平面定常超音速绕流问题的新的数值解法

用特征线法解平面定常超音速绕流问题虽然有效,但当激波很弱、几乎与特征线平行时则很难处理。用有限差分法计算此问题也比较复杂。本文把作者在文章中^[1]提出的新的数值解法,发展并应用到平面定常超音速绕流的问题。仍然采用了许为厚教授提出的新拉格朗日变量^[2],这使边界条件的提法大为简化。此新的数值解法按变量指标之和,一排排地往下计算,方法简单,可以处理各种形状物体的超音速绕流。本文对向上弯曲的抛物形固壁绕流向题的实例进行了具体计算。算出了激波的形状。当激波没有形成以前,相应的普朗特一迈耶气流是有准确分析解的,把数值解与准确解进行了l比较结果是满意的。     

三维Laplace方程及Poisson方程的有限分析解表达式和它的应用

本文给出三维Laplace方程及Poisson方程有限分析解的正确系数值,并与陈景仁^[1]给出的系数值进行了比较。给出了三维Laplace方程的有限分解表达式。利用本文的系数值求解热传导问題的算例,与用边界单元法^[6]结果相比,基本一致,但程序编制和花费机时却节省很多。     

Kasner 时空中的中微子振荡相位

研究了质量中微子在 Kasner 时空特殊情况下的传播相位和振荡特征长度,得到了中微子的零短程线相位是短程线相位一半的关系.当参数a=0时,Kasner 时空中的传播相位和史瓦希时空中的相同.这一问题的研究在宇宙学中是有意义的^[1-3]. 关键词： 传播相位 Kasner 时空 质量中微子 振荡特征长度     

岩石样品表面流体的核磁共振谱线

已经知道,磁化率对核磁共振(NMR)化学位移的测量有明显影响^[1,2],而且,磁化率效应与样品管的形状及取向(即与静磁场的夹角)等因素有关^[3-7].为了测准样品的化学位移,有多种方法可以消除磁化率的影响。样品形状引起的非均匀磁化会限制核磁共振成像的空间分辨率^[8,9].近来又发展了克服磁化率影响的非畸变成像方法^[10].但是,磁化率引起的多孔固体样品孔隙中和外壁上流体的核磁共振诸线的差异却尚未看到文献报道。本文首次报道岩石样品核磁共振实验中观测到的岩样外表流体产生的谱线,初步讨论了它们与岩石渗流性质的关系。     

完全守恒型差分格式对大型变截面激波管中流场的数值模拟

本文研究了А.А.Самарский提出的拉格朗日坐标下气体力学方程组的完全守恒型差分格式^[2],并给出了一种改进形式。对激波管问题所做的数值计算表明改进的格式具有激波过渡区窄,过跳与低亏小的优点,而且所需的计算时间远低于文[2]中的格式。     

在Skyrme模型中关于解析质量计算的研究

本文用Reduce语言^[1]研究了Skyrme模型^[2、3、4]中孤立子质量的计算方法。上机计算结果表明,矩阵方法和具体展开方法比一般算符表达式更为优越。     

P2O5-CuI-CuCl系统非晶态铜离子导体的EXAFS,IR,Raman光谱研究

本文用透射法EXAFS和IR,Raman光谱等手段研究了以P₂O₅,为基体的非晶态铜离子导体的微观结构,得出了非晶结构网络中存在[PO₄]^3-,[CuO₄]^6-,[CuO₃I]^5-,[PO₃I]^2-等四元骨架结构单元,Cu⁺在结构网络空隙中有两种不同的分布状况。并在此基础上对材料在50℃左右存在的二级相变及Cu⁺的其它传导性能进行了定性的描述。 关键词：     

Mixing of two-quasineutron and two-quasiproton Kπ=6+ configurations in the vicinity of 174Yb

In the framework of the projected shell model, we investigate the competition between the two-quasineutron and two-quasiproton K^π=6⁺ states in the ytterbium isotopes and N =104 isotones adjacent to ¹⁷⁴Yb. The ¹⁷⁴Yb results are compared with the experimental data.The K^π =6⁺ isomer observed in ¹⁷⁴ Yb is assigned as an admixture of the ν7/2^-[514] ν5/2^-[512] and π7/2⁺ [404]π5/2⁺ [402] intrinsic structure, which explains the experimental |g K-g R | value. Similar mixing would appear in ¹⁷⁴ Yb, ¹⁷⁶ Hf,and ¹⁷⁸ W. The low-lying K^π=6⁺ states are also predicted in ^170-178 Yb.     

