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1.
论动力相似预报的物理基础问题 总被引：1，自引：0，他引：1
为了更好地发展动力相似预报的策略和方法,基于非线性动力学成果,综合探讨了动力相似预报的物理基础问题。分析表明,“相似预报—低频流型—可预报性”在物理上存在密切联系,这在统计相似预报和动力相似预报问题中均适用。通过类比集合预报,并对实际大气不同尺度模式预报的个例分析,初步证实了相似初值对应的动力预报结果及其预报误差行为具有相似性。在此基础上,进一步提出三类相似性问题,并归纳了动力相似预报的物理基础：在初始状态相似性持续的情况下,动力预报结果以及预报误差行为具有相似性。 相似文献
2.
The results of two-dimensional gas-dynamical numerical simulations of the structure of matter flows in the envelopes of a
number of T Tauri binary systems with elliptical orbits are considered. The main flow elements in inner regions of protoplanetary
disks of these stars are described. The influence of shocks on the size of the gap—a rarified region in the inner parts of
the protoplanetary disk—is analyzed. A method is proposed for estimating the size of this gap from the numerical simulations,
and the gap sizes for the studied stars are determined and compared with observational results. The flow dynamics in the gap
is considered, and the periodic variations of the gap size on time scales of several orbital periods are analyzed. Possible
observational manifestations of the studied flows are discussed. 相似文献
3.
Helge Holden Kenneth Hvistendahl Karlsen Knut-Andreas Lie 《Computational Geosciences》2000,4(4):287-322
We present an accurate numerical method for a large class of scalar, strongly degenerate convection–diffusion equations. Important subclasses are hyperbolic conservation laws, porous medium type equations, two-phase reservoir flow equations, and strongly degenerate equations coming from the recent theory of sedimentation–consolidation processes. The method is based on splitting the convective and the diffusive terms. The nonlinear, convective part is solved using front tracking and dimensional splitting, while the nonlinear diffusion part is solved by an implicit–explicit finite difference scheme. In addition, one version of the implemented operator splitting method has a mechanism built in for detecting and correcting unphysical entropy loss, which may occur when the time step is large. This mechanism helps us gain a large time step ability for practical computations. A detailed convergence analysis of the operator splitting method was given in Part I. Here we present numerical experiments with the method for examples modelling secondary oil recovery and sedimentation–consolidation processes. We demonstrate that the splitting method resolves sharp gradients accurately, may use large time steps, has first order convergence, exhibits small grid orientation effects, has small mass balance errors, and is rather efficient. 相似文献
4.
Ensemble size is critical to the efficiency and performance of the ensemble Kalman filter, but when the ensemble size is small,
the Kalman gain generally cannot be well estimated. To reduce the negative effect of spurious correlations, a regularization
process applied on either the covariance or the Kalman gain seems to be necessary. In this paper, we evaluate and compare
the estimation errors when two regularization methods including the distance-dependent localization and the bootstrap-based
screening are applied on the covariance and on the Kalman gain. The investigations were carried out through two examples:
1D linear problem without dynamics but for which the true Kalman gain can be computed and a 2D highly nonlinear reservoir
fluid flow problem. The investigation resulted in three primary conclusions. First, if localizations of two covariance matrices
are not consistent, the estimate of the Kalman gain will generally be poor at the observation location. The consistency condition
can be difficult to apply for nonlocal observations. Second, the estimate of the Kalman gain that results from covariance
regularization is generally subject to greater errors than the estimate of the Kalman gain that results from Kalman gain regularization.
Third, in terms of removing spurious correlations in the estimation of spatially correlated variables, the performance of
screening Kalman gain is comparable as the performance of localization methods (applied on either covariance or Kalman gain),
but screening Kalman gain outperforms the localization methods in terms of generality for application, as the screening method
can be used for estimating both spatially correlated and uncorrelated variables, and moreover, no assumption about the prior
covariance is required for the screening method. 相似文献
5.
