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1.
波动问题有限元离散后会引起数值误差, 数值频散的本质就是数值误差传播引起的非物理解. 数值频散不仅没有实际意义, 而且还会影响对真实波动现象的认识. 为厘清有限元三角网格中波动数值频散的影响因素, 本文推导了集中质量矩阵和一致质量矩阵的频散函数, 同时给出了组合质量矩阵的频散函数, 并对不同质量矩阵的数值频散进行了对比研究. 理论分析和数值计算结果表明: 有限元三角网格中波动的数值频散受网格布局、 波传播方向、 单元网格纵横比以及质量矩阵的影响; 一致质量矩阵的数值频散比集中质量矩阵更易受到波传播方向的影响; 不合理的三角网格单元会对数值相速度(数值频散)产生不良影响; 正三角网格中波动的数值频散几乎不受波传播方向的影响; 一致质量矩阵与集中质量矩阵的线性组合能够有效地压制数值频散. 相似文献
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波动方程有限差分法是一种使用广泛的地震波数值模拟方法.但是有限差分法本身固有存在着数值频散问题，会降低地震波场模拟的精度与分辨率.为了克服常规有限差分算子的数值频散，本文针对VTI介质地震波数值模拟问题，构造了频率-空间域qP波波动方程高精度有限差分优化算子，根据最优化理论中高斯-牛顿法确定了高精度有限差分算子的优化系数.利用常规差分算子和高精度优化差分算子对归一化相速度的频散关系精度进行了对比分析，并对均匀各向同性介质和均匀VTI介质中的qP波地震波场进行了有限差分数值模拟，通过频散关系精度分析和波场数值模拟结果表明：有限差分优化算子具有较高的波场数值模拟精度，有效压制了传统有限差分算子数值模拟中的数值频散现象，提高了有限差分算子精度，为VTI介质频率-空间域qP波正演模拟奠定了基础. 相似文献
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本文对声波与弹性波方程进行有限元法离散,构造有限元法频散关系的一般特征值问题,分析了时间离散格式为中心差分的三角网格有限元法声波与弹性波模拟的频散特性. 比较了三种质量矩阵即分布式质量矩阵、集中质量矩阵和混合质量矩阵对有限元法频散的影响;选取四种典型三角网格,分析了混合质量矩阵有限元（MFEM）频散的方向各向异性;数值频散、方向各向异性随插值阶数的增加逐渐减弱,当空间为三阶插值时,频散主要表现为随采样率的变化而几乎无明显方向各向异性, 其频散幅值也较小. 控制其他影响因素不变的情况下,研究了不同波速比介质中弹性波的数值频散. 最后给出了三角网格MFEM的数值耗散性. 相似文献
4.
波动方程有限差分法是波场模拟的一个重要方法,为解决常规有限差分法存在着数值频散的问题,本文从具有垂直对称轴的三维横向各向同性(VTI)介质频率-空间域qP波动方程出发,在常规差分算子的基础上构造了适合三维VTI介质的频率空间域有限差分优化算子,然后利用最优化理论中的Gauss-Newton法求解了优化算子的系数,使差分方程的相速度与波动方程的相速度尽量吻合,从而在理论上使网格数值频散达到极小,精度对比分析及数值测试表明,有限差分优化算子具有较高的波场数值模拟精度,有效地压制了数值频散现象,为三维VTI介质频率一空间域qP波正演模拟研究提供了理论基础. 相似文献
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We derive a meshless numerical method based on smoothed particle hydrodynamics (SPH) for the simulation of conservative solute transport in heterogeneous geological formations. We demonstrate that the new proposed scheme is stable, accurate, and conserves global mass. We evaluate the performance of the proposed method versus other popular numerical methods for the simulation of one- and two-dimensional dispersion and two-dimensional advective–dispersive solute transport in heterogeneous porous media under different Pèclet numbers. The results of those benchmarks demonstrate that the proposed scheme has important advantages over other standard methods because of its natural ability to control numerical dispersion and other numerical artifacts. More importantly, while the numerical dispersion affecting traditional numerical methods creates artificial mixing and dilution, the new scheme provides numerical solutions that are “physically correct”, greatly reducing these artifacts. 相似文献
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Numerical dispersion, numerical oscillation, and peak clipping are common numerical difficulties in solving advection-dispersion equations. The development of numerical approaches that can handle these numerical difficulties with reasonable computational efforts is an ongoing challenge. In this paper, an interpolation-corrected modified method of characteristics (ICMMOC) is proposed for solving advection-dispersion equations. The ICMMOC is an improved version of the modified method of characteristics (MMOC). It uses a high-order (second-order or higher) interpolation scheme to reduce numerical dispersion and an interpolation-correction procedure to eliminate numerical oscillation. A simple peak capturing scheme to overcome the peak clipping problem is also developed in this study. Simulation results show that the ICMMOC is able to overcome the aforementioned numerical difficulties for a large range of grid Peclet numbers. 相似文献
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Development of a family of unconditionally stable explicit direct integration algorithms with controllable numerical energy dissipation 