轻丰中子素11Li,14Be和17B的三体动力学

在任中洲、徐躬耦提出的三体模型^[1]基础上，对试探波函数进行了改进。利用关联密度函数研究了¹¹Ｌｉ，¹⁴Ｂｅ和¹⁷Ｂ的内部结构和粒子关联，定性地找到了支持中子晕结构的证据。 关键词：     

含次环己基有机硅单体及二聚体的NMR谱与结构

含次环已基有机硅单体及其二聚体业已成功地合成^[1],本文研究了这类新单体和二聚体的¹H-NMR、¹³C-NMR、和²⁹Si-NMR谱,从而确定了它们的结构。     

Dispersive of propagation wave structures to the dullin-Gottwald-Holm dynamical equation in a shallow water waves

This article secures the new exact wave structures to Dullin-Gottwald-Holm (DGH) equation which is used as a governing model to explain the behaviour of waves in shallow water. The wave structures in the forms of solitary, shock, singular, shock-singular as well as hyperbolic, singular periodic and rational solutions are secured with the aid of computational strategy namely modified direct algebraic and ansatz approaches. The constraint conditions which ensure the validity of new wave structures are also reported. Moreover, the graphs of the solution attained are recorded in terms of 3D, 2D and contour plots by fixing parameters. The achieved outcomes show that the applied computational strategy is direct, efficient, concise and can be implemented in more complex phenomena with the assistant of symbolic computations.     

New solitons and periodic wave solutions for nonlinear evolution equations

The extended Jacobi elliptic function expansion methods with a computerized symbolic computation are used to construct the exact periodic solutions of some polynomials or nonlinear evolution equations. As a result, many exact travelling wave solutions are obtained which include new solitary or shock wave solution and envelope solitary and shock wave solutions.     

Multi-domain Fourier-continuation/WENO hybrid solver for conservation laws

We introduce a multi-domain Fourier-continuation/WENO hybrid method (FC–WENO) that enables high-order and non-oscillatory solution of systems of nonlinear conservation laws, and which enjoys essentially dispersionless, spectral character away from discontinuities, as well as mild CFL constraints (comparable to those of finite difference methods). The hybrid scheme employs the expensive, shock-capturing WENO method in small regions containing discontinuities and the efficient FC method in the rest of the computational domain, yielding a highly effective overall scheme for applications with a mix of discontinuities and complex smooth structures. The smooth and discontinuous solution regions are distinguished using the multi-resolution procedure of Harten [J. Comput. Phys. 115 (1994) 319–338]. We consider WENO schemes of formal orders five and nine and a FC method of order five. The accuracy, stability and efficiency of the new hybrid method for conservation laws is investigated for problems with both smooth and non-smooth solutions. In the latter case, we solve the Euler equations for gas dynamics for the standard test case of a Mach three shock wave interacting with an entropy wave, as well as a shock wave (with Mach 1.25, three or six) interacting with a very small entropy wave and evaluate the efficiency of the hybrid FC–WENO method as compared to a purely WENO-based approach as well as alternative hybrid based techniques. We demonstrate considerable computational advantages of the new FC-based method, suggesting a potential of an order of magnitude acceleration over alternatives when extended to fully three-dimensional problems.     

