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1.
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
2.
瑞利阻尼介质有限元离散模型动力分析的数值稳定性 总被引：12，自引：0，他引：12
本文针对几种有一般阻尼的动力系数数值积分的显式方法，讨论了阻尼对稳定性的影响，并建议了瑞利阻尼介质有限元离散模型中动力分析数值稳定性的实用稳定判别方法。 相似文献
3.
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
4.
A numerical study of 1-D nonlinear P-wave propagation in solid 总被引：3，自引：0，他引：3
IntroductionBecauseoftheextensivedistributionofruptures,micro-cracksandcrystalfracturesintheearth,therelationshipsbetweenthestressandstrainarenolongerlinear,infact,theyarenonlinear.Inordertoinvestigateandusethenonlinearcharacteristicsofsolidmediumintheearth,weshouldconsidertheinfluenceofnonlinearresponseduringthecourseofseismicmodelingandinversion.Thisisoneoftheimportantstudyfieldsthathavebeenpaidgreatattentionsinthere-centyearsintheworld(Minster,etal,1991;ZHANG,TENG,1993).Thenonlinearchar… 相似文献
5.
M. Fakharifar M. K. Sharbatdar Z. Lin A. Dalvand A. Sivandi-Pour G. Chen 《地震工程与工程振动(英文版)》2014,13(1):59-73
This paper presents a new FRP retrofi tting scheme to strengthen local beam-column joints in reinforced concrete(RC) frames.The new retrofi tting scheme was proposed following a preliminary study of four different existing retrofi tting schemes.A numerical simulation was conducted to evaluate the effectiveness of FRP-strengthened reinforced concrete frames by bridging behavior of local joints to the whole structure.Local confi nement effects due to varying retrofi tting schemes in the joints were simulated in the frame model.The seismic behavior factor was used to evaluate the seismic performance of the strengthened RC frames.The results demonstrated that the new proposed retrofi tting scheme was robust and promising,and fi nite element analysis appropriately captured the strength and global ductility of the frame due to upgrading of the local joints. 相似文献
6.
We present numerical methods for a system of equations consisting of the two dimensional Saint–Venant shallow water equations (SWEs) fully coupled to a completely generalized Exner formulation of hydrodynamically driven sediment discharge. This formulation is implemented by way of a discontinuous Galerkin (DG) finite element method, using a Roe Flux for the advective components and the unified form for the dissipative components. We implement a number of Runge–Kutta time integrators, including a family of strong stability preserving (SSP) schemes, and Runge–Kutta Chebyshev (RKC) methods. A brief discussion is provided regarding implementational details for generalizable computer algebra tokenization using arbitrary algebraic fluxes. We then run numerical experiments to show standard convergence rates, and discuss important mathematical and numerical nuances that arise due to prominent features in the coupled system, such as the emergence of nondifferentiable and sharp zero crossing functions, radii of convergence in manufactured solutions, and nonconservative product (NCP) formalisms. Finally we present a challenging application model concerning hydrothermal venting across metalliferous muds in the presence of chemical reactions occurring in low pH environments. 相似文献
7.
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
8.
Steve Wallis 《Acta Geophysica》2007,55(1):85-94
The simulation of solute transport in rivers is frequently based on numerical models of the Advection-Dispersion Equation.
The construction of reliable computational schemes, however, is not necessarily easy. The paper reviews some of the most important
issues in this regard, taking the finite volume method as the basis of the simulation, and compares the performance of several
types of scheme for a simple case of the transport of a patch of solute along a uniform river. The results illustrate some
typical (and well known) deficiencies of explicit schemes and compare the contrasting performance of implicit and semi-Lagrangian
versions of the same schemes. It is concluded that the latter have several benefits over the other types of scheme. 相似文献
9.
