共查询到20条相似文献，搜索用时 187 毫秒
1.
近年来,随着地震波数值模拟对计算精度和效率的要求越来越高,间断有限元方法开始受到越来越多的关注.本文中,针对具有吸收边界条件的二维地震声波波动方程,作者提出了一种基于局部间断有限元方法的数值模拟算法.该算法在空间上使用局部间断有限元方法进行离散,在时间上采用了显式蛙跳格式.在这种时空离散的组合方式下,每个时间步上,此算法在空间剖分的每个单元上的求解计算是相互独立的,因而具有极高的并行性.通过数值算例,我们将该算法与连续有限元方法进行了比较.结果表明,本算法不仅具有对起伏构造的良好适应性,而且在计算效率和计算精度等方面,都具有优越性. 相似文献
2.
An efficient and accurate numerical model for multicomponent compressible single-phase flow in fractured media is presented. The discrete-fracture approach is used to model the fractures where the fracture entities are described explicitly in the computational domain. We use the concept of cross flow equilibrium in the fractures. This will allow large matrix elements in the neighborhood of the fractures and considerable speed up of the algorithm. We use an implicit finite volume (FV) scheme to solve the species mass balance equation in the fractures. This step avoids the use of Courant–Freidricks–Levy (CFL) condition and contributes to significant speed up of the code. The hybrid mixed finite element method (MFE) is used to solve for the velocity in both the matrix and the fractures coupled with the discontinuous Galerkin (DG) method to solve the species transport equations in the matrix. Four numerical examples are presented to demonstrate the robustness and efficiency of the proposed model. We show that the combination of the fracture cross-flow equilibrium and the implicit composition calculation in the fractures increase the computational speed 20–130 times in 2D. In 3D, one may expect even a higher computational efficiency. 相似文献
3.
Richard Comblen Sébastien Blaise Vincent Legat Jean-François Remacle Eric Deleersnijder Jonathan Lambrechts 《Ocean Dynamics》2010,60(6):1395-1414
We describe the time discretization of a three-dimensional baroclinic finite element model for the hydrostatic Boussinesq
equations based upon a discontinuous Galerkin finite element method. On one hand, the time marching algorithm is based on
an efficient mode splitting. To ensure compatibility between the barotropic and baroclinic modes in the splitting algorithm,
we introduce Lagrange multipliers in the discrete formulation. On the other hand, the use of implicit–explicit Runge–Kutta
methods enables us to treat stiff linear operators implicitly, while the rest of the nonlinear dynamics is treated explicitly.
By way of illustration, the time evolution of the flow over a tall isolated seamount on the sphere is simulated. The seamount
height is 90% of the mean sea depth. Vortex shedding and Taylor caps are observed. The simulation compares well with results
published by other authors. 相似文献
4.
Sébastien Blaise Richard Comblen Vincent Legat Jean-François Remacle Eric Deleersnijder Jonathan Lambrechts 《Ocean Dynamics》2010,60(6):1371-1393
We describe the space discretization of a three-dimensional baroclinic finite element model, based upon a discontinuous Galerkin
method, while the companion paper (Comblen et al. 2010a) describes the discretization in time. We solve the hydrostatic Boussinesq equations governing marine flows on a mesh made
up of triangles extruded from the surface toward the seabed to obtain prismatic three-dimensional elements. Diffusion is implemented
using the symmetric interior penalty method. The tracer equation is consistent with the continuity equation. A Lax–Friedrichs
flux is used to take into account internal wave propagation. By way of illustration, a flow exhibiting internal waves in the
lee of an isolated seamount on the sphere is simulated. This enables us to show the advantages of using an unstructured mesh,
where the resolution is higher in areas where the flow varies rapidly in space, the mesh being coarser far from the region
of interest. The solution exhibits the expected wave structure. Linear and quadratic shape functions are used, and the extension
to higher-order discretization is straightforward. 相似文献
5.
采用模拟离散的有限体积法实现了双轴各向异性地层回线源瞬变电磁三维正演.首先引入内积定义,采用自然边界条件,将瞬变电磁法的控制方程转化为弱形式表示.将计算区域划分为一系列的控制体积单元,采用交错网格对控制方程进行模拟有限体积空间离散,包括旋度算子离散和空间内积离散.基于斯托克斯定理的旋度积分定义公式实现旋度算子离散.中点平均实现电导率双轴各向异性的空间内积离散,从而得到离散化的控制方程.时间步迭代采用无条件稳定的欧拉后向差分格式.并通过均匀全空间中稳定电流回线源的磁场解析表达式得到回线源初始时刻的电磁场分布.为了同时保证计算精度和效率,本文采用分段等间隔的时间步迭代,利用直接法求解器PARDISO实现其快速求解.最后通过对比层状模型和各向异性半空间模型的正演计算结果,验证了本文算法的计算精度和计算效率;计算三维双轴各向异性模型的正演响应可知,水平方向电导率变化对电磁响应产生显著影响,而垂直方向的电导率变化对电磁响应几乎没有影响.产生这一现象的主要原因是回线源产生的感应电流主要是水平方向的,因此响应主要受到水平方向电导率的影响,垂直方向的电导率影响很小. 相似文献
6.
