共查询到20条相似文献，搜索用时 713 毫秒
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In this study, a probabilistic collocation method (PCM) on sparse grids is used to solve stochastic equations describing flow and transport in three-dimensional, saturated, randomly heterogeneous porous media. The Karhunen–Loève decomposition is used to represent log hydraulic conductivity Y=lnKs. The hydraulic head h and average pore-velocity v are obtained by solving the continuity equation coupled with Darcy’s law with random hydraulic conductivity field. The concentration is computed by solving a stochastic advection–dispersion equation with stochastic average pore-velocity v computed from Darcy’s law. The PCM approach is an extension of the generalized polynomial chaos (gPC) that couples gPC with probabilistic collocation. By using sparse grid points in sample space rather than standard grids based on full tensor products, the PCM approach becomes much more efficient when applied to random processes with a large number of random dimensions. Monte Carlo (MC) simulations have also been conducted to verify accuracy of the PCM approach and to demonstrate that the PCM approach is computationally more efficient than MC simulations. The numerical examples demonstrate that the PCM approach on sparse grids can efficiently simulate solute transport in randomly heterogeneous porous media with large variances. 相似文献
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The objective of this work is to explore the use of flow dimensions as a tool for characterizing hydraulic conditions in faulted media. Transient flow is numerically simulated in synthetic vertically-faulted reservoirs. Analysis of the obtained time series following the Generalized Radial Flow (GRF) model displays combined radial and fractional signals with a flow dimension n=1.5. Investigating the transient geometry of the frontal equipotential surface shows that fractional flow occurrence is due to abnormal fault diffusion as a consequence of water supply from the matrix under specific conditions. An original hydrodynamical explanation for fractional flow in vertically faulted media is suggested, along with a reinterpretation of the bilinear regime. It is shown that the GRF theory remains valid in such discontinuum as the fundamental relationship between n and the cross-flow area is satisfied. These results provide insights in the use of the flow dimension as a hydraulic diagnostic tool in faulted media. 相似文献
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A nonlinear regression method is developed that can be used to estimate parameters of a ground waterflow model from a combination of observations of hydrological variables and observations of geophysical properties that are functionally related with the hydraulic conductivity. The procedure estimates: parameters characterizing the hydraulic conductivity field (e.g., zonal or pilot point values); geophysical properties that have been observed and that are functionally related with the hydraulic conductivity parameters; and a few parameters of the function that relates the hydraulic conductivity parameters with the geophysical properties (the type of function is assumed known). A fidelity factor, sigma(r)2, of a term of the minimized objective function reflects the faith one has in the validity of this functional relationship. The estimation methodology has been tested by means of synthetic models. The experimental results demonstrate that the number of estimated hydraulic conductivity parameters can be increased by adding geophysical observations to the set of hydrological observations that are traditionally used for model calibration. The improvement of the estimated hydraulic conductivity field and the simulated hydraulic head field can be significant but is dependent on the number, the locations, and the uncertainty of geophysical observations. The sensitivity of the estimation results to the value of sigma(r) is small for the studied problems except when the uncertainty of geophysical observations is high. In the latter case, a large sigma(r) value was found to be optimal to avoid that hydraulic conductivity estimates are closely tied to corresponding but highly uncertain geophysical observations. 相似文献
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Kimberly Novick Ram Oren Paul Stoy Jehn-Yih Juang Mario Siqueira Gabriel Katul 《Advances in water resources》2009
Terrestrial ecosystems are dominated by vascular plants that form a mosaic of hydraulic conduits to water movement from the soil to the atmosphere. Together with canopy leaf area, canopy stomatal conductance regulates plant water use and thereby photosynthesis and growth. Although stomatal conductance is coordinated with plant hydraulic conductance, governing relationships across species has not yet been formulated at a practical level that can be employed in large-scale models. Here, combinations of published conductance measurements obtained with several methodologies across boreal to tropical climates were used to explore relationships between canopy conductance rates and hydraulic constraints. A parsimonious hydraulic model requiring sapwood-to-leaf area ratio and canopy height generated acceptable agreement with measurements across a range of biomes (r2=0.75). The results suggest that, at long time scales, the functional convergence among ecosystems in the relationship between water-use and hydraulic architecture eclipses inter-specific variation in physiology and anatomy of the transport system. Prognostic applicability of this model requires independent knowledge of sapwood-to-leaf area. In this study, we did not find a strong relationship between sapwood-to-leaf area and physical or climatic variables that are readily determinable at coarse scales, though the results suggest that climate may have a mediating influence on the relationship between sapwood-to-leaf area and height. Within temperate forests, canopy height alone explained a large amount of the variance in reference canopy conductance (r2=0.68) and this relationship may be more immediately applicable in the terrestrial ecosystem models. 相似文献
