共查询到20条相似文献，搜索用时 578 毫秒
1.
Physics-based distributed models for simulating flow in karst systems are generally based on the discrete–continuum approach in which the flow in the three-dimensional fractured limestone matrix continuum is coupled with the flow in discrete one-dimensional conduits. In this study we present a newly designed discrete–continuum model for simulating flow in karst systems. We use a flexible spatial discretization such that complicated conduit networks can be incorporated. Turbulent conduit flow and turbulent surface flow are described by the diffusion wave equation whereas laminar variably saturated flow in the matrix is described by the Richards equation. Transients between free-surface and pressurized conduit flow are handled by changing the capacity term of the conduit flow equation. This new approach has the advantage that the transients in mixed conduit flow regimes can be handled without the Preissmann slot approach. Conduit–matrix coupling is based on the Peaceman’s well-index such that simulated exchange fluxes across the conduit–matrix interface are less sensitive to the spatial discretization. Coupling with the surface flow domain is based on numerical techniques commonly used in surface–subsurface models and storm water drainage models. Robust algorithms are used to simulate the non-linear flow processes in a coupled fashion. The model is verified and illustrated with simulation examples. 相似文献
2.
Analytical solutions for the water flow and solute transport equations in the unsaturated zone are presented. We use the Broadbridge and White nonlinear model to solve the Richards’ equation for vertical flow under a constant infiltration rate. Then we extend the water flow solution and develop an exact parametric solution for the advection-dispersion equation. The method of characteristics is adopted to determine the location of a solute front in the unsaturated zone. The dispersion component is incorporated into the final solution using a singular perturbation method. The formulation of the analytical solutions is simple, and a complete solution is generated without resorting to computationally demanding numerical schemes. Indeed, the simple analytical solutions can be used as tools to verify the accuracy of numerical models of water flow and solute transport. Comparison with a finite-element numerical solution indicates that a good match for the predicted water content is achieved when the mesh grid is one-fourth the capillary length scale of the porous medium. However, when numerically solving the solute transport equation at this level of discretization, numerical dispersion and spatial oscillations were significant. 相似文献
3.
Weiming Wu 《Ocean Dynamics》2014,64(7):1061-1071
A 3-D shallow-water flow model has been developed to simulate the flow in coastal vegetated waters with short waves. The model adopts the 3-D phase-averaged shallow-water flow equations with radiation stresses induced by short waves. It solves the governing equations using an implicit finite volume method based on quadtree rectangular mesh in the horizontal plane and stretching mesh in the vertical direction. The flow model is coupled with a spectral wave deformation model called CMS-Wave. The wave model solves the spectral wave-action balance equation and provides wave characteristics to the flow model. The model considers the effects of vegetation on currents and waves by including the drag and inertia forces of vegetation in the momentum equations and the wave energy loss due to vegetation resistance in the wave-action balance equation. The model has been tested using several sets of laboratory experiments, including steady flows in a straight channel with submerged vegetation and in a compound channel with vegetated floodplain and random waves through a vegetated channel and on a vegetated beach slope. The calculated water levels, current velocities, and wave heights are in general good agreement with the measured data. 相似文献
4.
《Advances in water resources》1999,23(1):83-95
We present a numerical model for two-phase porous media flow, where the phases are separated by a sharp interface. The model is based on a unified pressure equation, and an advection equation for tracking a pseudo-concentration function. The zero-level set of this function defines the interface between the fluids. The finite element method is used for spatial discretization, with local grid refinements in the vicinity of the interface. Examples on applications involving moving interface and steady-state seepage problems are investigated. 相似文献
5.
本研究实现了一套基于有限差分（FD）方法的大地电磁测深数据带地形三维反演算法及代码.其中,在大地电磁场正演数值模拟方面,开发了起伏地形条件下基于交错网格剖分、有限差分方法的大地电磁测深三维正演代码;在满足平面波场假设的前提下,使用长方体网格剖分模拟三维起伏地形,实现了带地形三维正演计算;并设计理论模型进行试算,经试算结果与前人的有限元法计算结果对比,验证了所研发的带地形三维正演计算的正确性与可靠性.在反演方面,本研究基于非线性共轭梯度方法编写了大地电磁测深带地形三维反演代码,试验了不同的共轭梯度搜索因子β,避免了目标函数对海森矩阵（参数二次导数矩阵）的显式计算和存储,初步实现了大地电磁资料的带地形三维反演.最后,对一系列理论模型进行正演计算,利用其生成的合成数据模拟实测数据进行反演,并与现有的不带地形大地电磁测深三维反演结果比较,检验了所研发的带地形三维反演计算的可靠性与稳定性. 相似文献
6.
