共查询到20条相似文献，搜索用时 15 毫秒
1.
提出混合ADI-FDTD亚网格技术开展频散介质GPR正演,即在物性参数变化剧烈局部区域采用细网格剖分ADI-FDTD计算,其他的区域采用粗网格剖分常规FDTD计算,ADI-FDTD突破了CFL条件的限制,可选取与粗网格一致的大时间步长,有效地提高了计算效率.本文首先基于Debye方程,推导了粗网格FDTD及细网格ADI-FDTD频散介质差分格式,着重对粗细两种网格结合的场值交换方式进行了深入探讨,给出了该算法的计算流程.然后以一个薄层模型为例,分别应用粗网格、细网格、混合ADI-FDTD亚网格算法对该模型进行正演,计算资源的占用及模拟精度说明了混合ADI-FDTD亚网格算法的优势.最后,建立频散介质与非频散介质的组合模型,应用3种方法对该模型进行正演,对比3种方法优劣,分析雷达剖面中非频散介质及频散介质中波形特征,有效地指导雷达资料的精确解释. 相似文献
2.
An innovative method of analysis was developed to simulate the non-linear seismic finite-amplitude liquid sloshing in two-dimensional containers. In view of the irregular and time-varying liquid surface, the method employed a curvilinear mesh system to transform the non-linear sloshing problem from the physical domain with an irregular free-surface boundary into a computational domain in which rectangular grids can be analysed by the finite difference method. Non-linearities associated with both the unknown location of the free surface and the high-order differential terms were considered. The Crank–Nicolson time marching scheme was employed and the resulting finite difference algorithm is unconditionally stable and very lightly damped with respect to the temporal co-ordinate. In order to minimize numerical instability caused by the computational dispersion in spatially discretized surface wave, a second-order dissipation term was added to the system to filter out the spurious high-frequency waves. Sloshing effects and structural response were measured in terms of sloshing amplitude, base shear and overturning moment generated by the hydrodynamic pressure of the liquid exerted on the container walls. Simulation results of liquid sloshing induced by earthquake and harmonic base excitations were compared with those of the linear wave theory and the limitations of the latter in assessing the response of seismically excited liquids were addressed. 相似文献
3.
A technique for modeling transient wave propagation in unbounded media is extended and applied to seismic soil–structure interaction analysis in the time domain. The technique, based on the discontinuous Galerkin method, requires lower computational cost and less storage than the boundary element method, and the time‐stepping scheme resulting from Newmark's method in conjunction with the technique is unconditionally stable, allowing for efficient and robust time‐domain computations. To extend the technique to cases characterized by seismic excitation, the free‐field motion is used to compute effective forces, which are introduced on the boundary of the computational domain containing the structure and the soil in the vicinity of the structure. A numerical example on a dam–foundation system subjected to seismic excitation demonstrates the performance of the method. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
4.
交替方向隐式差分(ADI-FDTD)法突破了Courand-Friedrich-Levy(CFL)条件的约束,具有无条件稳定的特点;而单轴各向异性完全匹配层(UPML)边界条件具有宽频带吸收特性,不需要对电场和磁场进行分裂,迭代公式简单,便于编程的特点.综合两者优势,本文提出了基于UPML边界条件的ADI-FDTD探地雷达数值模拟算法,通过对3个二维Maxwell方程进行离散化,推导了GPR波的ADI-FDTD及其UPML边界条件的两个子时间步的迭代差分公式,并分别给出了详细计算步骤.在此基础上,开发了相应的模拟程序,应用该程序对两个GPR模型进行了正演模拟,得到了两个正演模型的wiggle图、扫描图与全波场快照.通过分析这些雷达剖面图与波场快照,可以了解雷达波形在空间中的传播过程及变化规律,有助于雷达资料更可靠、更准确的解释.模拟结果表明,基于UPML边界条件的ADI-FDTD算法可取较大的时间步长,消除了截断边界处的强反射,能对简单与复杂GPR模型进行快速、高效模拟. 相似文献
5.