Ocean is a highly complex and nonlinear dynamical system. The inevitable errors in both data and numerical models lead to uncertainties in ocean numerical prediction. By understanding features and properties in the ocean on multiple scales, it is important to quantify and estimate the predictability of the ocean, and analyze the reasons and mechanism of error growth. The efforts focus on investigating the method to reduce the uncertainties and errors in forecasting and increase the time limit of ocean predictability. The advances will result in improved marine forecasting models and forecasting skill. Understanding limitations and identifying the research needed to increase accuracy will lead to fundamental progress in ocean forecast, which is of great significance. The present study described and illustrated the mechanics and computations involved in modeling and predicting uncertainties for ocean prediction and its modern applications. Firstly, it discussed the fundamental concept and classification of the ocean predictability. The research status of ocean predictability is introduced including the dynamics methodologies and the ocean ensemble prediction. Three of the dynamical computational methodologies including the singular vector, Lyapunov exponent and bred vector method were introduced. Three ocean ensemble prediction methods including initial condition ensemble, multi-model ensemble and atmospheric forcing ensemble were described and illustrated. Finally, this paper gave a future prospective of ocean predictability and its application. 相似文献
6.
Wang Mingyu The University of Arizona Tucson Arizona USA Department of Water Resources Environmental Engineering China University of Geosciences Beijing Chen Jinsong Wan Li Department of Water Resources Environmental Engineering 《中国地质大学学报(英文版)》2001,12(3)
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7.
We consider a stationary flow of an incompressible non-Newtonian flow through a porous medium, induced by an injection velocity when inertial effects are negligible. At the pore scale, the governing equations are based on a nonlinear relation between the stress and the rate of deformation. In such a situation, the limit problem obtained when the pore size tends to zero, is called the homogenized problem that leads to the filtration law. This filtration law is given by a non-linear system coupling a local problem on a typical cell of the porous medium to a global problem at the scale of the whole porous medium. We propose, in this work, a numerical method to solve this homogenized problem and apply this method when the velocity dependent viscosity is given by the power law. Finally, we propose some numerical experiments to illustrate our approach. 相似文献
8.
Coupled formulation and algorithms for the simulation of non‐planar three‐dimensional hydraulic fractures using the generalized finite element method 
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下载免费PDF全文 This paper presents a coupled hydro‐mechanical formulation for the simulation of non‐planar three‐dimensional hydraulic fractures. Deformation in the rock is modeled using linear elasticity, and the lubrication theory is adopted for the fluid flow in the fracture. The governing equations of the fluid flow and elasticity and the subsequent discretization are fully coupled. A Generalized/eXtended Finite Element Method (G/XFEM) is adopted for the discretization of the coupled system of equations. A Newton–Raphson method is used to solve the resulting system of nonlinear equations. A discretization strategy for the fluid flow problem on non‐planar three‐dimensional surfaces and a computationally efficient strategy for handling time integration combined with mesh adaptivity are also presented. Several three‐dimensional numerical verification examples are solved. The examples illustrate the generality and accuracy of the proposed coupled formulation and discretization strategies. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
9.
Hybrid time integration and coupled solution methods for nonlinear finite element analysis of partially saturated deformable porous media at small strain 下载免费PDF全文
下载免费PDF全文 The goal of the paper is to determine the most efficient, yet accurate and stable, finite element nonlinear solution method for analysis of partially saturated deformable porous media at small strain. This involves a comparison between fully implicit, semi‐implicit, and explicit time integration schemes, with monolithically coupled and staggered‐coupled nonlinear solution methods and the hybrid combination thereof. The pore air pressure pa is assumed atmospheric, that is, pa=0 at reference pressure. The solid skeleton is assumed to be pressure‐sensitive nonlinear isotropic elastic. Coupled partially saturated ‘consolidation’ in the presence of surface infiltration and traction is simulated for a simple one‐dimensional uniaxial strain example and a more complicated plane strain slope example with gravity loading. Three mixed plane strain quadrilateral elements are considered: (i) Q4P4; (ii) stabilized Q4P4S; and (iii) Q9P4; “Q” refers to the number of solid skeleton displacement nodes, and “P” refers to the number of pore fluid pressure nodes. The verification of the implementation against an analytical solution for partially saturated pore water flow (no solid skeleton deformation) and comparison between the three time integration schemes (fully implicit, semi‐implicit, and explicit) are presented. It is observed that one of the staggered‐coupled semi‐implicit schemes (SIS(b)), combined with the fully implicit monolithically coupled scheme to resolve sharp transients, is the most efficient computationally. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
10.