Various numerical methods have been used in the literature to simulate single and multiphase flow in fractured media. A promising approach is the use of the discrete-fracture model where the fracture entities in the permeable media are described explicitly in the computational grid. In this work, we present a critical review of the main conventional methods for multiphase flow in fractured media including the finite difference (FD), finite volume (FV), and finite element (FE) methods, that are coupled with the discrete-fracture model. All the conventional methods have inherent limitations in accuracy and applications. The FD method, for example, is restricted to horizontal and vertical fractures. The accuracy of the vertex-centered FV method depends on the size of the matrix gridcells next to the fractures; for an acceptable accuracy the matrix gridcells next to the fractures should be small. The FE method cannot describe properly the saturation discontinuity at the matrix–fracture interface. In this work, we introduce a new approach that is free from the limitations of the conventional methods. Our proposed approach is applicable in 2D and 3D unstructured griddings with low mesh orientation effect; it captures the saturation discontinuity from the contrast in capillary pressure between the rock matrix and fractures. The matrix–fracture and fracture–fracture fluxes are calculated based on powerful features of the mixed finite element (MFE) method which provides, in addition to the gridcell pressures, the pressures at the gridcell interfaces and can readily model the pressure discontinuities at impermeable faults in a simple way. To reduce the numerical dispersion, we use the discontinuous Galerkin (DG) method to approximate the saturation equation. We take advantage of a hybrid time scheme to alleviate the restrictions on the size of the time step in the fracture network. Several numerical examples in 2D and 3D demonstrate the robustness of the proposed model. Results show the significance of capillary pressure and orders of magnitude increase in computational speed compared to previous works. 相似文献
7.
《Advances in water resources》2004,27(2):129-140
The discontinuous spectral Galerkin method uses a finite-element discretization of the groundwater flow domain with basis functions of arbitrary order in each element. The independent choice of the basis functions in each element permits discontinuities in transmissivity in the flow domain. This formulation is shown to be of high order accuracy and particularly suitable for accurately calculating the flow field in porous media. Simulations are presented in terms of streamlines in a bidimensional aquifer, and compared with the solution calculated with a standard finite-element method and a mixed finite-element method. Numerical simulations show that the discontinuous spectral Galerkin approximation is more efficient than the standard finite-element method (in computing fluxes and streamlines/pathlines) for a given accuracy, and it is more accurate on a given grid. On the other hand the mixed finite-element method ensures the continuity of the fluxes at the cell boundaries and it is particular efficient in representing complicated flow fields with few mesh points. Simulations show that the mixed finite-element method is superior to the discontinuous spectral Galerkin method producing accurate streamlines even if few computational nodes are used. The application of the discontinuous Galerkin method is thus of interest in groundwater problems only when high order and extremely accurate solutions are needed. 相似文献
8.
间断Galerkin有限元法（DG-FEM）作为一种有效的高阶有限元法受到了国内外学者的广泛关注.本文基于任意高阶间断Galerkin有限元法对弹性波方程进行空间离散,并将离散后所得的非齐次线性常微分方程系统齐次化,最后结合针对齐次问题的强稳定性保持龙格库塔（SSP Runge-Kutta）算法,将DG-FEM推广至时间任意高阶精度.另外,借鉴近最佳匹配层（NPML）的思想,基于复频移（CFS）拉伸坐标变换推导了一种新的PML吸收边界条件（简称为CFS-NPML）,该CFS-NPML能够与DG-FEM算法很好地结合,形成有效的起伏地表地震波传播数值模拟技术.数值试验结果表明,DG-FEM具有高阶精度,可以适应任意复杂起伏地表和复杂构造情况下的弹性波传播数值模拟.同时,CFS-NPML对包括面波等震相的人为边界反射都具有良好的吸收效果. 相似文献
9.
