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1.
This paper presents and compares several numerical solutions of the coupled system of Navier–Stokes and Darcy equations. The schemes are based on combinations of the finite element method and the discontinuous Galerkin method. Accuracy and robustness of the methods are investigated for heterogeneous porous media. The importance of local mass conservation for filtration problems is also discussed.  相似文献   

2.
In this paper, we describe an efficient approach for quantifying uncertainty in two-phase flow applications due to perturbations of the permeability in a multiscale heterogeneous porous medium. The method is based on the application of the multiscale finite element method within the framework of Monte Carlo simulation and an efficient preprocessing construction of the multiscale basis functions. The quantities of interest for our applications are the Darcy velocity and breakthrough time and we quantify their uncertainty by constructing the respective cumulative distribution functions. For the Darcy velocity we use the multiscale finite element method, but due to lack of conservation, we apply the multiscale finite volume element method as an alternative for use with the two-phase flow problem. We provide a number of numerical examples to illustrate the performance of the method.  相似文献   

3.
As illustrated variously by wetting and drying scanning curves, flow in unsaturated porous media is inherently nonlocal. This nonlocality is also manifest in hysteresis in the classical Darcy conductivity. It is the authors' belief that most current theories of unsaturated/saturated flow are often inadequate, as they do not account for spatial nonlocality and memory. Here we provide a fundamental theory in which nonlocality of the flow constitutive theory is a natural consequence of force balances. The results are derived from general principles in statistical physics and under appropriate limiting conditions, the classical Darcy's Law is recovered for saturated flow. A notable departure in this theory from other nonlocal flow theories is that a classical Darcy type equation on a small scale need not exist.  相似文献   

4.
Overland flow, sediments, and nutrients transported in runoff are important processes involved in soil erosion and water pollution. Modelling transport of sediments and chemicals requires accurate estimates of hydraulic resistance, which is one of the key variables characterizing runoff water depth and velocity. In this paper, a new theoretical power–velocity profile, originally deduced neglecting the impact effect of rainfall, was initially modified for taking into account the effect of rainfall intensity. Then a theoretical flow resistance law was obtained by integration of the new flow velocity distribution. This flow resistance law was tested using field measurements by Nearing for the condition of overland flow under simulated rainfall. Measurements of the Darcy–Weisbach friction factor, corresponding to flow Reynolds number ranging from 48 to 194, were obtained for simulated rainfall with two different rainfall intensity values (59 and 178 mm hr−1). The database, including measurements of flow velocity, water depth, cross-sectional area, wetted perimeter, and bed slope, allowed for calibration of the relationship between the velocity profile parameter Γ, the slope steepness s, and the flow Froude number F, taking also into account the influence of rainfall intensity i. Results yielded the following conclusions: (a) The proposed theoretical flow resistance equation accurately estimated the Darcy–Weisbach friction factor for overland flow under simulated rainfall, (b) the flow resistance increased with rainfall intensity for laminar overland flow, and (c) the mean flow velocity was quasi-independent of the slope gradient.  相似文献   

5.
Numerous cold regions water flow and energy transport models have emerged in recent years. Dissimilarities often exist in their mathematical formulations and/or numerical solution techniques, but few analytical solutions exist for benchmarking flow and energy transport models that include pore water phase change. This paper presents a detailed derivation of the Lunardini solution, an approximate analytical solution for predicting soil thawing subject to conduction, advection, and phase change. Fifteen thawing scenarios are examined by considering differences in porosity, surface temperature, Darcy velocity, and initial temperature. The accuracy of the Lunardini solution is shown to be proportional to the Stefan number. The analytical solution results obtained for soil thawing scenarios with water flow and advection are compared to those obtained from the finite element model SUTRA. Three problems, two involving the Lunardini solution and one involving the classic Neumann solution, are recommended as standard benchmarks for future model development and testing.  相似文献   

6.
Abstract

A simplified method has been developed for solving leaky aquifer non-Darcian flow hydraulics. The principle of volumetric approach is combined with the confined-aquifer, time-dependent drawdown equation in an observation well. The groundwater flow in the leaky aquifer is assumed to obey a non-Darcian flow law of exponential type. The results are obtained in the form of type-curve expressions from which the necessary bundles of curves are drawn for a set of selective non-Darcian flow aquifer parameters. Although application of the methodology appears as rather limited but it provides a scientific contribution and extension of leaky aquifer theory towards nonlinear flow conditions. The methodology developed herein is applied to some actual field data from the eastern sedimentary basin in the Kingdom of Saudi Arabia.  相似文献   