在采用有限差分方法开展探地雷达复杂目标体精细结构模拟时,为了提高计算精度,常采用非均匀网格对目标区域划分小尺寸的网格,以压制离散网格频散现象和保证有限差分方法的稳定性.常规非均匀网格和自适应亚网格技术在网格剖分数量和粗细网格边界处理上难以达到计算效率和计算精度的均衡.本文根据隐形斗篷(invisible cloak)理论,将基于变换光学(Transformation optics)理论应用于有限差分探地雷达数值计算中.该理论的主要思想是基于目标参数变化而保持电磁场的传播不变性,在坐标变换后,Maxwell方程的形式可以维持不变,而使得相对介电常数与磁导率的表达式变得复杂.通过这种方式可以虚拟地扩大目标体所占的网格节点数,减少背景介质区域的网格数,不增加模型空间的网格总数.另外,这种网格划分方式不但提高了计算效率,同时也可以克服亚网格技术边界反射误差的影响.本文推导实现了基于变换光学的二维有限差分方法,通过典型探地雷达模型测试,对比分析了该方法与常规有限差分、变网格有限差分和自适应亚网格有限差分的优缺点.计算结果验证了基于变换光学的有限差分可用于探地雷达目标精细结构模拟,具有较高的计算精度和计算效率. 相似文献
6.
Qian-Jiang Zhang Shi-Kun Dai Long-Wei Chen Jian-Ke Qiang Kun Li Dong-Dong Zhao 《应用地球物理》2016,13(2):257-266
To deal with the problem of low computational precision at the nodes near the source and satisfy the requirements for computational efficiency in inversion imaging and finite-element numerical simulations of the direct current method, we propose a new mesh refinement and recoarsement method for a two-dimensional point source. We introduce the mesh refinement and mesh recoarsement into the traditional structured mesh subdivision. By refining the horizontal grids, the singularity owing to the point source is minimized and the topography is simulated. By recoarsening the horizontal grids, the number of grid cells is reduced significantly and computational efficiency is improved. Model tests show that the proposed method solves the singularity problem and reduces the number of grid cells by 80% compared to the uniform grid refinement. 相似文献
7.
8.
时域有限差分(FDTD)方法使用Yee网格剖分电磁场的空间采样,通过时间步迭代实现电磁场数值模拟,具有内存消耗低、计算简单等特点,常用于瞬变电磁三维正演.然而,常规FDTD方法的时间迭代步长Δt受Courant-Friedrich-Lewy(CFL)条件严格限制,过多的迭代次数以及过密的采样往往导致计算速度慢、累积误差不断增大.本文提出一种不受CFL条件约束的无条件稳定隐式差分算法Crank-Nicolson FDTD(CN-FDTD)用于瞬变电磁三维正演.基于Crank-Nicolson差分方法对Maxwell方程组重新离散,空间网格仍然采用Yee元胞,时间步进采用在整时间步电场、磁场同时采样的策略,建立无条件稳定FDTD格式,突破CFL条件限制.与常规FDTD交替采样相比,CN-FDTD电场、磁场同时采样的策略构成的隐式差分格式,需要求解大型稀疏矩阵方程组.通常,瞬变电磁三维正演模型中产生的矩阵阶数往往较大,需要占用大量内存和求解时间.为解决上述问题,采用Crank-Nicolson-cycle-sweep-uniform(CNCSU-FDTD)方法近似求解CN-FDTD方程,在保证求解精度的同时,计算效率大幅提高.在边界条件处理上,采用双线性变换推导了复频率参数完全匹配层(CFS-PML)吸收边界.采用均匀半空间模型、四类三层模型进行精度验证,发现CN-FDTD三维正演结果与解析解、线性数字滤波解吻合较好.之后,与接触带上的低阻复杂模型进行对比,结果显示CN-FDTD正演结果与矢量有限元、有限体积法以及FDTD计算结果吻合较好.在此基础上,研究了时间步放大对CN-FDTD计算精度的影响,发现最大时间步放大到常规FDTD的3200倍时才会在晚期出现较明显的误差.在一台CPU为Intel Core i5-7300HQ的笔记本电脑单线程计算条件下,模拟到关断后30 ms仅需要50 min.在进行并行化后,将有望实现复杂模型分钟级的三维正演,从而为三维反演提供可靠、快速的正演方法. 相似文献
9.
