A new discrete Boltzmann model, the discrete ellipsoidal statistical Bhatnagar-Gross-Krook （ES- BGK） model, is proposed to simulate nonequilibrium compressible flows. Compared with the original discrete BGK model, t...A new discrete Boltzmann model, the discrete ellipsoidal statistical Bhatnagar-Gross-Krook （ES- BGK） model, is proposed to simulate nonequilibrium compressible flows. Compared with the original discrete BGK model, the discrete ES-BGK has a flexible Prandtl number. For the discrete ES-BGK model in the Burnett level, two kinds of discrete velocity model are introduced and the relations between nonequilibrium quantities and the viscous stress and heat flux in the Burnett level are established. The model is verified via four benchmark tests. In addition, a new idea is introduced to recover the actual distribution function through the macroscopic quantities and their space derivatives. The recovery scheme works not only for discrete Boltzmann simulation but also for hydrodynamic ones, for example, those based on the Navier-Stokes or the Burnett equations.展开更多
This paper reports the PVTx properties of R22/R152a system in the ranges of temperature from 298.15 K to 353.15 K and pressure from 0.288 MPa to 1.288 MPa. Sixty seven PVTx measurements for three compositions, i.e., 0...This paper reports the PVTx properties of R22/R152a system in the ranges of temperature from 298.15 K to 353.15 K and pressure from 0.288 MPa to 1.288 MPa. Sixty seven PVTx measurements for three compositions, i.e., 0.2712, 0.4094 and 0.7911 mole fraction of R22, have been measured along 16 isotherms. The uncertainties of temperature and pressure measurements are less than 0.01 K and ±500 Pa respectively. The reliability of the experimental measurements is confirmed by using REFPROP program, a computer program suggested by Morrison et al[4].展开更多
It is shown that the basis of the ellipsoidal acoustic infinite elementBurnett method, the multipole expansion, cannot represent real ellipsoidal acoustic field exactly.To solve the problem, a weight of angular direct...It is shown that the basis of the ellipsoidal acoustic infinite elementBurnett method, the multipole expansion, cannot represent real ellipsoidal acoustic field exactly.To solve the problem, a weight of angular direction is added to the multipole expansion. Thecomparison of the modified method and the prime method shows that the modified method can describeand solve the ellipsoidal acoustic field more accurately than ever. A dilating sphere is used totest the new method further. Unlike other infinite element methods, varied ratio of the ellipsoidalartificial boundary instead of sphere is used. The pressure value of the artificial boundary isutilized as the initial value of the new method. Then the radiating phenomena of the ellipsoidalacoustic field can be researched using the new method. These examples show the feasibility of theadaptive method.展开更多
In [16] a visco-elastic relaxation system, called the relaxed Burnett system, was proposed by Jin and Slemrod as a moment approximation to the Boltzmann equation. The relaxed Burnett system is weakly parabolic, has a ...In [16] a visco-elastic relaxation system, called the relaxed Burnett system, was proposed by Jin and Slemrod as a moment approximation to the Boltzmann equation. The relaxed Burnett system is weakly parabolic, has a linearly hyperbolic convection part, and is endowed with a generalized entropy inequality. It agrees with the solution of the Boltzmann equation up to the Burnett order via the Chapman-Enskog expansion. We develop a one-dimensional non-oscillatory numerical scheme based on the relaxed Burnett system for the Boltzmann equation. We compare numerical results for stationary shocks based on this relaxation scheme, and those obtained by the DSMC (Direct Simulation Monte Carlo), by the Navier-Stokes equations and by the extended thermodynamics with thirteen moments (the Grad equations). Our numerical experiments show that the relaxed Burnett gives more accurate approximations to the shock profiles of the Boltzmann equation obtained by the DSMC, for a range of Mach numbers for hypersonic flows, than those obtained by the other hydrodynamic systems.展开更多
This paper reports the PVT x properties of R22/R152a system in the ranges of temperature from 298.15K to 353.15K and pressure from 0.288 MPa to 1.288 MPa. Sixty seven PVT x measurements for three compositions, i...This paper reports the PVT x properties of R22/R152a system in the ranges of temperature from 298.15K to 353.15K and pressure from 0.288 MPa to 1.288 MPa. Sixty seven PVT x measurements for three compositions, i.e., 0.2712, 0.4094 and 0.7911 mole fraction of R22, have been measured along 16 isotherms. The uncertainties of temperature and pressure measurements are less than ±0.01K and ±500 Pa respectively. The reliability of the experimental measurements is confirmed by the CSD equation.展开更多
The Lorentz gas, a point particle making mirror-like reflections from an extended collection of scatterers,has been a useful model of deterministic diffusion and related statistical properties for over a century. This...The Lorentz gas, a point particle making mirror-like reflections from an extended collection of scatterers,has been a useful model of deterministic diffusion and related statistical properties for over a century. This survey summarises recent results, including periodic and aperiodic models, finite and infinite horizon, external fields, smooth or polygonal obstacles, and in the Boltzmann–Grad limit. New results are given for several moving particles and for obstacles with flat points. Finally, a variety of applications are presented.展开更多
