Verification of the nature of the approximation of the Boltzmann integral by Krook's kinetic relaxation model

Up to now a significant number of aerodynamic problems have been solved with the aid of Krook's kinetic relaxation model. However, because of the absence of reliable solutions of boundary problems for the Boltzmann equation, the correctness of the assumed model of the collision integral remains unclarified. In the present paper, in order to verify the nature of the approximation of the collision operator by the given model, a machine experiment is undertaken. The Boltzmann collision operator is computed for a variety of test functions characteristic of the motion of a rarefied gas and the values obtained according to it are compared to the Krook model. Some physical hypotheses embedded in the relaxation model are also examined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 3–7, July–August, 1970.     

转轴上裂纹开闭模型的研究

本文提出了一种新的描述转轴裂纹开闭状态的数学模型,此模型描述了裂纹开、闭及过渡状态的持续过程,它将开裂纹、方波和余弦模型统一于同一模型中,它的使用不受动、静挠度关系的限制.用这个模型算得的裂纹轴刚度变化曲线与实验结果吻合程度比余弦和方波模型好.文中还以Jeffcott裂纹转子为例,对各模型进行了理论探讨.结果表明:当研究非同步运动时,本文模型与方波和余弦模型所得的解差别较大,且轴心位移矢量的方向角在静平衡位置处的波动,影响到所得响应的特性.而对同步运动,这种差别及影响都很小.     

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.     

Large-eddy simulation of the temporal mixing layer using the Clark model

The Clark model for the turbulent stress tensor in large-eddy simulation is investigated from a theoretical and computational point of view. In order to be applicable to compressible turbulent flows, the Clark model has been reformulated. Actual large-eddy simulation of a weakly compressible, turbulent, temporal mixing layer shows that the eddy-viscosity part of the original Clark model gives rise to an excessive dissipation of energy in the transitional regime. On the other hand, the model gives rise to instabilities if the eddy-viscosity part is omitted and only the gradient part is retained. A linear stability analysis of the Burgers equation supplemented with the Clark model is performed in order to clarify the nature of the instability. It is shown that the growth-rate of the instability is infinite in the inviscid limit and that sufficient (eddy-)viscosity can stabilize the model. A model which avoids both the excessive dissipation of the original Clark model as well as the instability of the gradient part, is obtained when the dynamic procedure is applied to the Clark model. Large-eddy simulation using this new dynamic Clark model is found to yield satisfactory results when compared with a filtered direct numerical simulation. Compared with the standard dynamic eddy-viscosity model, the dynamic Clark model yields more accurate predictions, whereas compared with the dynamic mixed model the new model provides equal accuracy at a lower computational effort.     

六面体单元柔性桁架结构模型与逆模型的辨识

介绍了用自适应LMS滤波器离线辨识六面体单元柔性结构模型和逆模型的方法。文中论述了自适应滤波理论和自适应逆控制之间的关系，讨论了LMS算法，并以实验法测得的六面体单元柔性结构随机振动数据为基础对其模型和逆模型进行了辨识，为进一步开展该结构的自适应逆控制研究奠定了基础。     

On the model formulations for the interaction of nonlinear waves and current

We study the model formulations of wave–current interactions in the framework of Euler equations. This work is intrigued by a recent paper from Wang et al. (2018) (hereafter WMY), which proposes such a model for the evolution of nonlinear broadband surface waves under the influence of a prescribed steady and irrotational current without vertical shear. We show that WMY’s model can be derived from a more general model accounting for an arbitrary steady and irrotational current. Under further assumption of scale separation between waves and current (i.e. horizontally slowly-varying current), WMY’s model is equivalent to an earlier model, in contrast to WMY’s claim that their model includes additional higher-order effects in wave steepness. We demonstrate the usefulness of such models in a numerical study on wave blocking by opposing current, where the nonlinear effect on the caustic location and wave amplitude amplification is elucidated. We further show that the model formulation in the framework of Euler equations form a Hamiltonian system conserving the total energy of waves and current, justifying the theoretical significance of the model equations. Finally, we generalize the formulation to nonlinear wave evolution in the presence of a rotational current with constant vorticity, which overcomes a limitation of such models that has been overlooked in previous work.     

Identification of the viscoelastic parameters of a polymer model by the aid of a MCMC method

A procedure to identify the viscoelastic material parameters of a solid amorphous polymer and to estimate their values is presented. Stress–strain material data is obtained for the polymer by a compression experiment. The material behavior of the polymer is modeled according to the generalized Maxwell model, which is fitted to the experimental data by the method of least squares to obtain a first approximation for the model parameters. The identification of the model parameters is completed by a Markov chain Monte Carlo (MCMC) method, which generates the probability distributions of the relevant parameters of the material. The utilized MCMC method enables us to determine a suitable complexity (i.e., the number of Maxwell elements) for the generalized Maxwell model, so that the model best fits the data and, simultaneously, leads to an identifiable set of parameters. The numerical results imply that the uniqueness of the solution is lost when the number of model parameters becomes redundant.     