三角网格有限元法具有网格剖分的灵活性,能有效模拟地震波在复杂介质中的传播.但传统有限元法用于地震波场模拟时计算效率较低,消耗较大计算资源.本文采用改进的核矩阵存储(IKMS)策略以提高有限元法的计算效率,该方法不用组合总体刚度矩阵,且相比于常规有限元法节省成倍的内存.对于时间离散,将有限元离散后的地震波运动方程变换至Hamilton体系,在显式二阶辛Runge-Kutta-Nystr9m(RKN)格式的基础之上加入额外空间离散算子构造修正辛差分格式,通过Taylor展开式得到具有四阶时间精度时间格式,且辛系数全为正数.本文从理论上分析了时空改进方法相比传统辛-有限元方法在频散压制、稳定性提升等方面的优势.数值算例进一步证实本方法具有内存消耗少、稳定性强和数值频散弱等优点. 相似文献
7.
A boundary element method using finite strip discretization is proposed to investigate the three-dimensional scattering behaviour of waves in a half space. The scatterers examined are an irregular surface and a cavity in a half space. The numerical examples demonstrate the remarkably good accuracy of the results and validate the application of the present method to solve three-dimensional scattering problems. 相似文献
8.
基于精细积分法的三维弹性波数值模拟(英文) 总被引：1，自引：0，他引：1
波动方程有限差分法是地震数值模拟中的一种重要的方法,对理解和分析地震传播规律、分析地震属性和解释地震资料有着非常重要的意义。但是有限差分法由于其离散化的思想,产生了不稳定性。精细积分法在有限差分法的基础上,在时间域采用解析解的表达形式,在空间域保留任意差分格式,发展成为半解析的数值方法。本文结合并发展了以往学者的成果,推导了任意精细积分法的三维弹性波正演模拟计算公式,并对其稳定性进行了数值分析。在计算实例中,实现了精细积分法二维和三维弹性波模型的地震正演模拟,对计算结果的分析表明,精细积分法反射信号走时准确,稳定性好,弹性波场相较于声波波场,弹性波波场成分更为丰富,包含了更多波型成分(PP-和PS-反射波、透射波和绕射波),这对实际地震资料的解释和储层分析有重要的意义。实践证明,该方法可直接应用到弹性波的地质模型的数值模拟中。 相似文献
9.
有限差分法广泛应用于地震波场的数值延拓,确定合适的有限差分算子以减小数值频散是有限差分法的一个重要研究内容。近年来为了进一步抑制数值频散和增加时间步长,新的有限差分模板得到了应用,对于此,前人使用泰勒展开方法和最小二乘方法确定有限差分算子系数。本文在以前工作的基础上,使用改进的线性方法确定新模板的有限差分系数,并与传统模板线性方法进行对比;通过频散分析和正演模拟验证出新模板线性方法能够更好地保持频散关系,在相同的精度下效率提高了一倍,从而说明了改进的线性方法的有效性。 相似文献
10.
Use of spectral acceleration data for determination of three-dimensional attenuation structure in the Pithoragarh region of Kumaon Himalaya 总被引：1，自引：0，他引：1
Three-dimensional attenuation structures are related to the subsurface heterogeneities present in the earth crust. An algorithm
for estimation of three-dimensional attenuation structure in the part of Garhwal Himalaya, India has been presented by Joshi
(Curr Sci 90:581–585, 2006b; Nat Hazards 43:129–146, 2007). In continuation of our earlier approach, we have presented a method in which strong motion data have been used to estimate
frequency-dependent three-dimensional attenuation structure of the region. The border district of Pithoragarh in the Higher
Himalaya, India, lies in the central seismic gap region of Himalaya. This region falls in the seismic zones IV and V of the
seismic zoning map of India. A dense network consisting of eight accelerographs has been installed in this region. This network
has recorded several local events. An algorithm based on inversion of strong motion digital data is developed in this paper
to estimate attenuation structure at different frequencies using the data recorded by this network. Twenty strong motion records
observed at five stations have been used to estimate the site amplification factors using inversion algorithm defined in this
paper. Site effects obtained from inversion has been compared with that obtained using Nakamura (1988) and Lermo et al. (Bull Seis Soc Am 83:1574–1594, 1993) approach. The obtained site amplification term has been used for correcting spectral acceleration data at different stations.
The corrected spectral acceleration data have been used as an input to the developed algorithm to avoid effect of near-site
soil amplification term. The attenuation structure is estimated by dividing the entire area in several three-dimensional block
of different frequency-dependent shear wave quality factor Q
β
(f). The input to this algorithm is the spectral acceleration of S phase of the corrected accelerogram. The outcome of the algorithm
is given in terms of attenuation coefficient and source acceleration spectra. In the present study, this region has been divided
into 25 rectangular blocks with thickness of 10 km and surface dimension of 12.5 × 12.1 km, respectively. Present study gives
three-dimensional attenuation model of the region which can be used for both hazard estimation and simulation of strong ground
motion. 相似文献
11.