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下载免费PDF全文 James M. Ricles 《地震工程与结构动力学》2014,43(9):1361-1380
The implicit dissipative generalized‐ α method is analyzed using discrete control theory. Based on this analysis, a one‐parameter family of explicit direct integration algorithms with controllable numerical energy dissipation, referred to as the explicit KR‐α method, is developed for linear and nonlinear structural dynamic numerical analysis applications. Stability, numerical dispersion, and energy dissipation characteristics of the proposed algorithms are studied. It is shown that the algorithms are unconditionally stable for linear elastic and stiffness softening‐type nonlinear systems, where the latter indicates a reduction in post yield stiffness in the force–deformation response. The amount of numerical damping is controlled by a single parameter, which provides a measure of the numerical energy dissipation at higher frequencies. Thus, for a specific value of this parameter, the resulting algorithm is shown to produce no numerical energy dissipation. Furthermore, it is shown that the influence of the numerical damping on the lower mode response is negligible. It is further shown that the numerical dispersion and energy dissipation characteristics of the proposed explicit algorithms are the same as that of the implicit generalized‐ α method. A numerical example is presented to demonstrate the potential of the proposed algorithms in reducing participation of undesired higher modes by using numerical energy dissipation to damp out these modes. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
8.
多次透射公式（MTF）物理概念简单,便于在计算机上实现时空解藕的高精度波动数值模拟。然而,MTF与其它局部人工边界条件类似,存在数值模拟失稳问题,如高频振荡便是可能出现的失稳现象。本文在分析MTF高频振荡失稳机理的基础上,提出了在波动有限元数值模拟中消除MTF高频振荡失稳的一种措施,即在整个有限元数值模拟区内施加与应变速率成正比的较小粘性阻尼;同时,讨论了这一稳定措施的有效性及其对数值计算精度的影响,并通过数值试验检验了这一稳定措施的可行性。结果表明,消除高频振荡失稳的措施行之有效,且只对波动有限元数值模拟中无意义的高频分量具有抑制作用,而对有意义的较低频段内的波动有限元数值模拟精度影响较小。 相似文献
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This paper aims to provide a guideline for numerical modeling of reinforced concrete (RC) frame elements for the seismic performance assessment of a structure. Several types of numerical models of RC frame elements are available in nonlinear structural analysis packages. Because the numerical models are formulated based on different assumptions and theories, the models' accuracy, computing time, and applicability vary, which poses a great difficulty to practicing engineers and limits their confidence in the analysis results. In this study, the applicability of five representative numerical models of RC frame elements is evaluated through comparison with 320 experimental results available from the Pacific Earthquake Engineering Research column database. The accuracy of a numerical model is evaluated according to its initial stiffness, peak strength, and energy dissipation capacity of the global responses. In addition, a parametric study of a cantilever RC column subjected to earthquake excitation is carried out to systematically evaluate the consequence of the adopted numerical models on the maximum inelastic structural responses. It is found from this study that the accuracy of the numerical models is sensitive to shear force demand–capacity ratio. If a structural period is short and the structure is shear critical, the use of numerical models that can explicitly capture the shear deformation and failure is suggested. If the structural period is long, the selection of a numerical model does not greatly influence the global response of the structure. The paper also presents statistical parameters of each numerical model, which can be used for probabilistic seismic performance assessment. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
10.
