基于二阶Godunov格式的SPH方法模拟弹塑性波的传播

针对一阶Godunov格式的SPH方法的计算精度和激波分辨率不高的问题,提出了二阶Godunov格式的SPH方法。新方法在求解相互作用的粒子间黎曼问题时,认为粒子内物理量呈线性分布,用线性插值后求得的值作为黎曼问题的初始值,然后把黎曼解和Taylor展开引入到SPH方法中。应用新方法对一维弹塑性应力波的传播进行了数值模拟,并与一阶Godunov格式的SPH方法进行比较.计算结果显示新方法有效地提高了计算精度和激波分辨率,同时验证了它的稳定性。     

箱梁断面气动导数的CFD模拟研究

采用强迫振动方法试验和计算流体力学（CFD）动网格法模拟识别了薄平板以及某一大跨度桥梁断面的气动导数。结果表明,对流线型的薄平板断面,数值模拟值与理论值相当吻合;而对于箱梁断面,数值识别的气动导数与试验值存在较大误差,数值模拟结果在低折减风速更接近试验值,而在高折减风速处差别明显。为提高钝体断面气动导数的数值模拟精度,须加密空间网格和延长计算时间,从而必须付出高昂的计算时间代价。由此可知,对于钝体特性十分明显的桥梁断面,目前CFD在识别其气动导数方面尚存在明显不足之处,尤其是算法的稳定性及效率问题,还不能取代物理风洞研究钝体桥梁断面的流固耦合问题。     

畸形波作用下二阶波浪载荷对张力腿平台动力响应的影响

畸形波易对海上的建筑物造成极大的危害。为研究畸形波作用下张力腿平台的动力响应特性,考虑张力腿平台的六自由度运动与张力腿非线性恢复刚度,建立非线性耦合运动方程。结合随机频率相位角调制法生成的畸形波波面时历,计算在畸形波条件下平台所受的一阶及二阶和、差频波浪载荷,并采用数值方法求解平台六自由度的运动。结果表明,在畸形波作用下,一阶、二阶波浪载荷均受到畸形波的影响,但各波浪载荷成分的增幅在不同自由度上并不相同。以纵荡为代表的低频运动主要受二阶差频波浪载荷影响,以垂荡、纵摇为代表的高频运动受二阶和频波浪载荷的影响。而由平台水平面内运动引发的下沉运动在二阶差频波浪载荷的作用下显著增大,从而诱发了垂荡运动产生了显著增加,因此在畸形波作用下垂荡运动同时受到二阶和频及差频波浪载荷的影响。此外,由于畸形波具有冲击载荷的特性,不同自由度运动幅值出现时刻并不相同。     

改进的高阶加权紧致非线性差分格式

基于中心紧致三对角系数矩阵的四阶、六阶格式，通过非线性组合五阶WENO差分格式大模板和两个对称小模板对网格半节点函数值的插值计算，得到求解双曲守恒律方程的四阶、五阶加权紧致非线性差分格式。线性对流方程的计算结果验证了格式的计算精度和计算效率；一维无粘Burgers方程的计算结果验证了格式分辨率；一、二维欧拉方程的计算结果验证了格式对非线性问题中激波间断的捕捉能力。所有数值实验均表明，构造的新格式是一个高效、高精度、高分辨率的激波捕捉格式。     

一族无条件稳定的显式结构动力学算法

利用离散控制理论分析HHT-α算法,提出了一族具有可控数值阻尼的无条件稳定显式结构动力学算法—显式HHT-α法,用于线性和非线性结构动力学分析。新算法采用显式的位移、速度递推式。研究了所提算法的精度,稳定性,数值色散和能量耗散特性。研究表明该算法对于线弹型和刚度软化型非线性系统是无条件稳定的,算法数值阻尼由单个参数控制,对于特定的参数值,所提算法不会产生数值能量耗散。此外所提出的显式算法的数值色散和能量耗散特性与隐式HHT-α算法相同。数值算例验证了理论分析的正确性。     

