共查询到18条相似文献，搜索用时 156 毫秒
1.
弹性波方程作为一类重要的数学物理方程在地球物理方面有着许多广泛的应用前景.本文应用多辛守恒算法来研究弹性波方程,首先给出了弹性波方程的多辛结构,然后通过引入正则动量,验证了弹性波方程具有Hamilton系统多辛格式,并证实此格式具有多辛守恒律、局部能量守恒律和动量守恒律.利用中心Preissmann方法构造离散多辛格式的途径,并构造了一种多辛格式,该格式满足离散多辛守恒律,局部能量守恒律,局部动量守恒律.数值算例结果表明该多辛离散格式具有较好的长时间数值稳定性. 相似文献
2.
3.
将弹性波方程变换至Hamilton体系,构造适用于弹性波模拟的高效显式二阶辛Runge-Kutta-Nystrm(RKN)格式,运用根数理论得到此格式的阶条件方程组.通过给定系数的限定条件,得到方程的对称解.为了使时间离散误差达到极小,提出数值频率与真实频率比较,通过Taylor展开,得到关于辛系数的限定方程,求解方程组得到最小频散辛RKN格式.对比分析时间演进方程的稳定性,得到使库朗数达到极大值的限定方程,求解方程组得到最稳定辛RKN格式.发现此两种格式为同一格式.新得到的辛RKN格式不依赖于空间离散方法,为了对比的需要,选取有限差分法进行空间离散.在频散、稳定性分析中,与常见辛格式对比,从理论上分析了本文提出的格式在数值频散压制、稳定性提升等方面的优势,数值实验进一步证实了理论分析的正确性. 相似文献
4.
通过将地震波位移运动方程变换至Hamilton体系,引入广义动量和广义坐标,并定义系统动能和势能的Lie算子,构造了一类新的适用于高效长时间地震波模拟的二阶辛格式,同时将此格式用Baker-Campbell-Hausdorff(BCH)公式展开,基于截断误差原理极小得到了三组优化系数.在与常见辛格式对比中,从理论上和数值实验中分析了本文构造的这类优化二阶格式高精度高效率性;在与经典Newmark格式对比中,从长时间计算角度论证了本文格式具有长时间地震波计算能力;在非均匀介质地震波模拟中,本文格式与三阶辛格式得到了一致的地面合成地震记录和单道地震记录. 相似文献
5.
将声波方程变换至Hamiltion体系,构造了适用于高效声波模拟的二阶显式辛Runge-Kutta-Nyström（RKN）格式,运用根数理论得到此格式的阶条件方程组. 针对两个自由度的辛条件方程组,根据三次项截断误差最小原理得到一种误差最小辛格式;通过分析声波的时间演进方程的稳定性,选择不同的辛系数使演进方程更稳定,并得到了另一种更为稳定辛格式;在频散关系分析中,选择使数值频散最小的辛系数,得到第三种最小频散辛格式. 在理论分析中,这组辛RKN格式相比常见格式在精度控制、数值频散压制以及稳定性提升等方面均具有明显优势;在数值实验中,通过具体算例验证了理论分析的正确性. 相似文献
6.
声波方程数值模拟已广泛应用于理论地震计算,同时构成了地震逆时偏移成像技术的基础.对于有限差分法而言,在满足一定的稳定性条件时,普遍存在着因网格化而形成的数值频散效应.如何有效地缓解或压制数值频散是有限差分方法研究的关键所在.为精确求解空间偏导数,相继发展了高阶差分格式优化方法和伪谱方法.近期,为更好地缓解数值频散,提出了时间-空间域有限差分方法,该方法采用了泰勒展开近似方法来确定有限差分格式系数,因而只能保证在一定的小范围内很好的拟合波场传播规律.为进一步压制数值频散效应,本文引入了时间-空间域特定波数点满足频散关系的方法,根据震源、波速和网格间距确定波数范围,同时考虑了多个传播角度,然后建立方程确定了相应的有限差分格式系数,使得差分系数能在更大范围符合波场传播规律.通过频散分析和正演模拟,验证了本文方法的有效性. 相似文献
7.