Xinya Li Bill X. Hu 《Stochastic Environmental Research and Risk Assessment (SERRA)》2013,27(5):1181-1191
Numerical models with fine discretization normally demand large computational time and space, which lead to computational burden for state estimations or model parameter inversion calculation. This article presented a reduced implicit finite difference scheme that based on proper orthogonal decomposition (POD) for two-dimensional transient mass transport in heterogeneous media. The reduction of the original full model was achieved by projecting the high-dimension full model to a low-dimension space created by POD bases, and the bases are derived from the snapshots generated from the model solutions of the forward simulations. The POD bases were extracted from the ensemble of snapshots by singular value decomposition. The dimension of the Jacobian matrix was then reduced after Galerkin projection. Thus, the reduced model can accurately reproduce and predict the original model’s transport process with significantly decreased computational time. This scheme is practicable with easy implementation of the partial differential equations. The POD method is illustrated and validated through synthetic cases with various heterogeneous permeability field scenarios. The accuracy and efficiency of the reduced model are determined by the optimal selection of the snapshots and POD bases. 相似文献
10.
Soil erosion by water is the root cause of ecological degradation in the Shiwalik foothills of Northern India. Simulation of runoff and its component processes is a pre‐requisite to develop the management strategies to tackle the problem, successfully. A two‐dimensional physically based distributed numerical model, ROMO2D has been developed to simulate runoff from small agricultural watersheds on an event basis. The model employs the 2‐D Richards equation with sink term to simulate infiltration and soil moisture dynamics in the vadoze zone under variable rainfall conditions, and 2‐D Saint‐Venant equations under the kinematic wave approximation along with Manning's equation as the stage‐discharge equation for runoff routing. The various flow‐governing equations have been solved numerically by employing a Galerkin finite element method for spatial discretization using quadrilateral elements and finite difference techniques for temporal solutions. The ROMO2D computer program has been developed as a class‐based program, coded in C + + in such a way that with minor modifications, the model can be used to simulate runoff on a continuous basis. The model writes output for a runoff hydrograph of each storm. Model development is described in this paper and the results of model testing and field application are to be presented in a subsequent paper. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
11.
We present a vertex-centered finite volume method for the fully coupled, fully implicit discretization of two-phase flow in fractured porous media. Fractures are discretely modeled as lower dimensional elements. The method works on unstructured, locally refined grids and on parallel computers with distributed memory. An implicit time discretization is employed and the nonlinear systems of equations are solved with a parallel Newton-multigrid method. Results from two-dimensional and three-dimensional simulations are presented. 相似文献
12.
This paper examines the effectiveness of open and filled trenches for screening Rayleigh waves due to impulse loads for 3D problems. The effects of the geometric parameters of trench reducing ground displacements are studied in detail. The computational scheme involves the use of finite element method to discretize a large computational domain and the resulting integration dynamic equilibrium equations are integrated to get the response using Newmark's β method. Soil has been idealized as linear, isotropic continuum. 相似文献
13.
Analytical and numerical analysis of pressure drawdown in a poroelastic reservoir with complete overburden effect considered 总被引：1，自引：0，他引：1
Starting from an analytical reservoir model that incorporates full interaction with an elastic overburden, a new hybrid mathematical approach is developed by combining two numerical discretization methods. A tabular reservoir (petroleum reservoir or an aquifer) in an infinite or semi-infinite domain is viewed as a macroscopic displacement discontinuity, allowing use of the efficient displacement discontinuity mathematical method to calculate stresses and displacements that arise because of pressure changes. A 3-D finite element method using a poroelastic formulation is used to discretize the reservoir itself. By coupling the displacement discontinuity and finite element methods, a 3-D large-scale poroelastic reservoir can be simulated within an infinite or semi-infinite domain. The numerical model has been verified through comparison to known solutions, and some time-dependent pressure drawdown problems are analyzed. Results indicate that including the complete overburden (reservoir surroundings) response has a significant effect on pressure drawdown in a poroelastic reservoir during pumping, and should be incorporated in appropriate applications such as well test equations and subsidence analyses. 相似文献
14.
We propose a novel computational method for the efficient simulation of two-phase flow in fractured porous media. Instead of refining the grid to capture the flow along the faults or fractures, we represent the latter as immersed interfaces, using a reduced model for the flow and suitable coupling conditions. We allow for non matching grids between the porous matrix and the fractures to increase the flexibility of the method in realistic cases. We employ the extended finite element method for the Darcy problem and a finite volume method that is able to handle cut cells and matrix-fracture interactions for the saturation equation. Moreover, we address through numerical experiments the problem of the choice of a suitable numerical flux in the case of a discontinuous flux function at the interface between the fracture and the porous matrix. A wrong approximate solution of the Riemann problem can yield unphysical solutions even in simple cases. 相似文献
15.
