A self-consistent field for the H2 molecule

We investigate the simple harmonic oscillator in a 1D box, and the 2D isotropic harmonic oscillator problem in a circular cavity with perfectly reflecting boundary conditions. The energy spectrum has been calculated as a function of the self-adjoint extension parameter. For sufficiently negative values of the self-adjoint extension parameter, there are bound states localized at the wall of the box or the cavity that resonate with the standard bound states of the simple harmonic oscillator or the isotropic oscillator. A free particle in a circular cavity has been studied for the sake of comparison. This work represents an application of the recent generalization of the Heisenberg uncertainty relation related to the theory of self-adjoint extensions in a finite volume.     

The numerical prediction of planar viscoelastic contraction flows using the pom–pom model and higher-order finite volume schemes

This study investigates the numerical solution of viscoelastic flows using two contrasting high-order finite volume schemes. We extend our earlier work for Poiseuille flow in a planar channel and the single equation form of the extended pom–pom (SXPP) model [M. Aboubacar, J.P. Aguayo, P.M. Phillips, T.N. Phillips, H.R. Tamaddon-Jahromi, B.A. Snigerev, M.F. Webster, Modelling pom–pom type models with high-order finite volume schemes, J. Non-Newtonian Fluid Mech. 126 (2005) 207–220], to determine steady-state solutions for planar 4:1 sharp contraction flows. The numerical techniques employed are time-stepping algorithms: one of hybrid finite element/volume type, the other of pure finite volume form. The pure finite volume scheme is a staggered-grid cell-centred scheme based on area-weighting and a semi-Lagrangian formulation. This may be implemented on structured or unstructured rectangular grids, utilising backtracking along the solution characteristics in time. For the hybrid scheme, we solve the momentum-continuity equations by a fractional-staged Taylor–Galerkin pressure-correction procedure and invoke a cell-vertex finite volume scheme for the constitutive law. A comparison of the two finite volume approaches is presented, concentrating upon the new features posed by the pom–pom class of models in this context of non-smooth flows. Here, the dominant feature of larger shear and extension in the entry zone influences both stress and stretch, so that larger stretch develops around the re-entrant corner zone as Weissenberg number increases, whilst correspondingly stress levels decline.     

激光对碳纤维增强复合材料的热烧蚀数值模拟

高能激光对复合材料的辐照效应研究,可以拓展激光技术的应用范围。为了预测激光辐照下碳纤维增强复合材料的瞬态热响应,提出了一个简化计算模型。采用隐式有限体积方法求解控制方程,边界条件包括激光辐照加热、对流换热、辐射换热以及材料表面烧蚀。考虑了激光辐照过程中基体热分解、质量迁移、比热容变化情况。基于该烧蚀模型,预测了激光辐照下碳纤维增强复合材料的瞬态温度场和表面烧蚀速率,计算结果与文献试验数据一致。最后,通过修正烧蚀模型分析了高速气流剥蚀对激光辐照复合材料热效应的影响。     

The Optimal Error Estimate of the Fully Discrete Locally Stabilized Finite Volume Method for the Non-Stationary Navier-Stokes Problem

This paper proves the optimal estimations of a low-order spatial-temporal fully discrete method for the non-stationary Navier-Stokes Problem. In this paper, the semi-implicit scheme based on Euler method is adopted for time discretization, while the special finite volume scheme is adopted for space discretization. Specifically, the spatial discretization adopts the traditional triangle P1−P0 trial function pair, combined with macro element form to ensure local stability. The theoretical analysis results show that under certain conditions, the full discretization proposed here has the characteristics of local stability, and we can indeed obtain the optimal theoretic and numerical order error estimation of velocity and pressure. This helps to enrich the corresponding theoretical results.     