A numerical method has been proposed by Ross [Ross PJ. Modeling soil water and solute transport-fast, simplified numerical solutions. Agron J 2003; 95(6): 1352–1361.] to solve one-dimensional soil water movement problems. The Ross method is a noniterative numerical scheme, that can reduce computational time without sacrificing computational accuracy. The main aim of this study is to present a general form of the Ross method for two- and three-dimensional variably saturated flow. The established numerical model (R3D) is widely tested using five problems, in which the numerical solutions of R3D are compared with analytical solutions, laboratory data, and solutions from a traditional iterative numerical model. The comparison shows that R3D accommodates various hydraulic functions and boundary conditions. Results from R3D, which does not require iteration, are as accurate as results from iterative model. With the help of the primary variable switching technique, this model is unconditionally mass conservative, and computes infiltration into dry soil more efficiently. R3D is thus considered as an efficient tool for its high accuracy and efficiency for solving two- and three-dimensional variably saturated flow problems. 相似文献
10.
The effect of mesh type on the accuracy and computational demands of a two-dimensional Godunov-type flood inundation model is critically examined. Cartesian grids, constrained and unconstrained triangular grids, constrained quadrilateral grids, and mixed meshes are considered, with and without local time stepping (LTS), to determine the approach that maximizes computational efficiency defined as accuracy relative to computational effort. A mixed-mesh numerical scheme is introduced so all grids are processed by the same solver. Analysis focuses on a wide range of dam-break type test cases, where Godunov-type flood models have proven very successful. Results show that different mesh types excel under different circumstances. Cartesian grids are 2–3 times more efficient with relatively simple terrain features such as rectilinear channels that call for a uniform grid resolution, while unstructured grids are about twice as efficient in complex domains with irregular terrain features that call for localized refinements. The superior efficiency of locally refined, unstructured grids in complex terrain is attributable to LTS; the locally refined unstructured grid becomes less efficient using global time stepping. These results point to mesh-type tradeoffs that should be considered in flood modeling applications. A mixed mesh model formulation with LTS is recommended as a general purpose solver because the mesh type can be adapted to maximize computational efficiency. 相似文献
11.
This paper proposes a non‐iterative time integration (NITI) scheme for non‐linear dynamic FEM analysis. The NITI scheme is constructed by combining explicit and implicit schemes, taking advantage of their merits, and enables stable computation without an iteration process for convergence even when used for non‐linear dynamic problems. Formulation of the NITI scheme is presented and its stability is studied. Although the NITI scheme is not unconditionally stable when applied to non‐linear problems, it is stable in most cases unless stiffness hardening occurs or the problem has a large velocity‐dependent term. The NITI scheme is applied to dynamic analysis of the non‐linear soil–structure system and computation results are compared with those by the central difference method (CDM). Comparison shows that the stability of the NITI scheme is superior to that of the CDM. Accuracy of the NITI scheme is verified because its results are identical with those by the CDM in which the time step is set as 1/10 of that for the NITI scheme. The application of the NITI scheme to the mesh‐partitioned FEM is also proposed. It is applied to dynamic analysis of the linear soil–structure system. It yields the same results as a conventional single‐domain FEM analysis using the Newmark β method. This result verifies the usability of mesh‐partitioned FEM analysis using the NITI scheme. Copyright © 2003 John Wiley& Sons, Ltd. 相似文献
12.
A mesh grading approach based on investigated lump method has been presented for simulating wave propagation in high velocity-contrast media. Unstructured fine grids are used to discretize the low wave-velocity medium in order to ensure the accuracy of numerical computation, and unstructured coarse grids are used for the high wave-velocity medium in order to substantially reduce the computational cost. On the interface, one coarse grid can match the fine grids of arbitrary odd number. The key feature of the proposed method is the constructions of investigated lumps on the interfaces of media. The transition zone, which is commonly used in the discontinuous grid scheme based on the staggered-grid finite-difference method, will not be used any more. Moreover, the computational instability that the discontinuous grid schemes frequently encountered does not arise in the proposed method. The comparisons with the analytical solutions and the application in studying the effects of sedimentary basin demonstrated that the mesh grading approach is a valid, accurate, convenient and flexible algorithm in simulating wave propagations in high velocity-contrast media with irregular interfaces. 相似文献
13.