本文实现了2.5维电导率正交各向异性海洋可控源电磁等参有限元数值模拟.利用傅里叶变换导出了电导率正交各向异性2.5维海洋可控源电磁法波数域电磁场耦合方程,采用伽里金加权余量法推导了相应的有限元方程;采用任意四边形单元对研究区域进行剖分,在单元中进行双二次插值,将有限元方程化为线性代数方程组;最后,求解线性方程组并进行反傅里叶变换获得空间域电磁场值.这个方法可以模拟海底起伏地形条件下地下任意形状电导率正交各向异性的复杂模型.与一维模型的数值模拟结果对比表明,电磁场数值解与解析解吻合.二维模型的计算结果与二维自适应非结构有限元模拟结果也吻合.水平海底二维地电模型考察了不同各向异性系数对海洋可控源电磁响应的影响特征.海底起伏地形地电模型的数值结果表明,电导率各向异性对海洋可控源电磁响应影响明显,有可能淹没海底地形和高阻油气藏引起的异常. 相似文献
16.
《Advances in water resources》1998,21(1):27-46
This work examines variable density flow and corresponding solute transport in groundwater systems. Fluid dynamics of salty solutions with significant density variations are of increasing interest in many problems of subsurface hydrology. The mathematical model comprises a set of non-linear, coupled, partial differential equations to be solved for pressure/hydraulic head and mass fraction/concentration of the solute component. The governing equations and underlying assumptions are developed and discussed. The equation of solute mass conservation is formulated in terms of mass fraction and mass concentration. Different levels of the approximation of density variations in the mass balance equations are used for convection problems (e.g. the Boussinesq approximation and its extension, fully density approximation). The impact of these simplifications is studied by use of numerical modelling.Numerical models for nonlinear problems, such as density-driven convection, must be carefully verified in a particular series of tests. Standard benchmarks for proving variable density flow models are the Henry, Elder, and salt dome (HYDROCOIN level 1 case 5) problems. We studied these benchmarks using two finite element simulators - ROCKFLOW, which was developed at the Institute of Fluid Mechanics and Computer Applications in Civil Engineering and FEFLOW, which was developed at the Institute for Water Resources Planning and Systems Research Ltd. Although both simulators are based on the Galerkin finite element method, they differ in many approximation details such as temporal discretization (Crank-Nicolson vs predictor-corrector schemes), spatial discretization (triangular and quadrilateral elements), finite element basis functions (linear, bilinear, biquadratic), iteration schemes (Newton, Picard) and solvers (direct, iterative). The numerical analysis illustrates discretization effects and defects arising from the different levels of the density of approximation. We contribute new results for the salt dome problem, for which inconsistent findings exist in literature. Applications of the verified numerical models to more complex problems, such as thermohaline and three-dimensional convection systems, will be presented in the second part of this paper. 相似文献
17.
18.
A shallow flow generally features complex hydrodynamics induced by complicated domain topography and geometry. A numerical scheme with well-balanced flux and source term gradients is therefore essential before a shallow flow model can be applied to simulate real-world problems. The issue of source term balancing has been exhaustively investigated in grid-based numerical approaches, e.g. discontinuous Galerkin finite element methods and finite volume Godunov-type methods. In recent years, a relatively new computational method, smooth particle hydrodynamics (SPH), has started to gain popularity in solving the shallow water equations (SWEs). However, the well-balanced problem has not been fully investigated and resolved in the context of SPH. This work aims to discuss the well-balanced problem caused by a standard SPH discretization to the SWEs with slope source terms and derive a corrected SPH algorithm that is able to preserve the solution of lake at rest. In order to enhance the shock capturing capability of the resulting SPH model, the Monotone Upwind-centered Scheme for Conservation Laws (MUSCL) is also explored and applied to enable Riemann solver based artificial viscosity. The new SPH model is validated against several idealized benchmark tests and a real-world dam-break case and promising results are obtained. 相似文献
19.
Vadym Aizinger Jennifer Proft Clint Dawson Dharhas Pothina Solomon Negusse 《Ocean Dynamics》2013,63(1):89-113
In this work, we present results of a numerical study of Corpus Christi Bay, Texas and surrounding regions and compare simulated model results to recorded data. The validation data for the year 2000 include the water elevation, velocity, and salinity at selected locations. The baroclinic computations were performed using the University of Texas Bays and Estuaries 3D (UTBEST3D) simulator based on a discontinuous Galerkin finite element method for unstructured prismatic meshes. We also detail some recent advances in the modeling capabilities of UTBEST3D, such as a novel turbulence scheme and the support for local vertical discretization on parts of the computational domain. All runs were conducted on parallel clusters; an evaluation of parallel performance of UTBEST3D is included. 相似文献