落石冲击作用下环形网耗能性能的理论及数值模拟研究

本文推导了环形网中单个圆环耗散能量的计算公式,建立了两种不同约束条件下环形网受落石冲击的计算模型,讨论了环形网耗能的计算方法。采用LS-DYNA软件对两种模型下环形网受到落石冲击作用的力学性能进行了数值模拟分析,对比分析了两种模型对环形网耗能性能的影响,同时对模型2中影响环形网耗能性能的因素进行了参数分析,并与理论计算结果进行了比较,理论计算结果能较好的预测环形网吸收的最大能量,可为环形网耗能性能的评价及应用提供一定的参考依据。     

基于投影法求解不可压缩流的高精度紧致格式

本文建立了一种基于投影法的求解不可压缩Navier-Stokes(N-S)方程的高精度紧致差分格式。该方法时间上采用Kim和Moin二阶投影法离散,空间上采用高精度紧致格式离散,并提出了一种新的离散压力边界的紧致格式,同时对计算结果进行分析以验证该投影法的精度和格式稳定性。文中Taylor涡列数值计算结果表明,Kim和Moin投影法能使得压力场和速度场均达到时间二阶精度,且高精度紧致格式投影法也具有空间高阶精度。驱动方腔数值模拟结果显示,本文对N-S方程的离散格式具有很好的可靠性,适用于对复杂流体流动的小尺度问题的数值模拟和研究。     

基于ANSYS/LS-DYNA的码头基桩完整性检测的数值模拟和方法研究

以一维应力波理论为基础,运用ANSYS/LS-DYNA显式分析方法,对脉冲荷载作用下的码头基桩完整性检测进行了数值模拟,并对得出的模拟结果进行信号处理,总结得出一种新的码头基桩检测方法。最后将数值模拟曲线与实测曲线进行对比,发现两者取得较好一致,表明数值模拟和检测方法是可靠的,对提高码头桩基检测结果的准确性具有较重要的意义。     

预应力CFRP布加固损伤RC梁的动力特性研究

从理论上推导了预张力与损伤RC梁固有频率之间的定量关系。同时进行了预应力CFRP布加固RC梁的动力特性试验,测定不同预张力条件下,完好梁与损伤梁的一阶频率值。而后利用ANSYS软件建立钢筋混凝土完好梁的有限元模型,根据损伤梁的动力测试结果,运用优化分析的方法得到损伤梁混凝土刚度折减系数;利用一阶频率的试验值对公式进行线性拟合,得到频率影响因素及损伤梁频率计算公式。最后将加固损伤梁一阶频率的理论值与试验值进行比较,发现在低预应力作用下,理论计算结果基本能反映出试验值随预张力变化的趋势,试验值与理论值吻合较好。     

气动噪声预测中非紧致格林函数的数值计算方法

采用声模拟理论预测非紧致结构与非定常流动相互作用诱发的气动噪声时,为考虑边界对声场的散射影响,需要应用非紧致格林函数。为此,发展了一种基于边界元思想的非紧致格林函数数值计算方法,该方法适用于任意外形结构,能直接计算非紧致格林函数及其偏导数。以二维圆柱边界为算例,采用理论解析方法推导了非紧致格林函数及其偏导数的正确表达式,并将数值计算方法结果与理论解析方法结果相比较,验证了数值方法的正确性。     

Weight‐adjusted discontinuous Galerkin methods: Matrix‐valued weights and elastic wave propagation in heterogeneous media

Weight‐adjusted inner products are easily invertible approximations to weighted L² inner products. These approximations can be paired with a discontinuous Galerkin (DG) discretization to produce a time‐domain method for wave propagation which is low storage, energy stable, and high‐order accurate for arbitrary heterogeneous media and curvilinear meshes. In this work, we extend weight‐adjusted DG methods to the case of matrix‐valued weights, with the linear elastic wave equation as an application. We present a DG formulation of the symmetric form of the linear elastic wave equation, with upwind‐like dissipation incorporated through simple penalty fluxes. A semidiscrete convergence analysis is given, and numerical results confirm the stability and high‐order accuracy of weight‐adjusted DG for several problems in elastic wave propagation.     