A novel ellipsoidal acoustic infinite element is proposed. It is based a new pressure representation, which can describe and solve the ellipsoidal acoustic field more exactly. The shape functions of this novel acousti...A novel ellipsoidal acoustic infinite element is proposed. It is based a new pressure representation, which can describe and solve the ellipsoidal acoustic field more exactly. The shape functions of this novel acoustic infinite element are similar to the (Burnett's) method, while the weight functions are defined as the product of the complex conjugates of the shaped functions and an additional weighting factor. The code of this method is cheap to generate as for 1-D element because only 1-D integral needs to be numerical. Coupling with the standard finite element, this method provides a capability for very efficiently modeling acoustic fields surrounding structures of virtually any practical shape. This novel method was deduced in brief and the conclusion was kept in detail. To test the feasibility of this novel method efficiently,in the examples the infinite elements were considered,excluding the finite elements relative. This novel ellipsoidal acoustic infinite element can deduce the analytic solution of an oscillating sphere. The example of a prolate spheroid shows that the novel infinite element is superior to the boundary element and other acoustic infinite elements. Analytical and numerical results of these examples show that this novel method is feasible.展开更多
从2001年起,总部设在瑞士的非营利组织ACT Responsible (Advertising Community Together,广告界联合)就开始在全球收集那些唤起人们对可持续性、合理发展及社会责任关注的广告,意在强调广告业人士的创造性在解决这些世界问题上能做出...从2001年起,总部设在瑞士的非营利组织ACT Responsible (Advertising Community Together,广告界联合)就开始在全球收集那些唤起人们对可持续性、合理发展及社会责任关注的广告,意在强调广告业人士的创造性在解决这些世界问题上能做出怎样的贡献。本年度,超过40个国家的140多家获奖广告机构递交了作品。这2500件关注环境和社会问题的广告作品涵盖的范围包括:森林砍伐、循环利用、保护水源、气候变化等等。展开更多
Stress boundary conditions for the lattice Boltzmann equation that are consistent to Burnett order are proposed and imposed using a moment-based method.The accuracy of the method with complicated spatially-dependent b...Stress boundary conditions for the lattice Boltzmann equation that are consistent to Burnett order are proposed and imposed using a moment-based method.The accuracy of the method with complicated spatially-dependent boundary conditions for stress and velocity is investigated using the regularized lid-driven cavity flow.The complete set of boundary conditions,which involve gradients evaluated at the boundaries,are implemented locally.A recently-derived collision operator with modified equilibria and velocity-dependent collision rates to reduce the defect in Galilean invariance is also investigated.Numerical results are in excellent agreement with existing benchmark data and exhibit second-order convergence.The lattice Boltzmann stress field is studied and shown to depart significantly from the Newtonian viscous stress when the ratio of Mach to Reynolds numbers is not negligibly small.展开更多
基金The authors would like to acknowledge the support of the National Natural Science Foundation of China （Grant Nos. 11475028, 11772064, 11502117, and U1530261）, and Science Challenge Project （Grant Nos. JCKY2016212A501 and TZ2016002）.
文摘A new discrete Boltzmann model, the discrete ellipsoidal statistical Bhatnagar-Gross-Krook （ES- BGK） model, is proposed to simulate nonequilibrium compressible flows. Compared with the original discrete BGK model, the discrete ES-BGK has a flexible Prandtl number. For the discrete ES-BGK model in the Burnett level, two kinds of discrete velocity model are introduced and the relations between nonequilibrium quantities and the viscous stress and heat flux in the Burnett level are established. The model is verified via four benchmark tests. In addition, a new idea is introduced to recover the actual distribution function through the macroscopic quantities and their space derivatives. The recovery scheme works not only for discrete Boltzmann simulation but also for hydrodynamic ones, for example, those based on the Navier-Stokes or the Burnett equations.
文摘This paper reports the PVTx properties of R22/R152a system in the ranges of temperature from 298.15 K to 353.15 K and pressure from 0.288 MPa to 1.288 MPa. Sixty seven PVTx measurements for three compositions, i.e., 0.2712, 0.4094 and 0.7911 mole fraction of R22, have been measured along 16 isotherms. The uncertainties of temperature and pressure measurements are less than 0.01 K and ±500 Pa respectively. The reliability of the experimental measurements is confirmed by using REFPROP program, a computer program suggested by Morrison et al[4].
文摘It is shown that the basis of the ellipsoidal acoustic infinite elementBurnett method, the multipole expansion, cannot represent real ellipsoidal acoustic field exactly.To solve the problem, a weight of angular direction is added to the multipole expansion. Thecomparison of the modified method and the prime method shows that the modified method can describeand solve the ellipsoidal acoustic field more accurately than ever. A dilating sphere is used totest the new method further. Unlike other infinite element methods, varied ratio of the ellipsoidalartificial boundary instead of sphere is used. The pressure value of the artificial boundary isutilized as the initial value of the new method. Then the radiating phenomena of the ellipsoidalacoustic field can be researched using the new method. These examples show the feasibility of theadaptive method.