频率域正演计算是频率域全波形反演的基础.传统的最优9点格式只具有二阶精度,不能满足高精度地震成像的需要.本文考虑两个四阶精度的格式,即经典的四阶9点格式和优化的17点格式.17点格式可将最小波长内所需网格点数减小到2.56.通过在简单模型和Overthrust模型上的数值实验,比较分析了三种格式的正演效果;简单模型数值实验显示了17点格式克服频散误差的能力优于四阶9点格式和最优9点格式;复杂模型数值实验则进一步承认了算法的可行性. 相似文献
8.
在岩石圈动力学数值模拟中，现有的黏弹塑性数值模型通常在每个时间步先使用迎风间断Galerkin方法对偏应力张量进行旋转，然后使用Particle-In-Cell (PIC)方法或场方法求解对流方程，所构成的时间离散格式为显格式或半隐格式.我们将黏弹塑性介质的经典数值模型和非牛顿流体力学领域的黏弹性流体问题计算方法相结合，提出了一种基于有限单元法的求解黏弹塑性介质流动的全隐格式算法.本文通过数值实验将这种全隐格式算法与PIC方法和半隐格式算法进行了详细的对比，实验结果表明全隐格式算法的数值稳定性优于PIC方法，而当Deborah数较高时精度优于半隐格式算法.同时，我们在应力场引入三阶WENO (Weighted Essentially Non-Oscillatory)限制器，可以在保留数值解精度的同时有效消除应力集中引起的数值振荡. 相似文献
9.
频率域数值模拟是频率域全波形反演的基础,在地震波场数值模拟中占有重要地位.相对于时间域数值模拟,频率域数值模拟具有两个明显的优势:没有时间累计误差,适合于并行计算.然而,严重的数值频散和巨大的内存损耗是阻碍其应用的两大瓶颈.为解决这两个问题,基于有限差分方法,学者提出了多种差分格式,如优化9点、15点、17点以及25点差分格式.本文从频散关系、计算效率和存储量三个方面,对比、分析了以上四种差分方法.基于2D声波方程,通过在均匀模型、层状模型以及Marmousi模型上的应用效果,对每种方法的优缺点进行了总结,为高精度数值模拟和声波频率域全波形反演提供方法选择上的参考. 相似文献
10.
为提高频率域有限差分（FD，finite-difference）正演模拟技术的计算精度和效率，基于旋转坐标系统的优化差分格式被广泛应用，但是只应用于正方形网格的情况.基于平均导数法（ADM）的优化差分格式，应用于正方形和长方形网格模拟.这些频率域有限差分算子，各自具有不同的差分格式和对应的优化系数求解表达式.本文基于三维声波方程发展了一种新的优化方法，只要给定FD模板形式，可直接构造频散方程，求取FD模板上各节点的优化系数.此方法的优点在于频率域FD算子的优化系数对应各个节点，可扩展优化其他格式.运用此优化方法，计算得到了不同空间采样间距比情况下27点和7点格式的优化系数.数值实验表明，优化27点格式与ADM 27点格式具有相同的精度，优化7点格式比经典的7点格式具有更小的数值频散. 相似文献
11.
The present paper focuses on the governing equations for the sensitivity of the variables to the parameters in flow models that can be described by one-dimensional scalar, hyperbolic conservation laws. The sensitivity is shown to obey a hyperbolic, scalar conservation law. The sensitivity is a conserved scalar except in the case of discontinuous flow solutions, where an extra, point source term must be added to the equations in order to enforce conservation. The propagation speed of the sensitivity waves being identical to that of the conserved variable in the original conservation law, the system of conservation laws formed by the original hyperbolic equation and the equation satisfied by the sensitivity is linearly degenerate. A consequence on the solution of the Riemann problem is that rarefaction waves for the variable of the original equation result in vacuum regions for the sensitivity. The numerical solution of the hyperbolic conservation law for the sensitivity by finite volume methods requires the implementation of a specific shock detection procedure. A set of necessary conditions is defined for the discretisation of the source term in the sensitivity equation. An application to the one-dimensional kinematic wave equation shows that the proposed numerical technique allows analytical solutions to be reproduced correctly. The computational examples show that first-order numerical schemes do not yield satisfactory numerical solutions in the neighbourhood of moving shocks and that higher-order schemes, such as the MUSCL scheme, should be used for sharp transients. 相似文献
12.