Numerical methods for solid mechanics on overlapping grids: Linear elasticity

This paper presents a new computational framework for the simulation of solid mechanics on general overlapping grids with adaptive mesh refinement (AMR). The approach, described here for time-dependent linear elasticity in two and three space dimensions, is motivated by considerations of accuracy, efficiency and flexibility. We consider two approaches for the numerical solution of the equations of linear elasticity on overlapping grids. In the first approach we solve the governing equations numerically as a second-order system (SOS) using a conservative finite-difference approximation. The second approach considers the equations written as a first-order system (FOS) and approximates them using a second-order characteristic-based (Godunov) finite-volume method. A principal aim of the paper is to present the first careful assessment of the accuracy and stability of these two representative schemes for the equations of linear elasticity on overlapping grids. This is done by first performing a stability analysis of analogous schemes for the first-order and second-order scalar wave equations on an overlapping grid. The analysis shows that non-dissipative approximations can have unstable modes with growth rates proportional to the inverse of the mesh spacing. This new result, which is relevant for the numerical solution of any type of wave propagation problem on overlapping grids, dictates the form of dissipation that is needed to stabilize the scheme. Numerical experiments show that the addition of the indicated form of dissipation and/or a separate filter step can be used to stabilize the SOS scheme. They also demonstrate that the upwinding inherent in the Godunov scheme, which provides dissipation of the appropriate form, stabilizes the FOS scheme. We then verify and compare the accuracy of the two schemes using the method of analytic solutions and using problems with known solutions. These latter problems provide useful benchmark solutions for time dependent elasticity. We also consider two problems in which exact solutions are not available, and use a posterior error estimates to assess the accuracy of the schemes. One of these two problems is additionally employed to demonstrate the use of dynamic AMR and its effectiveness for resolving elastic “shock” waves. Finally, results are presented that compare the computational performance of the two schemes. These demonstrate the speed and memory efficiency achieved by the use of structured overlapping grids and optimizations for Cartesian grids.     

Travelling Wave Solution of Korteweg-de Vries-Burger's Equation

An attempt has been made to obtain exact analytical travelling wave solution of Korteweg-de Vries-Burger's (KdVB) equation by the so-called tanh-method. This equation can be derived for dust ion acoustic shocks by using reduction perturbation method. It is found that an exact solution of the KdVB equation is obtained by tanh-method, provided the parameters involved satisfy a constraint relation. However a special exact analytical solution can be obtained where no such restriction is necessary. This solution has the structure of a shock wave. Numerical solution is also obtained for travelling wave with or without the assumption of the constraint relation. We have also found a singular solution in terms of cosech and coth functions.     

面向高超声速飞行器的激波智能预测方法

高超声速飞行器激波位置的准确预测能够有效提升数值模拟的精度和效率。一方面,对高超声速飞行器激波附近网格进行正交和加密处理,可有效提升数值计算精度;另一方面,使用高超声速飞行器激波位置对计算网格进行修正,能够加速CFD计算收敛过程。提出了一种基于机器学习的高超声速飞行器激波智能预测方法,对典型高超声速飞行器外形进行激波位置的高效准确预测。首先,针对典型高超声速飞行器外形和典型飞行状态,使用数值模拟方法获得收敛的流场,并采用基于Mach数等值线的激波提取方法,从流场中判别激波面并提取构成激波面的关键点位置,形成训练数据;然后采用有监督学习算法,学习关键点位置,并利用二次曲线沿流向拟合关键点形成初步的激波线族;最后,基于剖面压力云图,构造基于投影压力图像的智能预测神经网络,对初步形成的激波线族进行修正,并获得三维激波面。大量的实验结果表明,激波预测模型能够对高超声速飞行器激波位置做出准确预测,预测的激波面与CFD数值计算结果中提取的激波面误差在10^-4量级。     

Propagation of wave intensity shocks in nonlinear interaction of waves and particles

An exact solution of stationary propagating wave intensities is obtained for two waves which are interacting with particles. One of the wave intensity forms a rarefaction wave while the other forms a shock and both propagate at the same speed.     

Basic function method A new numerical method on unstructured grids

A new numerical method-basic function method is proposed. This method can directly discrete differential operators on unstructured grids. By using the expansion of basic function to approach the exact function, the central and upwind schemes of derivative are constructed. By using the polynomial as basic function, applying the technique of flux splitting method and the combination of central and upwind schemes, the non-physical fluctuation near the shock wave is suppressed. The first-order basic function scheme of polynomial type for solving inviscid compressible flow numerically is constructed in this paper. Several numerical results of many typical examples for one-, two- and three-dimensional inviscid compressible steady flow illustrate that it is a new scheme with high accuracy and high resolution for shock wave. Especially, combining with the adaptive remeshing technique, the satisfactory results can be obtained by these schemes.     

平面斜激波固壁反射的镶嵌网格解法

镶嵌网格法是自适应网格法的一种。本文提出的镶嵌网格法以Ni的二阶有限体积法为基础,用密度一阶差分作为察觉激波的特征参数,给出网格局部加密(一分为四)的原则,构造了较节省存贮的数据结构。用于平面斜激波固壁反射的计算结果表明:镶嵌网格对激波的分辨能力不仅比粗网格强得多,而且也稍好于细网格;计算时间仅为细网格的一半稍多些.可见,此方法对解决计算效率和精度的矛盾是有利的。