求解带有不连续波数的二维变系数 Helmholtz方程的一种高精度紧致差分方法

很多实际物理问题都可以由带有不连续波数的变系数 Helmholtz 方程进行数值模拟。Helmholtz 方程的数值方法研究是热点问题之一,具有重要的理论和实际意义。由于波数的不连续性,使用传统的有限差分方法求解带有不连续波数的 Helmholtz 方程时通常无法达到原有差分格式的精度。结合浸入界面方法的思想,对带有不连续波数的二维变系数 Helmholtz 方程构造了一类新的四阶紧致有限差分格式,数值实验验证了新方法的可靠性和有效性。     

A hybrid discontinuous in space and time Galerkin method for wave propagation problems

Medium‐frequency regime and multi‐scale wave propagation problems have been a subject of active research in computational acoustics recently. New techniques have attempted to overcome the limitations of existing discretization methods that tend to suffer from dispersion. One such technique, the discontinuous enrichment method, incorporates features of the governing partial differential equation in the approximation, in particular, the solutions of the homogeneous form of the equation. Here, based on this concept and by extension of a conventional space–time finite element method, a hybrid discontinuous Galerkin method (DGM) for the numerical solution of transient problems governed by the wave equation in two and three spatial dimensions is described. The discontinuous formulation in both space and time enables the use of solutions to the homogeneous wave equation in the approximation. In this contribution, within each finite element, the solutions in the form of polynomial waves are employed. The continuity of these polynomial waves is weakly enforced through suitably chosen Lagrange multipliers. Results for two‐dimensional and three‐dimensional problems, in both low‐frequency and medium‐frequency regimes, show that the proposed DGM outperforms the conventional space–time finite element method. Copyright © 2014 John Wiley & Sons, Ltd.     

Galerkin finite element methods for wave problems

We compare here the accuracy, stability and wave propagation properties of a few Galerkin methods. The basic Galerkin methods with piecewise linear basis functions (called G1FEM here) and quadratic basis functions (called G2FEM) have been compared with the streamwise-upwind Petrov Galerkin (SUPG) method for their ability to solve wave problems. It is shown here that when the piecewise linear basis functions are replaced by quadratic polynomials, the stencils become much larger (involving five overlapping elements), with only a very small increase in spectral accuracy. It is also shown that all the three Galerkin methods have restricted ranges of wave numbers and circular frequencies over which the numerical dispersion relation matches with the physical dispersion relation — a central requirement for wave problems. The model one-dimensional convection equation is solved with a very fine uniform grid to show the above properties. With the help of discontinuous initial condition, we also investigate the Gibbs’ phenomenon for these methods.     

Modeling of multicomponent diffusions and natural convection in unfractured and fractured media by discontinuous Galerkin and mixed methods

Computation of the distribution of species in hydrocarbon reservoirs from diffusions (thermal, molecular, and pressure) and natural convection is an important step in reservoir initialization. Current methods, which are mainly based on the conventional finite‐difference approach, may not be numerically efficient in fractured and other media with complex heterogeneities. In this work, the discontinuous Galerkin (DG) method combined with the mixed finite element (MFE) method is used for the calculation of compositional variation in fractured hydrocarbon reservoirs. The use of unstructured gridding allows efficient computations for fractured media when the cross flow equilibrium concept is invoked. The DG method has less numerical dispersion than the upwind finite‐difference methods. The MFE method ensures continuity of fluxes at the interface of the grid elements. We also use the local DG (LDG) method instead of the MFE to calculate the diffusion fluxes. Results from several numerical examples are presented to demonstrate the efficiency, robustness, and accuracy of the model. Various features of convection and diffusion in homogeneous, layered, and fractured media are also discussed.     