In this paper, a numerical model is developed for the fully coupled hydro‐mechanical analysis of deformable, progressively fracturing porous media interacting with the flow of two immiscible, compressible wetting and non‐wetting pore fluids, in which the coupling between various processes is taken into account. The governing equations involving the coupled solid skeleton deformation and two‐phase fluid flow in partially saturated porous media including cohesive cracks are derived within the framework of the generalized Biot theory. The fluid flow within the crack is simulated using the Darcy law in which the permeability variation with porosity because of the cracking of the solid skeleton is accounted. The cohesive crack model is integrated into the numerical modeling by means of which the nonlinear fracture processes occurring along the fracture process zone are simulated. The solid phase displacement, the wetting phase pressure and the capillary pressure are taken as the primary variables of the three‐phase formulation. The other variables are incorporated into the model via the experimentally determined functions, which specify the relationship between the hydraulic properties of the fracturing porous medium, that is saturation, permeability and capillary pressure. The spatial discretization is implemented by employing the extended finite element method, and the time domain discretization is performed using the generalized Newmark scheme to derive the final system of fully coupled nonlinear equations of the hydro‐mechanical problem. It is illustrated that by allowing for the interaction between various processes, that is the solid skeleton deformation, the wetting and the non‐wetting pore fluid flow and the cohesive crack propagation, the effect of the presence of the geomechanical discontinuity can be completely captured. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
11.
An iterative method is presented for solving a fully coupled and implicit formulation of fluid flow in a porous medium. The mathematical model describes a set of fully coupled three-phase flow of compressible and immiscible fluids in a saturated oil reservoir. The finite element method is applied to obtain the simultaneous solution (SS) for the resulting highly non-linear partial differential equations where fluid pressures are the primary unknowns. The final discretized equations are solved iteratively by using a fully implicit numerical scheme. Several examples, illustrating the use of the present model, are described. The increased stability achieved with this scheme has permitted the use of larger time steps with smaller material balance errors. 相似文献
12.
Using shallow water equations on an equatorial beta plane, the nonlinear dynamics of the equatorial waves is investigated. A general mathematical procedure to study the nonlinear dynamics of these waves is developed using the asymptotic method of multiple scales. On faster temporal and spatial scales the equations describe the equatorial wavesviz, the Rossby waves, Rossby gravity waves, the inertia gravity waves and the Kelvin waves. Assuming that the amplitude of these waves are functions of slower time and space scales, it is shown that the evolution of the amplitude of these waves is governed by the nonlinear Schrodinger equation. It is then shown that for the dispersive waves like Rossby waves and Rossby-gravity waves, the envelope of the amplitude of the waves has a ‘soliton’ structure. 相似文献
13.
Reservoir depletion results in rock failure, wellbore instability, hydrocarbon production loss, oil sand production, and ground surface subsidence. Specifically, the compaction of carbonate reservoirs with soft rocks often induces large plastic deformation due to rock pore collapse. On the other hand, following the compaction of reservoirs and failure of rock formations, the porosity and permeability of formations will, in general, decrease. These bring a challenge for reservoir simulations because of high nonlinearity of coupled geomechanics and fluid flow fields. In this work, we present a fully implicit, fully coupled, and fully consistent finite element formulation for coupled geomechanics and fluid flow problems with finite deformation and nonlinear flow models. The Pelessone smooth cap plasticity model, an important material model to capture rock compaction behavior and a challenging material model for implicit numerical formulations, is incorporated in the proposed formulation. Furthermore, a stress-dependent permeability model is taken into account in the formulation. A co-rotational framework is adopted for finite deformation, and an implicit material integrator for cap plasticity models is consistently derived. Furthermore, the coupled field equations are consistently linearized including nonlinear flow models. The physical theories, nonlinear material and flow models, and numerical formulations are the focus of part I of this work. In part II, we verify the proposed numerical framework and demonstrate the performance of our numerical formulation using several numerical examples including a field reservoir with soft rocks undergoing serious compaction. 相似文献
14.