Oscillation and numerical dispersion limit the reliability of numerical solutions of the convection-dispersion equation when finite difference methods are used. To eliminate oscillation and reduce the numerical dispersion, an optimal upstream weighting with finite differences is proposed. The optimal values of upstream weighting coefficients numerically obtained are a function of the mesh Peclet number used. The accuracy of the proposed numerical method is tested against two classical problems for which analytical solutions exist. The comparison of the numerical results obtained with different numerical schemes and those obtained by the analytical solutions demonstrates the possibility of a real gain in precision using the proposed optimal weighting method. This gain in precision is verified by interpreting a tracer experiment performed in a laboratory column. 相似文献
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In a pseudodynamic test, errors in restoring-force feedback are introduced into numerical computations. Some of these errors can excite the higher-frequency response of the specimen. In this paper, the use of viscous and numerical dampings to eliminate spurious higher-frequency effects is studied. Since the tangent stiffness of a non-linear specimen cannot be measured accurately, initial-stiffness-dependent viscous damping is considered. In addition, an explicit integration algorithm with desired numerical damping properties is proposed and examined. The analytical and numerical studies presented indicate that viscous-damping properties can be substantially changed by non-linear deformations. For this reason, the use of numerical damping appears to be more advantageous. 相似文献
13.
We propose a symplectic partitioned Runge-Kutta （SPRK） method with eighth-order spatial accuracy based on the extended Hamiltonian system of the acoustic waveequation. Known as the eighth-order NSPRK method, this technique uses an eighth-orderaccurate nearly analytic discrete （NAD） operator to discretize high-order spatial differentialoperators and employs a second-order SPRK method to discretize temporal derivatives.The stability criteria and numerical dispersion relations of the eighth-order NSPRK methodare given by a semi-analytical method and are tested by numerical experiments. We alsoshow the differences of the numerical dispersions between the eighth-order NSPRK methodand conventional numerical methods such as the fourth-order NSPRK method, the eighth-order Lax-Wendroff correction （LWC） method and the eighth-order staggered-grid （SG）method. The result shows that the ability of the eighth-order NSPRK method to suppress thenumerical dispersion is obviously superior to that of the conventional numerical methods. Inthe same computational environment, to eliminate visible numerical dispersions, the eighth-order NSPRK is approximately 2.5 times faster than the fourth-order NSPRK and 3.4 timesfaster than the fourth-order SPRK, and the memory requirement is only approximately47.17% of the fourth-order NSPRK method and 49.41% of the fourth-order SPRK method,which indicates the highest computational efficiency. Modeling examples for the two-layermodels such as the heterogeneous and Marmousi models show that the wavefields generatedby the eighth-order NSPRK method are very clear with no visible numerical dispersion.These numerical experiments illustrate that the eighth-order NSPRK method can effectivelysuppress numerical dispersion when coarse grids are adopted. Therefore, this methodcan greatly decrease computer memory requirement and accelerate the forward modelingproductivity. In general, the eighth-order NSPRK method has tremendous potential value forseismic exploration and seismology research. 相似文献
14.
《Advances in water resources》2005,28(8):793-806
In this paper, the numerical errors associated with the finite difference solutions of two-dimensional advection–dispersion equation with linear sorption are obtained from a Taylor analysis and are removed from numerical solution. The error expressions are based on a general form of the corresponding difference equation. The variation of these numerical truncation errors is presented as a function of Peclet and Courant numbers in X and Y direction, a Sink/Source dimensionless number and new form of Peclet and Courant numbers in X–Y plane. It is shown that the Crank–Nicolson method is the most accurate scheme based on the truncation error analysis. The effects of these truncation errors on the numerical solution of a two-dimensional advection–dispersion equation with a first-order reaction or degradation are demonstrated by comparison with an analytical solution for predicting contaminant plume distribution in uniform flow field. Considering computational efficiency, an alternating direction implicit method is used for the numerical solution of governing equation. The results show that removing these errors improves numerical result and reduces differences between numerical and analytical solution. 相似文献
15.
F.A. Radu N. Suciu J. HoffmannA. Vogel O. Kolditz C.-H. ParkS. Attinger 《Advances in water resources》2011,34(1):47-61
This work deals with a comparison of different numerical schemes for the simulation of contaminant transport in heterogeneous porous media. The numerical methods under consideration are Galerkin finite element (GFE), finite volume (FV), and mixed hybrid finite element (MHFE). Concerning the GFE we use linear and quadratic finite elements with and without upwind stabilization. Besides the classical MHFE a new and an upwind scheme are tested. We consider higher order finite volume schemes as well as two time discretization methods: backward Euler (BE) and the second order backward differentiation formula BDF (2). It is well known that numerical (or artificial) diffusion may cause large errors. Moreover, when the Péclet number is large, a numerical code without some stabilising techniques produces oscillating solutions. Upwind schemes increase the stability but show more numerical diffusion. In this paper we quantify the numerical diffusion for the different discretization schemes and its dependency on the Péclet number. We consider an academic example and a realistic simulation of solute transport in heterogeneous aquifer. In the latter case, the stochastic estimates used as reference were obtained with global random walk (GRW) simulations, free of numerical diffusion. The results presented can be used by researchers to test their numerical schemes and stabilization techniques for simulation of contaminant transport in groundwater. 相似文献
16.