四阶Cahn-Hilliard方程的间断有限元方法

Cahn-Hilliard方程是一类非常重要的四阶扩散方程,具有深刻的物理背景和丰富的理论内涵,对其设计高精度的数值格式具有重要的工程实践价值和科学意义．在本文中我们对四阶Cahn-Hilliard方程设计一种高精度的间断有限元,该方法不同于传统的局部间断有限元方法,不需要引进另外的辅助变量或将方程转化为一阶方程组,能够显著降低计算量和存储量．通过选取合适的数值流通量,我们证明了方法的稳定性和收敛性．数值实验结果表明该方法求解Cahn-Hilliard方程是收敛的和有效的．     

A GPU‐accelerated nodal discontinuous Galerkin method with high‐order absorbing boundary conditions and corner/edge compatibility

Discontinuous Galerkin finite element schemes exhibit attractive features for accurate large‐scale wave‐propagation simulations on modern parallel architectures. For many applications, these schemes must be coupled with nonreflective boundary treatments to limit the size of the computational domain without losing accuracy or computational efficiency, which remains a challenging task. In this paper, we present a combination of a nodal discontinuous Galerkin method with high‐order absorbing boundary conditions for cuboidal computational domains. Compatibility conditions are derived for high‐order absorbing boundary conditions intersecting at the edges and the corners of a cuboidal domain. We propose a GPU implementation of the computational procedure, which results in a multidimensional solver with equations to be solved on 0D, 1D, 2D, and 3D spatial regions. Numerical results demonstrate both the accuracy and the computational efficiency of our approach.     

A space–time discontinuous Galerkin method for the solution of the wave equation in the time domain

In recent years, the focus of research in the field of computational acoustics has shifted to the medium frequency regime and multiscale wave propagation. This has led to the development of new concepts including the discontinuous enrichment method. Its basic principle is the incorporation of features of the governing partial differential equation in the approximation. In this contribution, this concept is adapted for the simulation of transient problems governed by the wave equation. We present a space–time discontinuous Galerkin method with Lagrange multipliers, where the shape approximation in space and time is based on solutions of the homogeneous wave equation. The use of hierarchical wave‐like basis functions is enabled by means of a variational formulation that allows for discontinuities in both the spatial and the temporal discretizations. Numerical examples in one space dimension demonstrate the outstanding performance of the proposed method compared with conventional space–time finite element methods. Copyright © 2008 John Wiley & Sons, Ltd.     

Modelling of nonlinear dilatation response of fluids containing columns plastic and shear relaxation considered

Summary The non-linear wave equation governing the propagation and scatter of dilatation waves in discontinuous media is presented and its Eulerian numerical analogue is used to study scatter of acoustic dilatation waves by colums and ducts in elastic and visco-elastic fluids. Plastic and visco-elastic relaxation mechanisms are considered. The spectral form of the wave equation is developed and used to discuss dispersion. Selected applications of the numerical analogue to simulation of scatter, propagation and echo attenuation presented.     

An implicit discontinuous Galerkin finite element framework for modeling fracture failure of ductile materials undergoing finite plastic deformation

It is a challenge to achieve a complete simulation of fracture failure in ductile materials undergoing large plastic deformation within implicit finite element frameworks due to instability issues. Currently, traditional nodal force or crack surface traction release methods target the direct release of tractions on cracked surfaces within the current time/load step. An abrupt change from a system without cracks to another system with cracks may contribute to the instability issues. Specifically, because of broken meshes, discontinuous Galerkin (DG) methods have an advantage over traditional continuous elements in naturally accommodating crack openings along DG interfaces across elements. To improve the convergence in nonlinear iterations during crack openings, we propose a relaxation scheme for DG formulations to gradually recover the traction‐free condition on cracked surfaces. Furthermore, this DG‐based relaxation scheme for crack openings in finite plastic media has been consistently formulated within the incomplete interior penalty DG framework. Finally, we have demonstrated a good performance of the proposed implicit DG formulation along with the DG relaxation scheme by successfully solving a nuclear fuel rod structural failure problem with multiple hydride crack openings and the Sandia Fracture Challenge benchmark.