7.
A discontinuous Galerkin (DG) finite element method is described for the two-dimensional, depth-integrated shallow water equations (SWEs). This method is based on formulating the SWEs as a system of conservation laws, or advection–diffusion equations. A weak formulation is obtained by integrating the equations over a single element, and approximating the unknowns by piecewise, possibly discontinuous, polynomials. Because of its local nature, the DG method easily allows for varying the polynomial order of approximation. It is also “locally conservative”, and incorporates upwinded numerical fluxes for modeling problems with high flow gradients. Numerical results are presented for several test cases, including supercritical flow, river inflow and standard tidal flow in complex domains, and a contaminant transport scenario where we have coupled the shallow water flow equations with a transport equation for a chemical species.  相似文献   

8.
A quasi three-dimensional (QUASI 3-D) model is presented for simulating the subsurface water flow and solute transport in the unsaturated and in the saturated zones of soil. The model is based on the assumptions of vertical flow in the unsaturated zone and essentially horizontal groundwater flow. The 1-D Richards equation for the unsaturated zone is coupled at the phreatic surface with the 2-D flow equation for the saturated zone. The latter was obtained by averaging 3-D flow equation in the saturated zone over the aquifer thickness. Unlike the Boussinesq equation for a leaky-phreatic aquifer, the developed model does not contain a storage term with specific yield and a source term for natural replenishment. Instead it includes a water flux term at the phreatic surface through which the Richards equation is linked with the groundwater flow equation. The vertical water flux in the saturated zone is evaluated on the basis of the fluid mass balance equation while the horizontal fluxes, in that equation, are prescribed by Darcy law. A 3-D transport equation is used to simulate the solute migration. A numerical algorithm to solve the problem for the general quasi 3-D case was developed. The developed methodology was exemplified for the quasi 2-D cross-sectional case (QUASI2D). Simulations for three synthetic problems demonstrate good agreement between the results obtained by QUASI2D and two fully 2-D flow and transport codes (SUTRA and 2DSOIL). Yet, simulations with the QUASI2D code were several times faster than those by the SUTRA and the 2DSOIL codes.  相似文献   

9.
We review the state of the art in modeling of variable-density flow and transport in porous media, including conceptual models for convection systems, governing balance equations, phenomenological laws, constitutive relations for fluid density and viscosity, and numerical methods for solving the resulting nonlinear multifield problems. The discussion of numerical methods addresses strategies for solving the coupled spatio-temporal convection process, consistent velocity approximation, and error-based mesh adaptation techniques. As numerical models for those nonlinear systems must be carefully verified in appropriate tests, we discuss weaknesses and inconsistencies of current model-verification methods as well as benchmark solutions. We give examples of field-related applications to illustrate specific challenges of further research, where heterogeneities and large scales are important.  相似文献   

10.
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   

11.
Diganta Bhusan Das 《水文研究》2002,16(17):3393-3418
Hydrodynamic modelling for analysis of groundwater flow through permeable reactive barriers (PRBs) is addressed in this paper. Permeable reactive barriers constitute an emerging technology for in situ remediation of groundwater contamination and have many advantages over the traditional ex situ treatment methods. The transport domains during groundwater flow through PRBs often may involve free‐flow or non‐porous sections. To model the fluid mobility efficiently in such situations, the free and porous flow zones (PRBs) must be studied in conjunction with each other. The present paper is devoted to the analysis of groundwater flow through combined free flow domains and PRBs. The free‐flow regime is modelled using the Navier–Stokes equations whereas the permeable barriers are simulated by either the Darcy or the Brinkman equation. In order to couple the governing equations of motions, well‐posed mathematical formulations of matching boundary conditions are prescribed at the interface between the free‐groundwater‐flow zones and the permeable barriers. Combination of the Navier–Stokes equations with the Brinkman equation is more straightforward owing to their analogous forms. However, the Navier–Stokes and Darcy equations are incompatible mathematically and cannot be linked directly. The problem is resolved in this paper by invoking validated hydrodynamical expressions for describing the flow behaviour at the interfaces between free‐flow and porous zones. Three schemes for the analyses of fluid flow in combined domains are applied to the case of groundwater flow through permeable reactive barriers and different model results are compared. Copyright © 2002 John Wiley & Sons, Ltd.  相似文献   