本研究利用加入起电、放电参数化方案的数值模式（Weather Research and Forecasting Model（Version 3.7.1）,WRF3.7.1_ELEC）,通过设计五组不同非感应起电及感应起电参数化方案敏感性试验,对发生在青藏高原东北部青海大通地区的一次雷暴过程进行模拟研究,对比分析了不同非感应起电机制及感应起电机制对雷暴云电荷结构的影响.结果表明：在雷暴云发展旺盛阶段,Saunders（S91）、Riming Rate（RR）、和Saunders和Peck（SP98）三种非感应起电方案模拟的雷暴云最低层均为负电荷区,而混合方案（Brooks and SP98,BSP）模拟的雷暴云最低层为正电荷区,主电荷区自下而上为"+-+-"排列的四层电荷结构.与甚高频辐射源定位法推算的结果对比,BSP方案模拟的本次高原雷暴云电荷结构更接近实际情况;几种不同非感应起电方案模拟的主电荷区外围与主电荷区电荷结构不同,说明在雷暴发展的不同阶段雷暴云的电荷结构是不同的;几种非感应起电方案模拟的电荷结构不尽相同,主要是由于霰、冰和雪粒子在不同高度所带电荷的极性及电量的大小不同,霰粒子的电荷密度对低层的影响较大,冰粒子和雪粒子的电荷密度对中上层的影响较大;加入感应起电机制后,雷暴云电荷结构分布几乎没有变化,但能使雷暴云发展旺盛阶段低层和中层的正负电荷区电荷密度有所加强. 相似文献
10.
This work presents results from two complementary and interconnected approaches to study water temperature and salinity patterns
in an estuarine tidal channel. This channel is one of the four main branches of the Ria de Aveiro, a shallow lagoon located
in the Northwest coast of the Iberian Peninsula. Longitudinal and cross-sectional fields of water temperature and salinity
were determined by spatial interpolation of field measurements. A numerical model (Mohid) was used in a 2D depth-integrated
mode in order to compute water temperature and salinity patterns. The main purpose of this work was to determine the horizontal
patterns of water temperature and salinity in the study area, evaluating the effects of the main forcing factors. The field
results were depth-integrated and compared to numerical model results. These results obtained using extreme tidal and river
runoff forcing, are also presented. The field results reveal that, when the river flow is weak, the tidal intrusion is the
main forcing mechanism, generating saline and thermal fronts which migrate with the neap/spring tidal cycle. When the river
flow increases, the influence of the freshwater extends almost as far as the mouth of the lagoon and vertical stratification
is established. Results of numerical modelling reveal that the implemented model reproduces quite well the observed horizontal
patterns. The model was also used to study the hydrology of the study area under extreme forcing conditions. When the model
is forced with a low river flow (1 m3 s−1) the results confirm that the hydrology is tidally dominated. When the model is forced with a high river flow (1,000 m3 s−1) the hydrology is dominated by freshwater, as would be expected in such an area. 相似文献
11.
Optimal implicit staggered‐grid finite‐difference schemes based on the sampling approximation method for seismic modelling 
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下载免费PDF全文 We propose new implicit staggered‐grid finite‐difference schemes with optimal coefficients based on the sampling approximation method to improve the numerical solution accuracy for seismic modelling. We first derive the optimized implicit staggered‐grid finite‐difference coefficients of arbitrary even‐order accuracy for the first‐order spatial derivatives using the plane‐wave theory and the direct sampling approximation method. Then, the implicit staggered‐grid finite‐difference coefficients based on sampling approximation, which can widen the range of wavenumber with great accuracy, are used to solve the first‐order spatial derivatives. By comparing the numerical dispersion of the implicit staggered‐grid finite‐difference schemes based on sampling approximation, Taylor series expansion, and least squares, we find that the optimal implicit staggered‐grid finite‐difference scheme based on sampling approximation achieves greater precision than that based on Taylor series expansion over a wider range of wavenumbers, although it has similar accuracy to that based on least squares. Finally, we apply the implicit staggered‐grid finite difference based on sampling approximation to numerical modelling. The modelling results demonstrate that the new optimal method can efficiently suppress numerical dispersion and lead to greater accuracy compared with the implicit staggered‐grid finite difference based on Taylor series expansion. In addition, the results also indicate the computational cost of the implicit staggered‐grid finite difference based on sampling approximation is almost the same as the implicit staggered‐grid finite difference based on Taylor series expansion. 相似文献
12.