Generalized logistic growth modeling of the COVID-19 outbreak: comparing the dynamics in the 29 provinces in China and in the rest of the world

Nonlinear Dynamics - Started in Wuhan, China, the COVID-19 has been spreading all over the world. We calibrate the logistic growth model, the generalized logistic growth model, the generalized...     

Effect of mini-flaps on the structure of the near wake behind a model half-wing

The effect of mini-flaps on the vortex structure of the near wake flow behind a model of a half-wing, rectangular in plan, is investigated. In a subsonic wind tunnel the time-average flow parameters are measured in several sections behind a model with flaps mounted on both upper and lower surfaces near the trailing edge. The wake flow parameters are compared with those for a model with no flaps. The considerable effect of the flaps on the flow structure in the viscous core of a tip vortex formed behind the model half-wing is established.     

半圆柱壳挠曲问题解析解精确性的研究

壳体力学已于上世纪由多位专家发展成熟,其中简支柱壳挠曲问题采用改进莱维解法的三角级数法解出,但是其解法复杂,手算难以完成．为讨论其结果的精确性,通过编写运行基于MATLAB的运算程序导出实例化解析解,与基于力学基本理论的推想假设对比,再引入有限元计算结果进行比较研究．最终发现,理论解析解应力和位移具有分布形式大致准确性,但仍存在不容忽视的细节与局部性问题．研究表明,理论解法工程意义有限,结果尚需改进．     

Elongational-flow predictions of the Leonov constitutive equation

The basic thermodynamic ideas from rubber-elasticity theory which Leonov employed to derive his constitutive model are herein summarized. Predictions of the single-mode version are presented for homogeneous elongational flows including stress growth following start-up of steady flow, stress decay following sudden stretching and following cessation of steady flow, elastic recovery following cessation of steady flow, energy storage in steady-state flow, and the velocity profile in constantforce spinning. Using parameters of the multiple-mode version which fit the linearviscoelastic data, the Leonov-model predictions of elongational stress growth during, and elastic recovery following, steady elongation are calculated numerically and compared to the experimental results for Melt I and to the Wagner model. It is found that the Leonov model, as originally formulated, agrees qualitatively with the data, but not quantitatively; the Wagner model gives quantitative agreement, but requires much nonlinear data with which to fit model parameters. Quantitative agreement can be obtained with the Leonov model, if the nonequilibrium potential which relates recoverable strain to strain rate is adjusted empirically. This can most simply be done by making each relaxation time dependent upon the recoverable strain. The Leonov model, unlike the Wagner model, is derived from an entropic constitutive equation, which is advantageous for calculating stored elastic energy or viscous dissipation. The Leonov model also has an appealingly simple differential form, similar to the upper-convected Maxwell model, which, in numerical calculations, may be an important advantage over the integral Wagner model.     

Characteristic cones of the equations in the nonlinear theory of elasticity

The roots of the equation for the characteristic normals for two systems of differential equations in the nonlinear theory of elasticity are investigated. The first model is constructed using a thermodynamic identity. The second is a very simple hypoelastic model (the deviator of the stress-rate tensor is proportional to the deviator of the strain-rate tensor). It is shown that the roots of the equations for the normals to the characteristics for the second model are the same as the first-order terms in the expansion of the roots of the first model with respect to the strain-tensor deviator.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 126–132, May–June, 1974.The author is grateful to S. K. Godunov for discussions.     

一个基于恢复时间的新剪稀模型及其对聚合油PAO 650流变特性的模拟

用球-杆比拟流体层上的分子,通过分析两流体层上球-杆的接触、通过和恢复的过程,基于球-杆恢复到原状态的时间,建立了一个新剪稀模型.该模型虽然在形式上与Carreau模型有相似之处,但其公式仅含有两个流变参数,且是经由严格的理论推导得到的.通过与Carreau模型得到的广义黏度曲线的比较,确定了新流变公式的待定参数.在点接触流变热弹流润滑的数学模型中使用新流变公式,数值模拟了大黏度聚合油PAO 650的流变特性,并与该油在文献中的试验曲线进行了比对.结果表明新流变模型能够较好地模拟大黏度聚合油的流变特性,从而证实了其正确性.进一步,使用新公式计算得到了更多工况下的流变特性曲线,光滑的、合理的曲线分布说明新流变模型具有广泛的适用性.     