12.
Even with the flow of water over a soil surface in which roughness elements are well inundated, and in less erosive situations where erosional bed forms are not pronounced, the magnitude of resistance coefficients in equations such as those of Darcy–Weisbach, Chezy or Manning vary with flow velocity (at least). Using both original laboratory and field data, and data from the literature, the paper examines this question of the apparent variation of resistance coefficients in relation to flow velocity, even in the absence of interaction between hydraulics and resulting erosional bed forms. Resistance equations are first assessed as to their ability to describe overland flow velocity when tested against these data sources. The result is that Manning's equation received stronger support than the Darcy–Weisbach or Chezy equations, though all equations were useful. The second question addressed is how best to estimate velocity of overland flow from measurements of slope and unit discharge, recognizing that the apparent flow velocity variation in resistance coefficients is probably a result of shortcomings in all of the listed resistance equations. A new methodology is illustrated which gives good agreement between estimated and measured flow velocity for both well-inundated sheet and rill flow. Comments are given on the predictive use of this methodology. Copyright © 1999 John Wiley & Sons, Ltd.  相似文献   

13.
Biogeochemical and ecological transformations in hyporheic zones are dependent on the timing of hyporheic exchange. We show through linked modeling of open channel turbulent flow, groundwater flow, and solute transport that the residence time distributions of solutes advected by hyporheic flow induced by current–bedform interaction follow power-laws. This tailing behavior of solutes exiting the sediments is explained by the presence of multiple path lengths coupled with very large variability in Darcy flow velocity, both occurring without heterogeneity in sediment permeability. Hyporheic exchange through bedforms will result in short-time fractal scaling of stream water chemistry.  相似文献   

14.
Complexity of the pore geometry and the random nature of flow velocity make it difficult to predict and represent post laminar flow through porous media. Present study experimentally investigates the applicability of Forchheimer and Wilkins equations for post laminar flow where Darcy’s law is invalid due to predominant inertial effect. It is observed that both porosity and media size have significant influence over the coefficients of the Forchheimer coefficients. To incorporate the effect of porosity and media size, behaviour of Forchheimer coefficients are investigated with hydraulic radius as characteristic length. An inversely proportional variation trend is found for all the present and earlier reported data. A new empirical relation between Forchheimer coefficients and hydraulic radius is obtained which can be universally applicable for all media size and porosity. Coefficients of the Wilkins equation are found to be non-deviating for different hydraulic radius in the present study and in the reported literature validating its applicability in predicting the non laminar flow through porous media. Further the Wilkins equation is modified after incorporating the correction factors for better applicability on the field.  相似文献   

15.
Pore-scale forces have a significant effect on the macroscopic behaviour of multiphase flow through porous media. This paper studies the effect of these forces using a new volume-of-fluid based finite volume method developed for simulating two-phase flow directly on micro-CT images of porous media. An analytical analysis of the relationship between the pore-scale forces and the Darcy-scale pressure drops is presented. We use this analysis to propose unambiguous definitions of Darcy-scale viscous pressure drops as the rate of energy dissipation per unit flow rate of each phase, and then use them to obtain the relative permeability curves. We show that this definition is consistent with conventional laboratory/field measurements by comparing our predictions with experimental relative permeability. We present single and two-phase flow simulations for primary oil injection followed by water injection on a sandpack and a Berea sandstone. The two-phase flow simulations are presented at different capillary numbers which cover the transition from capillary fingering at low capillary numbers to a more viscous fingering displacement pattern at higher capillary numbers, and the effect of capillary number on the relative permeability curves is investigated. Overall, this paper presents a new finite volume-based methodology for the detailed analysis of two-phase flow directly on micro-CT images of porous media and upscaling of the results to the Darcy scale.  相似文献   