基金Supported by NSF grant DMS-0196106 Supported by NSF grant DMS-9803223 and DMS-00711463.
文摘In [16] a visco-elastic relaxation system, called the relaxed Burnett system, was proposed by Jin and Slemrod as a moment approximation to the Boltzmann equation. The relaxed Burnett system is weakly parabolic, has a linearly hyperbolic convection part, and is endowed with a generalized entropy inequality. It agrees with the solution of the Boltzmann equation up to the Burnett order via the Chapman-Enskog expansion. We develop a one-dimensional non-oscillatory numerical scheme based on the relaxed Burnett system for the Boltzmann equation. We compare numerical results for stationary shocks based on this relaxation scheme, and those obtained by the DSMC (Direct Simulation Monte Carlo), by the Navier-Stokes equations and by the extended thermodynamics with thirteen moments (the Grad equations). Our numerical experiments show that the relaxed Burnett gives more accurate approximations to the shock profiles of the Boltzmann equation obtained by the DSMC, for a range of Mach numbers for hypersonic flows, than those obtained by the other hydrodynamic systems.
文摘This paper reports the PVT x properties of R22/R152a system in the ranges of temperature from 298.15K to 353.15K and pressure from 0.288 MPa to 1.288 MPa. Sixty seven PVT x measurements for three compositions, i.e., 0.2712, 0.4094 and 0.7911 mole fraction of R22, have been measured along 16 isotherms. The uncertainties of temperature and pressure measurements are less than ±0.01K and ±500 Pa respectively. The reliability of the experimental measurements is confirmed by the CSD equation.
文摘The Lorentz gas, a point particle making mirror-like reflections from an extended collection of scatterers,has been a useful model of deterministic diffusion and related statistical properties for over a century. This survey summarises recent results, including periodic and aperiodic models, finite and infinite horizon, external fields, smooth or polygonal obstacles, and in the Boltzmann–Grad limit. New results are given for several moving particles and for obstacles with flat points. Finally, a variety of applications are presented.
文摘A novel ellipsoidal acoustic infinite element is proposed. It is based a new pressure representation, which can describe and solve the ellipsoidal acoustic field more exactly. The shape functions of this novel acoustic infinite element are similar to the (Burnett's) method, while the weight functions are defined as the product of the complex conjugates of the shaped functions and an additional weighting factor. The code of this method is cheap to generate as for 1-D element because only 1-D integral needs to be numerical. Coupling with the standard finite element, this method provides a capability for very efficiently modeling acoustic fields surrounding structures of virtually any practical shape. This novel method was deduced in brief and the conclusion was kept in detail. To test the feasibility of this novel method efficiently,in the examples the infinite elements were considered,excluding the finite elements relative. This novel ellipsoidal acoustic infinite element can deduce the analytic solution of an oscillating sphere. The example of a prolate spheroid shows that the novel infinite element is superior to the boundary element and other acoustic infinite elements. Analytical and numerical results of these examples show that this novel method is feasible.
文摘从2001年起,总部设在瑞士的非营利组织ACT Responsible (Advertising Community Together,广告界联合)就开始在全球收集那些唤起人们对可持续性、合理发展及社会责任关注的广告,意在强调广告业人士的创造性在解决这些世界问题上能做出怎样的贡献。本年度,超过40个国家的140多家获奖广告机构递交了作品。这2500件关注环境和社会问题的广告作品涵盖的范围包括:森林砍伐、循环利用、保护水源、气候变化等等。
文摘Stress boundary conditions for the lattice Boltzmann equation that are consistent to Burnett order are proposed and imposed using a moment-based method.The accuracy of the method with complicated spatially-dependent boundary conditions for stress and velocity is investigated using the regularized lid-driven cavity flow.The complete set of boundary conditions,which involve gradients evaluated at the boundaries,are implemented locally.A recently-derived collision operator with modified equilibria and velocity-dependent collision rates to reduce the defect in Galilean invariance is also investigated.Numerical results are in excellent agreement with existing benchmark data and exhibit second-order convergence.The lattice Boltzmann stress field is studied and shown to depart significantly from the Newtonian viscous stress when the ratio of Mach to Reynolds numbers is not negligibly small.
文摘导演:吉米·淘沃德(Jimmy Hayward)斯蒂夫·马蒂诺(Steve Martino)配音:吉姆·凯瑞(Jim Carrey)斯蒂夫·卡莱尔(Steve Carell)凯罗尔·伯内特(Carol Burnett)塞斯·罗根(Seth Rogen)类型:冒险/动画/家庭片长:88分钟级别:G级发行:20世纪福克斯(20th Century Fox Animation)上映日期:2008年3月14日(美国)推荐指数:★★★★剧情简介森林里天真可爱的小象霍顿(吉姆·凯瑞配音)快乐地享受着每天无忧无虑的生活.但突然有一天,一个惊人的发现.彻底改变了它的生活乃至它在所有动物眼中的可爱形象.