During seismic wave propagation on a free surface, a strong material contrast boundary develops in response to interference by P- and S- waves to create a surfacewave phenomenon. To accurately determine the effects of this interface on surface-wave propagation, the boundary conditions must be accurately modeled. In this paper, we present a numerical approach based on the dynamic poroelasticity for a space–time-domain staggeredgrid finite-difference simulation in porous media that contain a free-surface boundary. We propose a generalized stess mirror formulation of the free-surface boundary for solids and fluids in porous media for the grid mesh on which lays the free-surface plane. Its analog is that used for elastic media, which is suitable for precise and stable Rayleigh-type surface-wave modeling. The results of our analysis of first kind of Rayleigh (R1) waves obtained by this model demonstrate that the discretization of the mesh in a similar way to that for elastic media can realize stable numerical solutions with acceptable precision. We present numerical examples demonstrating the efficiency and accuracy of our proposed method. 相似文献
12.
《Advances in water resources》1999,23(3):199-216
This paper is concerned with the fast resolution of nonlinear and linear algebraic equations arising from a fully implicit finite volume discretization of two-phase flow in porous media. We employ a Newton-multigrid algorithm on unstructured meshes in two and three space dimensions. The discretized operator is used for the coarse grid systems in the multigrid method. Problems with discontinuous coefficients are avoided by using a newly truncated restriction operator and an outer Krylov-space method. We show an optimal order of convergence for a wide range of two-phase flow problems including heterogeneous media and vanishing capillary pressure in an experimental way. Furthermore, we present a data parallel implementation of the algorithm with speedup results. 相似文献
13.
We develop a new approach for solving the nonlinear Richards’ equation arising in variably saturated flow modeling. The growing complexity of geometric models for simulation of subsurface flows leads to the necessity of using unstructured meshes and advanced discretization methods. Typically, a numerical solution is obtained by first discretizing PDEs and then solving the resulting system of nonlinear discrete equations with a Newton-Raphson-type method. Efficiency and robustness of the existing solvers rely on many factors, including an empiric quality control of intermediate iterates, complexity of the employed discretization method and a customized preconditioner. We propose and analyze a new preconditioning strategy that is based on a stable discretization of the continuum Jacobian. We will show with numerical experiments for challenging problems in subsurface hydrology that this new preconditioner improves convergence of the existing Jacobian-free solvers 3-20 times. We also show that the Picard method with this preconditioner becomes a more efficient nonlinear solver than a few widely used Jacobian-free solvers. 相似文献
14.
The Newmark average acceleration method is non-dissipative and unconditionally stable, but its accuracy in transient analysis of wave propagation problems depends not only on the spatial discretization but also on the temporal discretization. It has been found that the effects of spatial and temporal discretization when considered separately as commonly done, are far from adequate for most transient analysis. A better criterion manipulating the interdependent relationship between mesh size and time-step magnitude is imperative to achieve sufficiently accurate results of analysis. In this paper, the accuracy of the Newmark method is investigated by considering the two basic sources of errors, namely, numerical amplitude dissipation and velocity dispersion. The effects of both spatial and temporal discretizations are considered. A new technique to describe the characteristics of various frequency spectra is established. A criterion for mesh design and the selection of time-step magnitude is also proposed based on the combined effects of the amplitude dissipation and velocity dispersion. The efficiency and effectiveness of the proposed criterion are demonstrated using two one-dimensional wave propagation problems. A two-dimensional application shows that this criterion is equally applicable to multidimensional problems. 相似文献
15.
New alternative formulations of exact boundary conditions for arbitrary three-dimensional (3D) free-surface topographies on seismic media have been derived. They are shown to be equivalent to previously published formulations, thereby verifying the validity of each set of formulations. The top of a curved grid represents the free-surface topography while the interior of the grid represents the physical medium. We assume the velocity–stress version of the viscoelastic wave equations to be valid in this grid before transforming the equations to a rectangular grid. In order to perform the numerical discretization we apply the latter version of the equations for seismic wave propagation simulation in the medium. The numerical discretization of the free-surface topography boundary conditions by second-order finite differences (FDs) is shown, as well as the spatially unconditional stability of the resulting system of equations. The FD order is increased by two for each point away from the free surface up to eight, which is the order used in the interior. We use staggered grids in both space and time and the second-order leap-frog and Crank– Nicholson methods for wavefield time propagation. An application using parameters typical of teleseismic earthquakes and explosions is presented using a 200 × 100 km2 area of real topography from southwestern Norway over a homogeneous medium. A dipping plane wave simulates a teleseismic P-wave incident on the surface topography. Results show conversion from P- to Rg- (short period fundamental mode Rayleigh) waves in the steepest and/or roughest topography, as well as attenuated waves in valleys and fjords. The codes are parallelized for simulation on fast supercomputers and PC-clusters to model high frequencies and/or large areas. 相似文献
16.