Accurate numerical modeling of biogeochemical ocean dynamics is essential for numerous applications, including coastal ecosystem
science, environmental management and energy, and climate dynamics. Evaluating computational requirements for such often highly
nonlinear and multiscale dynamics is critical. To do so, we complete comprehensive numerical analyses, comparing low- to high-order
discretization schemes, both in time and space, employing standard and hybrid discontinuous Galerkin finite element methods,
on both straight and new curved elements. Our analyses and syntheses focus on nutrient–phytoplankton–zooplankton dynamics
under advection and diffusion within an ocean strait or sill, in an idealized 2D geometry. For the dynamics, we investigate
three biological regimes, one with single stable points at all depths and two with stable limit cycles. We also examine interactions
that are dominated by the biology, by the advection, or that are balanced. For these regimes and interactions, we study the
sensitivity to multiple numerical parameters including quadrature-free and quadrature-based discretizations of the source
terms, order of the spatial discretizations of advection and diffusion operators, order of the temporal discretization in
explicit schemes, and resolution of the spatial mesh, with and without curved elements. A first finding is that both quadrature-based
and quadrature-free discretizations give accurate results in well-resolved regions, but the quadrature-based scheme has smaller
errors in under-resolved regions. We show that low-order temporal discretizations allow rapidly growing numerical errors in
biological fields. We find that if a spatial discretization (mesh resolution and polynomial degree) does not resolve the solution,
oscillations due to discontinuities in tracer fields can be locally significant for both low- and high-order discretizations.
When the solution is sufficiently resolved, higher-order schemes on coarser grids perform better (higher accuracy, less dissipative)
for the same cost than lower-order scheme on finer grids. This result applies to both passive and reactive tracers and is
confirmed by quantitative analyses of truncation errors and smoothness of solution fields. To reduce oscillations in un-resolved
regions, we develop a numerical filter that is active only when and where the solution is not smooth locally. Finally, we
consider idealized simulations of biological patchiness. Results reveal that higher-order numerical schemes can maintain patches
for long-term integrations while lower-order schemes are much too dissipative and cannot, even at very high resolutions. Implications
for the use of simulations to better understand biological blooms, patchiness, and other nonlinear reactive dynamics in coastal
regions with complex bathymetric features are considerable. 相似文献
13.
AbstractA generalized likelihood uncertainty estimation (GLUE) framework coupling with artificial neural network (ANN) models in two surrogate schemes (i.e. GAE-S1 and GAE-S2) was proposed to improve the efficiency of uncertainty assessment in flood inundation modelling. The GAE-S1 scheme was to construct an ANN to approximate the relationship between model likelihoods and uncertain parameters for facilitating sample acceptance/rejection instead of running the numerical model directly; thus, it could speed up the Monte Carlo simulation in stochastic sampling. The GAE-S2 scheme was to establish independent ANN models for water depth predictions to emulate the numerical models; it could facilitate efficient uncertainty analysis without additional model runs for locations concerned under various scenarios. The results from a study case showed that both GAE-S1 and GAE-S2 had comparable performances to GLUE in terms of estimation of posterior parameters, prediction intervals of water depth, and probabilistic inundation maps, but with reduced computational requirements. The results also revealed that GAE-S1 possessed a slightly better performance in accuracy (referencing to GLUE) than GAE-S2, but a lower flexibility in application. This study shed some light on how to apply different surrogate schemes in using numerical models for uncertainty assessment, and could help decision makers in choosing cost-effective ways of conducting flood risk analysis. 相似文献
14.
The development of numerical methods for stochastic differential equations has intensified over the past decade. The earliest methods were usually heuristic adaptations of deterministic methods, but were found to have limited accuracy regardless of the order of the original scheme. A stochastic counterpart of the Taylor formula now provides a framework for the systematic investigation of numerical methods for stochastic differential equations. It suggests numerical schemes, which involve multiple stochastic integrals, of higher order of convergence. We shall survey the literature on these and on the earlier schemes in this paper. Our discussion will focus on diffusion processes, but we shall also indicate the extensions needed to handle processes with jump components. In particular, we shall classify the schemes according to strong or weak convergence criteria, depending on whether the approximation of the sample paths or of the probability distribution is of main interest. 相似文献
15.
P. E. Kloeden E. Platen 《Stochastic Environmental Research and Risk Assessment (SERRA)》1989,3(3):155-178
The development of numerical methods for stochastic differential equations has intensified over the past decade. The earliest methods were usually heuristic adaptations of deterministic methods, but were found to have limited accuracy regardless of the order of the original scheme. A stochastic counterpart of the Taylor formula now provides a framework for the systematic investigation of numerical methods for stochastic differential equations. It suggests numerical schemes, which involve multiple stochastic integrals, of higher order of convergence. We shall survey the literature on these and on the earlier schemes in this paper. Our discussion will focus on diffusion processes, but we shall also indicate the extensions needed to handle processes with jump components. In particular, we shall classify the schemes according to strong or weak convergence criteria, depending on whether the approximation of the sample paths or of the probability distribution is of main interest. 相似文献
16.