Local coupling instability will occur when the numerical scheme of absorbing boundary condition and that of the field wave equation allow energies to spontaneously enter into the computational domain. That is, the two schemes support common wave solutions with group velocity pointed into the computation domain. The key to eliminate local coupling instability is to avoid such wave solutions. For lumped-mass finite element simulation of P-SV wave motion in a 2D waveguide, an approach for stable implementation of high order multi-transmitting formula is provided. With a uniform rectangular mesh, it is proven and validated that high-frequency local coupling instability can be eliminated by setting the ratio of the element size equal to or greater than \(\sqrt 2 \) times the ratio of the P wave velocity to the S wave velocity. These results can be valuable for dealing instability problems induced by other absorbing boundary conditions. 相似文献
14.
传统时间域航空电磁全波形正演模拟主要采用间接法(褶积算法)和直接法(时域有限差分方法等),然而褶积算法需要获得精确的电流二阶导数,这给发射电流数据采集工作带来极大挑战;时域有限差分方法受到网格和时间步长的严格限制,缺乏灵活性.为解决这些问题,本文采用时域有限元方法,通过直接改变每个时间道上的瞬时电流强度模拟任意发射波形的电磁响应.由于无需计算电流二阶导数,大大提高了正演结果的精度.利用基于非结构四面体网格的矢量有限元方法和后推欧拉技术对时间域电场扩散方程进行空间和时间离散,实现三维航空电磁时间域全波形的直接正演模拟.由此不仅可以模拟复杂的地电结构,而且基于后推欧拉法的无条件稳定性,可以更加灵活地选取时间步长,提高计算效率.通过与1D数值模拟结果进行对比验证了该方法的准确性.本文对三维柱状体模型上HELITEM MULTIPULSE和VTEM系统实际发射波形电磁响应进行模拟,并与褶积算法的结果进行比较,验证了本文算法模拟实际发射波形电磁响应的优越性.对复杂三维地质体模型上不同发射波形电磁响应进行模拟,验证了时间域有限元算法可有效处理复杂地下地质结构. 相似文献
15.
三维地震波走时计算技术是三维地震反演、层析成像、偏移成像等诸多地震数据处理技术中非常重要的正演计算工具.为了获得精度高且兼顾效率的三维走时计算方法:首先,在常规双线性插值公式推导过程中,充分利用平面波双线性假设的结论,获得了二元极小值超越方程的解析解,进而推导出了准确的局部走时计算公式,同时构造性地证明了该计算公式满足地震波的传播规律和Eikonal方程;其次,引入迎风差分的基本思想,提出迎风双线性插值的局部走时计算策略,该计算策略能简化算法、提高效率且保证无条件稳定性;然后,将上述计算公式和迎风双线性插值策略与常规快速推进法中的窄带技术结合,获得了一种新的基于快速推进迎风双线性插值法的三维地震波走时计算方法;最后,通过精度和效率分析检验了新算法的精度、效率和正确性,并通过计算实例验证了算法在面对复杂介质时的稳定性和有效性. 相似文献
16.
瞬变电磁三维时域有限差分（FDTD）正演的网格剖分受最小网格尺寸、时间步长、边界条件、目标尺寸、模型尺寸等的影响,结构化网格一直存在最小网格尺寸受限于异常目标尺寸的矛盾;尽管非均匀网格能够在保证模型尺寸的前提下尽可能的降低网格数量,但由于Yee网格结构的限制,非均匀网格不能无限制的扩大单一方向的尺寸,这是为了避免边界网格区域出现长宽比过大的畸形网格,影响计算精度甚至导致结果发散.在非均匀网格剖分的基础上,本文提出了瞬变电磁三维FDTD正演的多尺度网格方法,即首先使用较大尺寸的粗网格进行第一次剖分,然后在希望加密的区域进行二次剖分,使计算域中包含粗、细两套网格.尽管细网格包含在粗网格内部,但其具有Yee网格的全部属性,因而可以在网格中设置不同的电性参数模拟不同形状的目标.基于Maxwell方程组推导了细网格内电场和磁场的迭代公式,基于泰勒展开给出了设置粗、细网格后产生的内部边界条件,使电磁场的传播在粗、细网格和时间步进上得到统一.采用均匀半空间中包含三维低阻异常的经典模型和三维接触带复杂模型进行精度验证,发现多分辨网格方法计算结果满足精度要求.使用"L"型异常模型计算采用多分辨网格方法和不采用多分辨网格的传统FDTD方法对比计算效率,发现多分辨网格算法能够显著提高计算效率,并能够保证计算精度. 相似文献
17.