精确限定多期次岩浆-热液活动的时间尺度一直是剖析斑岩矿床形成过程的热点和难点。借助矿物的高精度同位素定年、热力学数值模拟以及石英的钛扩散模型等方法,斑岩矿床中岩浆-热液活动的时间尺度已经被限定在几万年之内。本文以三江特提斯超大型玉龙斑岩铜(钼)矿床为例,重点识别含矿热液脉中普遍存在的石英,利用钛元素的扩散年代学方法,精确限定斑岩矿床中多期岩浆-热液流体活动的时间尺度。扩散模型表明玉龙斑岩矿床热液活动的时间尺度为32000~870000年,有力支持了超大型斑岩矿床可以在几万至几十万年甚至更短时间内形成的观点。此外,为避免钛扩散模型产生较大的误差,需要在精确测定石英中钛含量的基础上,结合矿床地质背景或其他实验方法合理地估测温度和压力条件。研究认为,将矿物的高精度同位素定年与元素的扩散年代学相结合,可以在更为精细的尺度上完善斑岩矿床岩浆-热液活动的时间框架。 相似文献
15.
Justyna K. Przybysz-Jarnut Remus G. Hanea Jan-Dirk Jansen Arnold W. Heemink 《Computational Geosciences》2007,11(1):73-85
A data assimilation method was applied to estimate poorly known parameters (permeabilities) in a numerical reservoir model.
Most variational methods for data assimilation are based on the assumption that the model is perfect except for the poorly
known parameters. The representer method allows also for model errors, i.e. for uncertainties in the state variables (pressures
and saturations). The method is based on minimizing a cost functional, assuming all the errors and parameters to be multivariate
Gaussian random variables with given mean and covariances. The uncertain parameters and variables are expanded into a finite
sum of basis functions called representers, and the gradients of the cost functional are obtained with an adjoint method.
This approach gives an optimal parametrization in the sense that the final result is equal to the solution of the full inverse
problem. The method was tested on a simple one-dimensional model to simulate two-phase (oil-water) flow through a heterogeneous
reservoir. The results show that the method is able to provide an acceptable estimate of the permeability field. We used pressure
measurements from a small number of observation wells in between the injection and production wells, but the representer method
could be used equally well to assimilate data from other sources. The method appears to be a promising data assimilation tool
for applications in reservoir engineering. 相似文献
16.
Recent methods of analysis of so called disordered systems show that many objects and processes that earlier were considered as completely random reveal clear evidence of having some ordered structure in both time and space. These new methods (fractals, percolation, nonlinear dynamics and complexity theories) allow visualization and quantitative assessment of the level of complexity (orderliness) of these structures, using both theoretical models and experimental data. We consider sequentially some aspects of structural and evolutionary complexity of dynamics of seismic process and the technique of measuring this property.It is shown that the physical properties of geophysical medium are not always self-consistent and manifest fractal behavior on selected spatial and temporal scales. Mechanical percolation theory can be used for modeling geometry of fracture process. Namely, we consider fractal and connectivity aspects of delayed failure, including energy emission during fracturing. Special attention is paid to relating the intensity of geophysical anomalies to the strain in the framework of the pressure-induced anomalous strain-sensitivity (percolation) model, which explains naturally the observed heterogeneity of response of a geophysical media to the strain variation.Different methods of measuring the dynamic complexity of seismological time series are applied to magnitude and waiting time sequences of Caucasian earthquakes. The fractal (correlation) dimension d2 of the latter is high (larger than 8), but the former one has as low dimension as 1.6–2.5, which makes waiting time sequences a promising tool for revealing precursory changes.The same nonlinear technique allow detecting significant changes in the seismic regime during external electromagnetic forcing by MHD pulses; similar tests on the laboratory scale show the possibility of triggering/controlling stick-slip process by relatively weak electromagnetic or mechanical forcing.Lastly, the predictive potential of complexity analysis of seismological time series is considered. For example, percolation model predicts the increase of the number of large events and the scatter of magnitudes of events, decrease of the magnitude-frequency relation slope and appearance of multifractality at approaching the final rupture.It seems that seismology can benefit from using the new techniques to cope with the complexity of earthquake machine; for example, the measures of complexity can be characteristic for a given region and change before strong earthquake. 相似文献
17.