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We focus on the Bayesian estimation of strongly heterogeneous transmissivity fields conditional on data sampled at a set of locations in an aquifer. Log-transmissivity, Y, is modeled as a stochastic Gaussian process, parameterized through a truncated Karhunen–Loève (KL) expansion. We consider Y fields characterized by a short correlation scale as compared to the size of the observed domain. These systems are associated with a KL decomposition which still requires a high number of parameters, thus hampering the efficiency of the Bayesian estimation of the underlying stochastic field. The distinctive aim of this work is to present an efficient approach for the stochastic inverse modeling of fully saturated groundwater flow in these types of strongly heterogeneous domains. The methodology is grounded on the construction of an optimal sparse KL decomposition which is achieved by retaining only a limited set of modes in the expansion. Mode selection is driven by model selection criteria and is conditional on available data of hydraulic heads and (optionally) Y. Bayesian inversion of the optimal sparse KLE is then inferred using Markov Chain Monte Carlo (MCMC) samplers. As a test bed, we illustrate our approach by way of a suite of computational examples where noisy head and Y values are sampled from a given randomly generated system. Our findings suggest that the proposed methodology yields a globally satisfactory inversion of the stochastic head and Y fields. Comparison of reference values against the corresponding MCMC predictive distributions suggests that observed values are well reproduced in a probabilistic sense. In a few cases, reference values at some unsampled locations (typically far from measurements) are not captured by the posterior probability distributions. In these cases, the quality of the estimation could be improved, e.g., by increasing the number of measurements and/or the threshold for the selection of KL modes. 相似文献
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This paper proposes a novel strategy for the investigation of displacement amplitude () near and along an oblique-truncated semicircular canyon subjected to shear horizontal (SH) waves. Transfinite interpolation (TFI) was used to obtain the coordinates of nodes and determine the sequence of node numbering in the inner finite region including the canyon. The hybrid method, comprising finite element method and a Lamb series, was applied in conjunction with TFI to study the effects of canyon geometry, incident angle of SH waves (), and dimensionless frequency () on . We detailed the amplification of in the illuminated zone and variations in due to canyon-decay-effect along the canyon surface as well as the decay of resulting from the shield effect in the shadow zone. Interestingly, oblique-effects play an important role in the magnification of along the inclined bottom of canyons, and variations in and dominate the patterns of . 相似文献
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One-dimensional flows of gravity currents within horizontal and inclined porous channels are investigated combining theoretical and experimental analysis to evaluate the joint effects of channel shape and fluid rheology. The parameter governs the shape of the channel cross section, while the fluid rheology is characterised by a power-law model with behaviour index n. Self-similar scalings for current length and height are obtained for horizontal and inclined channels when the current volume increases with time as .For horizontal channels, the interplay of model parameters , and governs the front speed, height, and aspect ratio of the current (ratio between the average height and the length). The dependency is modulated by two critical values of and . For all channel shapes, discriminates between currents whose height decreases () or increases () with time at a particular point. For all power-law fluids, discriminates between decelerated currents, with time-decreasing aspect ratio (), and accelerated currents, with time-increasing aspect ratio (). Only currents with time-decreasing height () and aspect ratio () respect model assumptions asymptotically; the former constraint is more restrictive than the latter.For inclined channels, a numerical solution in self-similar form is obtained under the hypothesis that the product of the channel inclination and the slope of the free-surface is much smaller than unity; this produces a negligible error for , and is acceptable for . The action of gravity in inclined channels is modulated by both the behaviour index n and the shape factor . For constant flux, the current reaches at long times a steady state condition with a uniform thickness profile. In steep channels and for sufficiently long currents, the free-surface slope becomes entirely negligible with respect to channel inclination, and the constant thickness profile depends only on n.Theoretical results are validated by comparison with experiments (i) in horizontal and inclined channels with triangular or semicircular cross-section, (ii) with different shear-thinning fluids, and (iii) for constant volume and constant flux conditions. The experimental results show good agreement with theoretical predictions in the long-time regime.Our analysis demonstrates that self-similar solutions are able to capture the essential long-term behaviour of gravity currents in porous media, accounting for diverse effects such as non-Newtonian rheology, presence of boundaries, and channel inclination. This provides a relatively simple framework for sensitivity analysis, and a convenient benchmark for numerical studies. 相似文献