ZAHEER Iqbal CUI Guang Bai Ph D candidate College of Water Resources Environment Hohai University Nanjing China E-mail: zaheeriqbal@hotmail.com Prof. College of Water Resources Environment Hohai University Nanjing China 《国际泥沙研究》2002,17(2)
1 INTRODUCTION Numerical computation provides an easily extended and user-friendly environment with computer aided programming for the simulation of pollutants in river systems. In the most of water quality assessment and monitoring problems during water pollution control and environmental impact assessment studies of river systems, mathematical modeling has been playing a key role for the last two decades. The majority of existing water quality models are the mechanistic and are based o… 相似文献
17.
The success of transient storage (TS) modeling for natural streams depends, in part, on the ability to describe the dispersion process accurately. Evidence based on stream tracer data shows that solute transport processes often do not follow the classical second-order dispersion model (e.g., early breakthrough and faster than Fickian travel times were observed). While models based on space-fractional dispersion are a promising alternative, different definitions of fractional derivatives exist in the literature. Unlike integer-order derivatives, fractional derivatives represent convolutions of concentration with long-range spatial correlation and numerical approximations can produce dense matrices. Therefore issues of both accuracy and computational efficiency need to be examined to successfully identify model parameters for natural streams. In this paper, we first compare the performance of several numerical approaches for solving the space-fractional dispersion equation. We examine three different numerical approaches to approximate the space-fractional derivatives including: (a) a fully-implicit scheme based on the shifted Grünwald–Letnikov (GL) approximation (b) a three-point implicit representation based on the GL formula and (c) a three-point implicit scheme based on mass conservation and the Caputo definition of the fractional derivative. We then use an operator-splitting technique to evaluate a TS model based on space-fractional dispersion (the FSTS model) and test the model against analytical solutions and stream tracer data. A sequence acceleration method (Richardson extrapolation) significantly improves the performance of all schemes examined. Results indicate that the fully-implicit GL method with Richardson extrapolation produces the most accurate solutions while the three-point implicit GL scheme has a stringent time-step restriction to produce acceptable solutions. The three-point implicit scheme based on the Caputo derivative produces accurate solutions in a fraction of the time taken by the fully-implicit GL method and represents the best trade-off between accuracy and computational efficiency for practical applications. The scheme is suitable for parameter estimation and is used to successfully describe tracer data in a natural stream. 相似文献
18.
For the correct interpretation of data gathered in the seismic prospecting of complex heterogeneous structures, elastic effects must often be taken into consideration. The use of the elastic wave equations to model the seismic response of an hypothesized geological structure is a valuable tool for relating observed seismic data to the earth's inhomogeneities and verify an interpretation. Several methods may be used to integrate numerically the partial differential equations describing elastic wave propagation. Pseudospectral (Fourier) methods represent the leading numerical integration technique. Their main advantage is high accuracy and suitability to vector and parallel computer architectures, while their main drawback is high computational cost. However, for a given accuracy, the required grid size with pseudospectral methods is smaller than that required by finite-difference schemes, thus balancing the computational cost. We describe a two-dimensional pseudospectral elastic model implemented on the vector multiprocessor IBM 3090 VF. The algorithm has been suitably adapted to fully exploit the computer architecture and thereby maximize the performance. The elastic model has been validated in a variety of problems in geophysics and, in particular, in the amplitude-versus-offset analysis which has proved to be an effective technique to extract additional information from the recorded (prestack) data. With proper conditioning and processing of seismic data, and separating amplitude variations due to changes in reflectivity from variations due to other effects, the resulting offset signatures have been successfully used, for instance, to distinguish true bright spots due to gas-bearing sands, from false ones associated with lithological changes. To interpret the observed amplitude-versus-offset signatures, it is necessary to know the reflection coefficients as a function of angle and frequency for planar interfaces, as well as for other structures of geological interest. The modelling is first validated by computing the reflection coefficients for planar interfaces, and then used to analyse the reflection signatures of thin beds, corrugated interfaces and multilayers. Their implications, as well as impact on amplitude-versus-offset analysis, are discussed. We conclude that elastic modelling is an effective and valuable tool to further our understanding of the amplitude anomalies observed in field data. 相似文献
19.
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
20.
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