１ＩＮＴＲＯＤＵＣＴＩＯＮＲｉｖｅｒｓｉｎＴａｉｗａｎａｒｅｒｅｌａｔｉｖｅｌｙｓｔｅｅｐｅｒｃｏｍｐａｒｅｄｔｏｔｈｏｓｅｉｎｏｔｈｅｒｃｏｎｔｉｎｅｎｔ．Ｌｏｃａｌｙｏｃｕｒｅｄｓｕｐｅｒｃｒｉｔｉｃａｌｆｌｏｗａｒｅｆａｉｒｌｙｃｏｍｍｏｎｉｎ... 相似文献
13.
In this paper, we apply recently developed positivity preserving and conservative Modified Patankar-type solvers for ordinary
differential equations to a simple stiff biogeochemical model for the water column. The performance of this scheme is compared
to schemes which are not unconditionally positivity preserving (the first-order Euler and the second- and fourth-order Runge–Kutta
schemes) and to schemes which are not conservative (the first- and second-order Patankar schemes). The biogeochemical model
chosen as a test ground is a standard nutrient–phytoplankton–zooplankton–detritus (NPZD) model, which has been made stiff
by substantially decreasing the half saturation concentration for nutrients. For evaluating the stiffness of the biogeochemical
model, so-called numerical time scales are defined which are obtained empirically by applying high-resolution numerical schemes.
For all ODE solvers under investigation, the temporal error is analysed for a simple exponential decay law. The performance
of all schemes is compared to a high-resolution high-order reference solution. As a result, the second-order modified Patankar–Runge–Kutta
scheme gives a good agreement with the reference solution even for time steps 10 times longer than the shortest numerical
time scale of the problem. Other schemes do either compute negative values for non-negative state variables (fully explicit
schemes), violate conservation (the Patankar schemes) or show low accuracy (all first-order schemes). 相似文献
14.
LIU ShaoLin LI XiaoFan WANG WenShuai LIU YouShan ZHANG MeiGen & ZHANG Huan 《中国科学:地球科学(英文版)》2014,57(4):751-758
Here we introduce generalized momentum and coordinate to transform seismic wave displacement equations into Hamiltonian system. We define the Lie operators associated with kinetic and potential energy, and construct a new kind of second order symplectic scheme, which is extremely suitable for high efficient and long-term seismic wave simulations. Three sets of optimal coefficients are obtained based on the principle of minimum truncation error. We investigate the stability conditions for elastic wave simulation in homogeneous media. These newly developed symplectic schemes are compared with common symplectic schemes to verify the high precision and efficiency in theory and numerical experiments. One of the schemes presented here is compared with the classical Newmark algorithm and third order symplectic scheme to test the long-term computational ability. The scheme gets the same synthetic surface seismic records and single channel record as third order symplectic scheme in the seismic modeling in the heterogeneous model. 相似文献
15.
This paper presents an improved space-time conservation element and solution element(CESE)method by applying a non-staggered space-time mesh system and simply improving the calculation of flow variables and applies it to magnetohydrodynamics(MHD)equations.The improved CESE method can improve the solution quality even with a large disparity in the Courant number(CFL)when using a fixed global marching time.Moreover,for a small CFL(say<0.1),the method can significantly reduce the numerical dissipation and retain the solution quality,which are verified by two benchmark problems.And meanwhile,comparison with the original CESE scheme shows better resolution of the improved scheme results.Finally,we demonstrate its validation through the application of this method in three-dimensional coronal dynamical structure with dipole magnetic fields and measured solar surface magnetic fields as the initial input. 相似文献
16.