提出了声波正演数值模拟中计算网格间差分阶数(精度)的不衔接而引起的边界反射效应问题,采用不同中心网格有限差分法求解声波波动方程来验证.数值实例分析表明,同差分阶数间不存在任何边界效应,而当差分阶数较低且网格间差分阶数递变较大时,边界效应显著,通过缩小差分网格间的递变阶数并提高相应的离散阶数,可以有效压制该边界效应,并保... 相似文献
18.
《Advances in water resources》2001,24(8):899-911
A new computational method for the calculation of shallow water flows with moving physical boundaries is presented. The procedure can cope with shallow water problems having arbitrarily complex geometries and moving boundary elements. Although the method provides a fully boundary-fitted capability, no mesh generation is required in the conventional sense. Solid regions are simply cut out of a background Cartesian mesh with their boundaries represented by different types of cut cell. Moving boundaries are accommodated by up-dating the local cut cell information on a stationary background mesh as the boundaries move. No large-scale re-meshing is required. For the flow calculations, a multi-dimensional high resolution upwind finite volume scheme is used in conjunction with an efficient approximate Riemann solver at flow interfaces, and an exact Riemann solution for a moving piston at moving boundary elements. The method is validated for test problems that include a ship's hull moving at supercritical velocity and two hypothetical landslide events where material plunges laterally into a quiescent shallow lake and a fiord. 相似文献
19.
A dual-ship-towed marine electromagnetic (EM) system is a new marine exploration technology recently being developed in China. Compared with traditional marine EM systems, the new system tows the transmitters and receivers using two ships, rendering it unnecessary to position EM receivers at the seafloor in advance. This makes the system more flexible, allowing for different configurations (e.g., in-line, broadside, and azimuthal and concentric scanning) that can produce more detailed underwater structural information. We develop a three-dimensional goal-oriented adaptive forward modeling method for the new marine EM system and analyze the responses for four survey configurations. Oceanbottom topography has a strong effect on the marine EM responses; thus, we develop a forward modeling algorithm based on the finite-element method and unstructured grids. To satisfy the requirements for modeling the moving transmitters of a dual-ship-towed EM system, we use a single mesh for each of the transmitter locations. This mitigates the mesh complexity by refining the grids near the transmitters and minimizes the computational cost. To generate a rational mesh while maintaining the accuracy for single transmitter, we develop a goal-oriented adaptive method with separate mesh refinements for areas around the transmitting source and those far away. To test the modeling algorithm and accuracy, we compare the EM responses calculated by the proposed algorithm and semi-analytical results and from published sources. Furthermore, by analyzing the EM responses for four survey configurations, we are confirm that compared with traditional marine EM systems with only in-line array, a dual-ship-towed marine system can collect more data. 相似文献
20.
The restriction of the Babuska–Brezzi stability criteria for the mixed formulation requires non-uniform interpolation of displacement and pore-pressure variables, which complicates the coding in the finite element analysis. This will certainly preclude the use of many otherwise useful elements. A possible solution to overcome this problem introduced earlier by the authors requires a semi-explicit form. However, the effectiveness of the semi-explicit procedure is dependent on the time step length used, which presents difficulties for transient analysis. In this paper, an unconditionally stable staggered implicit-implicit algorithm is developed, which is generalised from the semi-explicit form. For non-uniform mesh configurations, the results indicate a significant improvement compared with those obtained by using the semi-explicit procedure. 相似文献