圆柱空腔内旋转流动中轴对称涡破裂现象的数值模拟

对于上端盖旋转圆柱空腔内旋转流动来说,当流动达到一定条件时,就会出现旋涡破裂现象。目前针对这种现象已经进行了大量的稳态和非稳态实验测量,获得了精确的实验数据。采用数值模拟方法,重现了涡破裂现象及其发生发展过程,同已经发表的相关实验数据进行了比较     

An adaptive multilevel local defect correction technique with application to combustion

The standard local defect correction (LDC) method has been extended to include multilevel adaptive gridding, domain decomposition and regridding. The domain decomposition algorithm provides a natural route for parallelization by employing many small tensor-product grids, rather than a single large unstructured grid; this algorithm can greatly reduce memory usage. The above properties are illustrated by successfully applying the new algorithm to a simple heat transfer problem with an analytical solution, and by subsequently solving the more complex problem of an axisymmetric laminar Bunsen flame with one-step chemistry. The simulation data show excellent agreement with results previously published in the literature.     

无结构网格有限体积方法及在热对流中的应用研究

首次将无结构三角网格的有限体积方法和压强连接半隐式算法相结合,用于求解非平行壁管道中的热对流问题。并由此分析了化学汽相淀积薄膜生长的均匀性问题。计算结果对于分析一类管道中热和动量输运现象均有普遍指导意义。     

空间遥感器高体份SiC/Al复合材料反射镜组件设计

为消除反射镜与支撑结构材料线胀系数差异产生的热变形对反射镜面形精度、系统成像质量的影响, 采用高体份SiC/Al复合材料作为新型反射镜组件的材料。首先, 通过合理的结构设计及有限元分析比较, 确定了Ф600 mm口径反射镜结构参数, 然后, 对反射镜组件进行了静力学和动力学分析, 在1 g重力载荷作用下, 反射镜X、Y、Z方向去除刚体位移后的镜面变形RMS值分别为12.6, 12.7, 12.6 nm, 达到了λ/50(λ=632.8 nm)。最后, 为了验证高体份SiC/Al复合材料反射镜组件的结构性能及检验结构在振动条件下的抗干扰能力, 对反射镜组件进行了力学试验, 反射镜组件的一阶谐振频率为556.6 Hz。力学试验前后, 反射镜镜面面形误差RMS分别为0.021λ、0.025λ, 没有明显变化。实验结果表明:高体份SiC/Al复合材料反射镜达到了与SiC材料反射镜相同的设计指标要求, 能够满足空间应用。     

A Finite Volume Method Based on the Constrained Nonconforming Rotated Q1-Constant Element for the Stokes Problem

We construct a finite volume element method based on the constrained nonconforming rotated Q₁-constant element (CNRQ₁-P₀) for the Stokes problem. Two meshes are needed, which are the primal mesh and the dual mesh. We approximate the velocity by CNRQ₁ elements and the pressure by piecewise constants. The errors for the velocity in the H¹ norm and for the pressure in the L² norm are O(h) and the error for the velocity in the L² norm is O(h²). Numerical experiments are presented to support our theoretical results.     

求解对流-扩散-反应问题的改进有限积分法

将求解偏微分方程的有限积分法应用于对流-扩散-反应问题,发现对于非对流占优的对流扩散问题,有限积分法的精度比QUICK法高一个数量级,比传统的有限体积法高两个数量级.处理对流占优的对流-扩散-反应问题时,对流项的离散时引进加权参数,通过调节该参数反映输运的方向性.结果表明这种改进的有限积分法的精度比传统的有限体积法至少高四个数量级,同时明显改进了原来的有限积分法的精度和稳定性.对于对流占优的对流-扩散-反应问题,即使采用粗网格,计算结果也未出现非物理振荡现象,表明改进的有限积分法具有很好的稳定性.     

各向同性紊流能量衰减的大涡模拟

在多重网格驱动的,高效且得到充分验证的有限体积方法的基础上发展了可压缩流大涡模拟的方法.空间离散采用Jameson的中心格式附加二阶和四阶耗散的方法,时间推进则采用了双时间步长的方法.亚格子剪切应力张量和亚格子热通量用Smagorinsky模型进行模拟.通过对各向同性紊流能量衰减的模拟来验证本方法的准确性和高效性,模拟得到的能量谱和紊流动能衰减历程与过滤后的CBC实验数据吻合良好.     