Alberto Canestrelli Annunziato Siviglia Michael Dumbser Eleuterio F. Toro 《Advances in water resources》2009
This paper concerns the development of high-order accurate centred schemes for the numerical solution of one-dimensional hyperbolic systems containing non-conservative products and source terms. Combining the PRICE-T method developed in [Toro E, Siviglia A. PRICE: primitive centred schemes for hyperbolic system of equations. Int J Numer Methods Fluids 2003;42:1263–91] with the theoretical insights gained by the recently developed path-conservative schemes [Castro M, Gallardo J, Parés C. High-order finite volume schemes based on reconstruction of states for solving hyperbolic systems with nonconservative products applications to shallow-water systems. Math Comput 2006;75:1103–34; Parés C. Numerical methods for nonconservative hyperbolic systems: a theoretical framework. SIAM J Numer Anal 2006;44:300–21], we propose the new PRICE-C scheme that automatically reduces to a modified conservative FORCE scheme if the underlying PDE system is a conservation law. The resulting first-order accurate centred method is then extended to high order of accuracy in space and time via the ADER approach together with a WENO reconstruction technique. The well-balanced properties of the PRICE-C method are investigated for the shallow water equations. Finally, we apply the new scheme to the shallow water equations with fix bottom topography and with variable bottom solving an additional sediment transport equation. 相似文献
17.
Multiphase flow in porous media is described by coupled nonlinear mass conservation laws. For immiscible Darcy flow of multiple fluid phases, whereby capillary effects are negligible, the transport equations in the presence of viscous and buoyancy forces are highly nonlinear and hyperbolic. Numerical simulation of multiphase flow processes in heterogeneous formations requires the development of discretization and solution schemes that are able to handle the complex nonlinear dynamics, especially of the saturation evolution, in a reliable and computationally efficient manner. In reservoir simulation practice, single-point upwinding of the flux across an interface between two control volumes (cells) is performed for each fluid phase, whereby the upstream direction is based on the gradient of the phase-potential (pressure plus gravity head). This upwinding scheme, which we refer to as Phase-Potential Upwinding (PPU), is combined with implicit (backward-Euler) time discretization to obtain a Fully Implicit Method (FIM). Even though FIM suffers from numerical dispersion effects, it is widely used in practice. This is because of its unconditional stability and because it yields conservative, monotone numerical solutions. However, FIM is not unconditionally convergent. The convergence difficulties are particularly pronounced when the different immiscible fluid phases switch between co-current and counter-current states as a function of time, or (Newton) iteration. Whether the multiphase flow across an interface (between two control-volumes) is co-current, or counter-current, depends on the local balance between the viscous and buoyancy forces, and how the balance evolves in time. The sensitivity of PPU to small changes in the (local) pressure distribution exacerbates the problem. The common strategy to deal with these difficulties is to cut the timestep and try again. Here, we propose a Hybrid-Upwinding (HU) scheme for the phase fluxes, then HU is combined with implicit time discretization to yield a fully implicit method. In the HU scheme, the phase flux is divided into two parts based on the driving force. The viscous-driven and buoyancy-driven phase fluxes are upwinded differently. Specifically, the viscous flux, which is always co-current, is upwinded based on the direction of the total-velocity. The buoyancy-driven flux across an interface is always counter-current and is upwinded such that the heavier fluid goes downward and the lighter fluid goes upward. We analyze the properties of the Implicit Hybrid Upwinding (IHU) scheme. It is shown that IHU is locally conservative and produces monotone, physically-consistent numerical solutions. The IHU solutions show numerical diffusion levels that are slightly higher than those for standard FIM (i.e., implicit PPU). The primary advantage of the IHU scheme is that the numerical overall-flux of a fluid phase remains continuous and differentiable as the flow regime changes between co-current and counter-current conditions. This is in contrast to the standard phase-potential upwinding scheme, in which the overall fractional-flow (flux) function is non-differentiable across the boundary between co-current and counter-current flows. 相似文献
18.
Two different approaches to finite-difference modeling of the elastodynamic equations have been used: the heterogeneous and the homogeneous. In the heterogeneous approach, boundary conditions at interfaces are treated implicitly; in the homogeneous, they are explicitly discretized. We present a homogeneous finite-difference scheme for the 2-D P-SV-wave case. This scheme represents a generalization of earlier such schemes, being able to model media with arbitrary non-uniformities, provided only that all interfaces are aligned with the numerical grid. We perform a detailed comparison of the generalized homogeneous scheme with the analogous heterogeneous scheme, and show the two schemes to be identical for media with a spatially constynt Poisson's ratio. For media where Poisson's ratio is spatially varying, the schemes differ by terms first-order in the spatial step size. However, a comparison of the numerical results produced by the two schemes shows that the resulting differences are negligible for a wide range of values of the Poisson's ratio contrast. 相似文献