基于非结构化风格的三维大地电磁矢量有限无模拟 总被引：3，自引：0，他引：3
Three-dimensional forward modeling magnetotellurics （MT） problems. We present a is a challenge for geometrically complex new edge-based finite-element algorithm using an unstructured mesh for accurately and efficiently simulating 3D MT responses. The electric field curl-curl equation in the frequency domain was used to deduce the H （curl） variation weak form of the MT forward problem, the Galerkin rule was used to derive a linear finite-element equation on the linear-edge tetrahedroid space, and, finally, a BI-CGSTAB solver was used to estimate the unknown electric fields. A local mesh refinement technique in the neighbor of the measuring MT stations was used to greatly improve the accuracies of the numerical solutions. Four synthetic models validated the powerful performance of our algorithms. We believe that our method will effectively contribute to processing more complex MT studies. 相似文献
17.
A one-dimensional non-linear diffusion wave equation is derived from the Saint Venant equations with neglect of the inertia terms. This non-linear equation has no general analytical solution. Numerical schemes are therefore employed to discretize the space and time axes and convert the differential equation to difference form. In this study, the mixing cell method is used to convert the diffusion wave equation to difference form, in which the difference term can be eliminated by selecting an optimal space step size Δx when time step size Δt is given. When the time step size Δt→0, the space step size Δx=Q/(2S0BC]k) where Q is discharge, S0 is bed slope, B is channel width and Ck is kinematic wave celerity, which is the same as the characteristic length proposed by Kalinin and Milyukov. The results of application to two cases show that the mixing cell and linear channel flow routing methods produce hydrographs that are in agreement with the observed flood hydrographs. © 1997 John Wiley & Sons, Ltd. 相似文献
18.
应用高精度人工边界条件可有效提升近场波动数值模拟计算效率.完美匹配层是吸收层形式高精度人工边界条件,匹配层内场方程和界面条件通常分别采用复坐标延伸技术变换强形式无限域内波动方程和界面条件得到,亦曾将无限域界面条件当作匹配层界面条件.场方程和界面条件构建过程相互独立,可能出现匹配不合理而引发数值失稳、计算精度低下等问题.本文提出采用复坐标延伸技术变换弱形式无限域波动方程以构建完美匹配层的方法.弱形式波动方程耦合了波动方程及界面条件,进而规避了变换后所得场方程与界面条件之间的匹配不合理问题.新方法可直接建立弱形式匹配层,在此基础上亦可给出强形式匹配层.弱形式便于有限元离散,强形式便于有限差分离散.基于弱形式完美匹配层,结合勒让德谱元建立了弹性介质近场波动谱元模拟方案.利用算例验证了新方案的精度及数值稳定性.本文工作可直接推广至多相耦合介质近场波动数值模拟. 相似文献
19.
有限差分方法是波场数值模拟的一个重要方法,交错网格差分格式比规则网格差分格式稳定性更好,但方法本身都存在因网格化而形成的数值频散效应,这会降低波场模拟的精度与分辨率.为了缓解有限差分算子的数值频散效应,精确求解空间偏导数,本文把求解波动方程的线性化方法推广到用于求解弹性波方程交错网格有限差分系数;同时应用最大最小准则作为模拟退火(SA)优化算法求解差分系数的数值频散误差判定标准来求解有限差分系数.通过上述两种方法,分别利用均匀各向同性介质和复杂构造模型进行了数值正演模拟和数值频散分析,并与传统泰勒展开算法、最小二乘算法进行比较,验证了线性化方法和模拟退火方法都能有效压制数值频散,并比较了各个算法的特点. 相似文献
20.
B. Nath 《地震工程与结构动力学》1981,9(1):33-51
A novel method has been proposed for the finite element solution of the steady-state scalar wave equation in three-dimensions. In this the governing equation and the prescribed boundary conditions in the physical space are transformed into a spherical polar space in which the radial direction is logarithmically condensed; the physical problem domain is also mapped into the new space. The transformed equation is then solved in the mapped domain using conventional finite elements. Because physical dimensions of the problem are logarithmically condensed in the proposed spherical polar space, the method is particularly suitable for solving truly three-dimensional problems in which the aspect ratio(s) is large or very large. A number of illustrative examples considered show that the proposed method is capable of a high degree of accuracy, achieved efficiently and economically. A hybrid scheme has also been proposed for dealing with awkward-shaped domains. 相似文献