基于节点重构的扩散方程有限体积格式

研究扭曲网格上扩散方程的九点格式.以经典的九点格式为基础,在通量连续条件下,构造出节点未知量一种新的计算方法,进而得到所希望的格式.分析及数值实验表明,在扭曲网格上,该格式对具有连续或间断扩散系数的问题能够保持较高的精度.     

用多重网格技术求解平面叶栅跨音绕流

1982年以来,Ni、Davis等人发展了一种与多重网格技术相结合的时间相关有限体积积分方法,这是一个快速求定常解的显式推进方法。本文采用这种方法计算平面叶栅跨音绕流,阐明了Ni-Davis格式的基本思想和处理原则,在物面边界近似处理上本文作了适当改进,为适当选取人工粘性项提出了具体平滑公式,又根据数值试验对多重网格技术提出了改进算法。两个跨音叶栅绕流算例表明,数值结果的精度和计算效率是令人满意的,可以满足航空发动机气动设计的需要。在IBM 4341计算机上,求解一个65×17网格上的跨音流场大约需CPU时间15分钟,使用四层网格技术后可节省CPU时间50%到60%。     

A hierarchical fracture model for the iterative multiscale finite volume method

An iterative multiscale finite volume (i-MSFV) method is devised for the simulation of multiphase flow in fractured porous media in the context of a hierarchical fracture modeling framework. Motivated by the small pressure change inside highly conductive fractures, the fully coupled system is split into smaller systems, which are then sequentially solved. This splitting technique results in only one additional degree of freedom for each connected fracture network appearing in the matrix system. It can be interpreted as an agglomeration of highly connected cells; similar as in algebraic multigrid methods. For the solution of the resulting algebraic system, an i-MSFV method is introduced. In addition to the local basis and correction functions, which were previously developed in this framework, local fracture functions are introduced to accurately capture the fractures at the coarse scale. In this multiscale approach there exists one fracture function per network and local domain, and in the coarse scale problem there appears only one additional degree of freedom per connected fracture network. Numerical results are presented for validation and verification of this new iterative multiscale approach for fractured porous media, and to investigate its computational efficiency. Finally, it is demonstrated that the new method is an effective multiscale approach for simulations of realistic multiphase flows in fractured heterogeneous porous media.     

Investigation of interaction between methanol fed tandem porous spheres burning in a mixed convective environment

Flame interaction during the burning of two porous spheres in tandem arrangement fed with methanol and subjected to a mixed convective environment, has been studied experimentally and numerically. Porous sphere technique is employed for experimentally simulating the burning characteristics of methanol transpired spheres of different sizes, separated by fixed distances. The mass burning rates from both the spheres and visible flame stand-off distances from the sphere surfaces have been measured in the experiments. In the numerical simulations, transient, axisymmetric, mass, momentum, species and energy conservation equations are solved using a finite volume technique based on non-orthogonal semi-collocated grids. Features of the numerical model include finite rate chemistry and temperature and mixture composition dependent thermo-physical properties. Burning of tandem porous spheres in an air stream flowing vertically upwards, at atmospheric pressure has been simulated for different sphere sizes, separation distances and free stream velocities. The numerical predictions have been compared with experimental results. Results reveal that when two spheres burn one over the other, the transition from envelope to wake flame is delayed when compared with that of an isolated sphere. For two spheres of same diameter burning one over the other, depending on the separation distance, flame blows-off after the occurrence of transition from envelope to wake flame in the bottom sphere. For the case of larger sphere at the top, either the flame stabilises in the recirculation zone formed in between the spheres or the flame from the smaller sphere lifts off and stabilises near the front portion of the larger sphere, depending on the separation distance. At higher separation distances, around four times the diameter of the sphere, both the spheres burn independently. The burning rate undergoes complex variations with air stream velocity depending on the sphere sizes and separation distances.     