Dimitris Pitilakis Matt Dietz David Muir Wood Didier Clouteau Arezou Modaressi 《Soil Dynamics and Earthquake Engineering》2008,28(6):453-467
This paper provides an insight into the numerical simulation of soil–structure interaction (SSI) phenomena studied in a shaking table facility. The shaking table test is purposely designed to confirm the ability of the numerical substructure technique to simulate the SSI phenomenon. A model foundation–structure system with strong SSI potential is embedded in a dry bed of sand deposited within a purpose designed shaking-table soil container. The experimental system is subjected to a strong ground motion. The numerical simulation of the complete soil–foundation–structure system is conducted in the linear viscoelastic domain using the substructure approach. The matching of the experimental and numerical responses in both frequency and in time domain is satisfying. Many important aspects of SSI that are apparent in the experiment are captured by the numerical simulation. Furthermore, the numerical modelling is shown to be adequate for practical engineering design purposes. 相似文献
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In recent years, various attempts have been made to estimate the amount of numerical mixing in numerical ocean models due
to discretisation errors of advection schemes. In this study, a high-resolution coastal model using the ocean circulationmodel
GETM is applied to the Western Baltic Sea, which is characterised by energetic and episodic inflows of dense bottom waters
originating from the Kattegat. The model is equipped with an easy-to-implement diagnostic method for obtaining the numerical
mixing which has recently been suggested. In this diagnostic method, the physical mixing is defined as the mean tracer variance
decay rate due to turbulent mixing. The numerical mixing due to discretisation errors of tracer advection schemes is defined
as the decay rate between the advected square of the tracer variance and the square of the advected tracer, which can be directly
compared to the physical variance decay. The source and location of numerical mixing is further investigated by comparing
different advection schemes and analysing the amount of numerical mixing in each spatial dimension during the advection time
step. The results show that, for the setup used, the numerically and physically induced mixing have the same orders of magnitude
but with different vertical and horizontal distributions. As the main mechanism for high numerical mixing, vertical advection
of tracers with strong vertical gradients has been identified. The main reason for high numerical mixing is due to bottom-following
coordinates when density gradients, especially for regions of steep slopes, are advected normal to isobaths. With the bottom-following
coordinates used here, the horizontal gradients are reproduced by a spurious sawtooth-type profile where strong advection
through, but not along, the vertical coordinate levels occurs. Additionally, the well known relation between strong tracer
gradients and high velocities on the one and high numerical mixing on the other hand is approved quantitatively within this
work. 相似文献
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混凝土的数值计算模型在滞回性能分析中往往比较难收敛,利用有限元软件ADINA提供Drucker-Prager模型的Cap修正屈服准则确立的非协调参数Drucker-Prager模型对预应力节段拼装混凝土桥墩进行数值分析,对预应力节段拼装桥墩在低周往复荷载作用下的滞回性能进行分析。通过比较采用非协调参数Drucker-Prager模型建立的数值模型计算得到的滞回曲线与试验得到的结果,两者吻合程度较高。基于这一成果可以通过数值模拟的方式获得预应力节段拼装桥墩的滞回曲线与相关数据,可应用于预应力节段拼装桥墩抗震计算和设计。 相似文献
20.
In the evaluation of potential risk from ingestion of groundwater near an impacted site, numerical simulation of fate and transport processes of chemicals of concern is often required. If there is potential concern about multiple chemicals, numerical simulation of each chemical separately is often needed. In this paper, a semi-analytical solution is presented based on a numerical solution of the transport of a conservative and nonreactive tracer. When multiple chemicals undergoing sorption and first-order degradation need to be modeled, we can avoid performing individual numerical simulations for each chemical by applying the semi-analytical solution. Numerical test runs were conducted to verify the semi-analytical solution; simulation results reveal that the concentrations derived from the semi-analytical solution are identical to those derived from the individual numerical fate and transport model simulations. The semi-analytical solution requires steady-state flow conditions, no continuing contaminant source, and similar initial source concentration distributions. 相似文献