16.
Effects of sediment load on hydraulics of overland flow on steep slopes   总被引：6，自引：0，他引：6  
Eroded sediment may have significant effects on the hydraulics of overland flow, but few studies have been performed to quantify these effects on steep slopes. This study investigated the potential effects of sediment load on Reynolds number, Froude number, flow depth, mean velocity, Darcy–Weisbach friction coefficient, shear stress, stream power, and unit stream power of overland flow in a sand‐glued hydraulic flume under a wide range of hydraulic conditions and sediment loads. Slope gradients were varied from 8·7 to 34·2%, unit flow rates from 0·66 to 5·26×10?3 m2 s?1, and sediment loads from 0 to 6·95 kg m?1 s?1. Both Reynolds number (Re) and Froude number (Fr) decreased as sediment load increased, implying a decrease in flow turbulence. This inverse relationship should be considered in modeling soil erosion processes. Flow depth increased as sediment load increased with a mean value of 1·227 mm, caused by an increase in volume of sediment‐laden flow (contribution 62·4%) and a decrease in mean flow velocity (contribution 37·6%). The mean flow velocity decreased by up to 0·071 m s?1 as sediment load increased. The Darcy–Weisbach friction coefficient (f) increased with sediment load, showing that the total energy consumption increased with sediment load. The effects of sediment load on f depended on flow discharge: as flow discharge increased, the influence of sediment load on f decreased due to increased flow depth and reduced relative roughness. Flow shear stress and stream power increased with sediment load, on average, by 80·5% and 60·2%, respectively; however, unit stream power decreased by an average of 11·1% as sediment load increased. Further studies are needed to extend and apply the insights obtained under these controlled conditions to real‐world overland flow conditions. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

17.
We present an efficient numerical method for solving stochastic porous media flow problems. Single-phase flow with a random conductivity field is considered in a standard first-order perturbation expansion framework. The numerical scheme, based on finite element techniques, is computationally more efficient than traditional approaches because one can work with a much coarser finite element mesh. This is achieved by avoiding the common finite element representation of the conductivity field. Computations with the random conductivity field only arise in integrals of the log conductivity covariance function. The method is demonstrated in several two- and three-dimensional flow situations and compared to analytical solutions and Monte Carlo simulations. Provided that the integrals involving the covariance of the log conductivity are computed by higher-order Gaussian quadrature rules, excellent results can be obtained with characteristic element sizes equal to about five correlation lengths of the log conductivity field. Investigations of the validity of the proposed first-order method are performed by comparing nonlinear Monte Carlo results with linear solutions. In box-shaped domains the log conductivity standard deviation σY may be as large as 1.5, while the head variance is considerably influenced by nonlinear effects as σY approaches unity in more general domains.  相似文献   

18.
This paper examines critically the use of the alternating direction implicit method for solving groundwater flow problems. Comparisons with alternative solutions show that inaccuracies can arise if the time increments are too large. A method is suggested whereby the computer chooses an optimum time increment. The representation of recharge, infiltration and wells is considered and a detailed example compares the alternating direction implicit, the explicit and the resistance-capacitance network methods.  相似文献   

19.
The fluid-structure interaction curvilinear immersed boundary (FSI-CURVIB) numerical method of Borazjani et al. [3] is extended to simulate coupled flow and sediment transport phenomena in turbulent open-channel flows. The mobile channel bed is discretized with an unstructured triangular mesh and is treated as a sharp-interface immersed boundary embedded in a background curvilinear mesh used to discretize the general channel outline. The unsteady Reynolds-averaged Navier-Stokes (URANS) equations closed with the k − ω turbulence model are solved numerically on a hybrid staggered/non-staggered grid using a second-order accurate fractional step method. The bed deformation is calculated by solving the sediment continuity equation in the bed-load layer using an unstructured, finite-volume formulation that is consistent with the CURVIB framework. Both the first-order upwind and the higher-order hybrid GAMMA schemes [12] are implemented to discretize the bed-load flux gradients and their relative accuracy is evaluated through a systematic grid refinement study. The GAMMA scheme is employed in conjunction with a sand-slide algorithm for limiting the bed slope at locations where the material angle of repose condition is violated. The flow and bed deformation equations are coupled using the partitioned loose-coupling FSI-CURVIB approach [3]. The hydrodynamic module of the method is validated by applying it to simulate the flow in an 180° open-channel bend with fixed bed. To demonstrate the ability of the model to simulate bed morphodynamics and evaluate its accuracy, we apply it to calculate turbulent flow through two mobile-bed open channels, with 90° and 135° bends, respectively, for which experimental measurements are available.  相似文献   

20.
A new Lagrangian particle model based on smoothed particle hydrodynamics (SPH) is developed and used to simulate Darcy scale flow and transport in porous media. The method has excellent conservation properties and treats advection exactly. The Lagrangian method is used in stochastic analysis of miscible density-driven fluid flows. Results show that heterogeneity significantly increases dispersion and slows development of Rayleigh–Taylor instability. The presented numerical examples illustrate the advantages of Lagrangian methods for stochastic transport simulations.  相似文献   

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