Finite volume effects on the QCD chiral phase transition in the finite size de-pendent Nambu-Jona-Lasinio model

The effective Lagrangian of a finite volume system should, in principle, depend on the system size. In the framework of the Nambu-Jona-Lasinio(NJL) model, by considering the influence of quark feedback on the effective coupling, we obtain a modified NJL model so that its Lagrangian depends on the volume. Based on the modified NJL model, we study the influence of finite volume on the chiral phase transition at finite temperature, and find that the pseudo-critical temperature of crossover is much lower than that obtained in the normal NJL model. This clearly shows that the volume dependent effective Lagrangian plays an important role in the chiral phase transitions at finite temperature.     

Symmetry Breaking in Finite Volume-a Study in the O(N) Model

Spontaneous symmetry breaking plays a crucial role in quantum field theories and it occurs only for systems with infinite degrees of freedom. For a system in a large but finite volume, although the symmetry is not broken spontaneously, an adiabatic approximation can be applied to study the would-be broken symmetry. Lattice O(N) model is studied within the Hamiltonian approach. It is shown that the low-lying spectrum of the system can be explained using an adiabatic, or Born-Oppenheimer approximation, which turns out to become 1 an expansion in the inverse power of volume. In the infinite volume limit, the symmetry is broken while in the finite volume the slow rotation of the zero-momentum mode restores the symmetry and gives rise to the rotator spectrum, which has been observed in real Monte Carlo simulations.     

求解辐射传递的非结构混合有限体积／有限元法

本文给了一种适用于任意非结构网格的有限体积/有限元法的混合算法用于求解多维半透明吸收、发射、散射性灰矩形介质内的辐射传递.该方法使用有限元法进行角度离散,有限体积法进行空间离散.与基于辐射传递离散坐标方程的方法不同的是,该方法在迭代求解的过程中,针对每一个空间体元,所有角度方向的辐射强度同时耦合求出.通过两个算例验证了该解法的正确性.     

耦合势有限体积法高效模拟各向异性地层中海洋可控源的三维电磁响应

本文基于电场矢势与标势分解的耦合势有限体积法研究建立一套各向异性地层中海洋可控源电磁法的三维响应的高效数值模拟技术.首先引入电场的矢势和标势,将电场分解为无散场和无旋场之和,Maxwell方程转换为关于矢势与标势的混合Helmholtz方程,克服低感应数问题.在此基础上,借助Yee氏交错网格和有限体积法以及非均质单元中等效电导率公式,建立混合Helmholtz方程的离散方程.并采用直接法求解器PARDISO求解离散方程,有效保证在大的求解空间中仍然能够获得电磁场稳定可靠的数值解.此外,在数值模拟中利用差异场技术,克服源的奇异性问题,尽可能提高近场的计算精度.与解析解的对比证明了该算法的有效性.数值模拟结果表明,海洋可控源电磁法沿测线方向的电场,对油气藏的纵向电阻率敏感,对横向电阻率不敏感;对油气藏上方的覆盖层的纵向电阻率和横向电阻率都敏感.     

Two-Scale Picard Stabilized Finite Volume Method for the Incompressible Flow

In this paper, we consider a two-scale stabilized finite volume method for the two-dimensional stationary incompressible flow approximated by the lowest equal-order element pair $P_1-P_1$ which does not satisfy the inf-sup condition. The two-scale method consists of solving a small non-linear system on the coarse mesh and then solving a linear Stokes equations on the fine mesh. Convergence of the optimal order in the $H^1$-norm for velocity and the $L^2$-norm for pressure is obtained. The error analysis shows there is the same convergence rate between the two-scale stabilized finite volume solution and the usual stabilized finite volume solution on a fine mesh with relation $h =\mathcal{O}(H^2)$. Numerical experiments completely confirm theoretic results. Therefore, this method presented in this paper is of practical importance in scientific computation.