS3)scheme is used to simulate the hypersonic shock wave/boundary layer ***,the scheme is presented with the achievement of low dissipation in smooth region and robust shock-capturing capabilities in *** Maxwell slip boundary conditions are employed to consider the rarefied effect near the ***,several validating tests are given to show the good resolution of the WENO-OS3 scheme and the feasibility of the Maxwell slip boundary ***,hypersonic flows around the hollow cylinder truncated flare(HCTF)and the25°/55°sharp double cone are *** are made on the characteristics of the hypersonic shock wave/boundary layer interactions with and without the consideration of the slip *** results indicate that the scheme has a good capability in predicting heat transfer with a high resolution for describing fluid *** the slip boundary conditions,the separation region at the corner is smaller and the prediction is more accurate than that with no-slip boundary conditions.

关键词： hypersonic flows shock wave/boundary layer interactions weighted essentially non-oscillatory(WENO)scheme slip boundary conditions

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Implementation of the Divergence-Free and Pressure-Oscillation-Free Projection Method for Solving the Incompressible Navier-Stokes Equations on the Collocated Grids

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Communications in Computational Physics 2007年第4期2卷 746-759页

作者： Yu-Xin Ren Miao’er Liu hanxin zhang Department of Engineering Mechanics Tsinghua UniversityBeijing 100084China CNOOC Research Center Beijing 100027China National Key Laboratory for CFD Beijing 100083China.

In this paper,a divergence-free and pressure-oscillation-free projection method for solving the incompressible Navier-Stokes equations on the non-staggered grid is *** exact discrete projection method is used to compute the velocity field,which ensures the discrete divergence of the velocity field is *** order to eliminate the odd-even decoupling in the pressure field,a filtering procedure is proposed and applied to the pressure *** have shown this filter recovers the grid scale ellipticity in the pressure field and the odd-even decoupling can be removed *** proposed numerical scheme is further verified through numerical experiments.

关键词： Incompressible Navier-Stokes equations projection methods non-staggered grids pressure filtering.

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High-Order and High Accurate CFD Methods and Their Applications for Complex Grid Problems

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Communications in Computational Physics 2012年第4期11卷 1081-1102页

作者： Xiaogang Deng Meiliang Mao Guohua Tu hanxin zhang Yifeng zhang State Key Laboratory of Aerodynamics Aerodynamics Research&Development CenterMianyang621000P.R.China

The purpose of this article is to summarize our recent progress in high-order and high accurate CFD methods for flow problems with complex grids as well as to discuss the engineering prospects in using these *** the rapid development of high-order algorithms in CFD,the applications of high-order and high accurate methods on complex configurations are still *** of the main reasons which hinder the widely applications of thesemethods is the complexity of *** aspects which can be neglected for low-order schemes must be treated carefully for high-order ones when the configurations are *** order to implement highorder finite difference schemes on complex multi-block grids,the geometric conservation lawand block-interface conditions are discussed.A conservativemetricmethod is applied to calculate the grid derivatives,and a characteristic-based interface condition is employed to fulfil high-order multi-block *** fifth-order WCNS-E-5 proposed by Deng[9,10]is applied to simulate flows with complex grids,including a double-delta wing,a transonic airplane configuration,and a hypersonic X-38 *** results in this paper and the references show pleasant prospects in engineering-oriented applications of high-order schemes.

关键词： WCNS complex configurations geometric conservation law conservative metric methods characteristic-based interface conditions

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