梁柱简化模型在自立塔塔线体系动态响应中的适用性研究

对输电塔进行合理简化可以提高塔线体系动力学仿真的效率。本文给出自立塔梁柱简化模型的计算方法,并提出利用梁柱简化模型计算方法建立自立塔塔线体系整体模型,同时采用桁梁混合模型建立精细化塔线体系整体模型,对两种模型塔线体系静力特性及振型和固有频率等动力特性进行对比分析。以脱冰工况为例,采用生死单元技术将施加在输电线节点上的集中质量单元杀死来模拟脱冰,实现对塔线体系动力学响应的有限元模拟,研究塔线体系简化模型在动态响应中的适用性。结果表明,两种模型弯曲变形误差小,低阶的振型相同,固有频率值误差小,动力特性基本相同;脱冰工况下,自立塔节点位移和塔材内力时程曲线一致,在提高计算效率的情况下,能有效保证计算精度。     

The mathematical model of the radial artery blood pressure waveform through monitoring of the age-related changes

Age-related changes in blood vessels affect the pulse wave propagation. These changes may cause an increase in wave reflection which leads to amplification of pulse pressure. The pulse pressure changes are associated with certain vascular diseases. Here we present a mathematical model of blood pressure for different age groups. The model is based on one-dimensional wave propagation theory and assumes that the pressure waveform is a superposition of forward propagating wave and backward waves from many reflection sites. The model is based on experimental data obtained by direct measurement of radial artery blood flow. The model clearly shows age-related changes in blood pressure waveform. The results of mathematical model correlate with the radial pressure waveform data. The model can be used in cases where it is not possible to measure the pressure due to movement of subject. Application of model to the direct blood flow measurements data allows the real-time pressure waveform monitoring. Furthermore, this approach enables monitoring of changes in pressure waveform due to the effects of medications.     

Turbulence modeling for the axially rotating pipe from the viewpoint of analytical closures

A single-point model eddy viscosity model of rotation effects on the turbulent flow in an axially rotating pipe is developed based on two-point closure theories. Rotation is known to impede energy transfer in turbulence; this fact is reflected in the present model through a reduced eddy viscosity, leading to laminarization of the mean velocity profile and return to a laminar friction law in the rapid rotation limit. This model is compared with other proposals including linear redistribution effects through the rapid pressure-strain correlation, Richardson number modification of the eddy viscosity in a model of non-rotating turbulence, and the reduction of turbulence through the suppression of near-wall production mechanisms. PACS 47.27.Eq, 47.32.-y     

A THREE-FLUID MODEL OF THE SAND-DRIVEN FLOW

ＡＴＨＲＥＥ－ＦＬＵＩＤＭＯＤＥＬＯＦＴＨＥＳＡＮＤ－ＤＲＩＶＥＮＦＬＯＷ￥(刘大有，董飞)ＬｉｕＤａｙｏｕ；ＤｏｎｇＦｅｉ（ＩｎｓｔｉｔｕｔｅｏｆＭｅｃｈａｎｉｃｓ，ＡｃａｄｅｍｉａＳｉｎｉｃａ，Ｂｅｉｊｉｎｇ１０００８０，Ｐ．Ｒ．Ｃｈｉｎａ）Ａｂｓ...     

对基于恢复时间的剪稀流变模型的进一步探讨及其对squalane油品流变特性的模拟

本文作者前期基于球-杆变形后恢复到原状态的时间,建立了新的形式较简单的流变模型,并模拟了黏度较高的聚合油PAO 650的摩擦系数曲线.本文中将该模型的应用范围进行了推广,模拟了黏度较低的squalane油品的流变特性.把该流变公式应用到点接触热流变弹流润滑的数学模型中,通过与试验测得的摩擦系数的比较确定了使用该模型时squalane油品的待定参数值,进而得到了点接触热流变弹流润滑的完全数值解.结果表明:解得的压力、膜厚和温度的变化规律均符合预期,且摩擦系数曲线与试验结果整体吻合性较好.新流变模型对高、低黏度的油品均能得到合理的流变特性曲线,说明作者的基于恢复时间的流变模型具有一定的正确性和可应用性.另外,由新模型计算得到的squalane油品的剪应力曲线呈现出一近似水平段,这也在一定程度上解释了流变试验文献中多次提到的极限剪应力现象.     

Progress in the study of retrospective numerical scheme and the climate prediction

The retrospective numerical scheme (RNS) is a numerical computation scheme designed for multiple past value problems of the initial value in mathematics and considering the self-memory property of the system in physics. This paper briefly presents the historical background of RNS, elaborates the relation of the scheme with other difference, schemes and other meteorological prediction methods, and introduces the application of RNS to the regional climatic self-memory model, simplified climate model, barotropic model, spectral model, and mesoscale model. At last, the paper sums up and points out the application perspective of the scheme and the direction for the future study. The project supported by the Research Program of the Climatic System Model of China, the National Natural Science Foundation of China (40275031 and 40231006) and the National Key Program for Developing Basic Sciences (1999043408)