We develop a new computational methodology for solving two‐phase flow in highly heterogeneous porous media incorporating geomechanical coupling subject to uncertainty in the poromechanical parameters. Within the framework of a staggered‐in‐time coupling algorithm, the numerical method proposed herein relies on a Petrov–Galerkin postprocessing approach projected on the Raviart–Thomas space to compute the Darcy velocity of the mixture in conjunction with a locally conservative higher order finite volume discretization of the nonlinear transport equation for the saturation and an operator splitting procedure based on the difference in the time‐scales of transport and geomechanics to compute the effects of transient porosity upon saturation. Notable features of the numerical modeling proposed herein are the local conservation properties inherited by the discrete fluxes that are crucial to correctly capture the fingering patterns arising from the interaction between heterogeneity and nonlinear viscous coupling. Water flooding in a poroelastic formation subject to an overburden is simulated with the geology characterized by multiscale self‐similar permeability and Young modulus random fields with power‐law covariance structure. Statistical moments of the poromechanical unknowns are computed within the framework of a high‐resolution Monte Carlo method. Numerical results illustrate the necessity of adopting locally conservative schemes to obtain reliable predictions of secondary recovery and finger growth in strongly heterogeneous deformable reservoirs. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
18.
This paper presents a numerical model for simulating free surface flow in porous media with spatially varying porosity. The governing equations are based on the mixture theory. The resistance forces between solid and fluid is assumed to be nonlinear. A multiphase SPH approach is presented to solve the governing equations. In the multiphase SPH, water is modeled as a weakly compressible fluid, and solid phase is discretized by fixed solid particles carrying information of porosity. The model is validated by several numerical examples including seepage through specimen, fast flow through rockfill dam and wave interaction with porous structure. Good agreements between numerical results and experimental data are obtained in terms of flow rate and evolution of free surface. Parameter study shows that (1) the nonlinear resistance law provides more accurate results; (2) particle size and porosity have significant influence on the porous flow. 相似文献
19.
A method is presented to estimate actual evapotranspiration (ETA) from potential evapotranspiration (ETP) by numerical modeling of water flow in the unsaturated zone. Water flow is described by the Richards equation with a sink term representing the root water uptake. Evaporation is included in the model as a Neumann boundary condition at the soil surface. The Richards equation is solved in a one-dimensional domain using a mixed finite element method. The values of ETA are obtained by applying a water stress factor to ETP to account for soil moisture changes during the simulation period. The proposed numerical model is used to estimate ETA in an experimental plot located in a flatland area in Buenos Aires (Argentina). Numerical results show that the proposed model is a useful tool for evaluating evapotranspiration under different scenarios. 相似文献
20.
Processes influencing estuarine phytoplankton growth occur over a range of time scales, but many conceptual and numerical models of estuarine phytoplankton production dynamics neglect mechanisms occurring on the shorter (e.g., intratidal) time scales. We used a numerical model to explore the influence of short time-scale variability in phytoplankton sources and sinks on long-term growth in an idealized water column that shallows and deepens with the semidiurnal tide. Model results show that tidal fluctuations in water surface elevation can determine whether long-term phytoplankton growth is positive or negative. Hourly-scale interactions influencing weekly-scale to monthly-scale phytoplankton dynamics include intensification of the depth-averaged benthic grazing effect by water column shallowing and enhancement of water column photosynthesis when solar noon coincides with low tide. Photosynthesis and benthic consumption may modulate over biweekly time scales due to spring-neap fluctuations in tidal range and the 15-d cycle of solar noon-low tide phasing. If tidal range is a large fraction of mean water depth, then tidal shallowing and deepening may significantly influence net phytoplankton growth. In such a case, models or estimates of long-term phytoplankton production dynamics that neglect water surface fluctuations may overestimate or underestimate net growth and could even predict the wrong sign associated with net growth rate. 相似文献