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1.
A distributed-parameter physically-based solute transport model using a novel approach to describe surface-subsurface interactions is coupled to an existing flow model. In the integrated model the same surface routing and mass transport equations are used for both hillslope and channel processes, but with different parametrizations for these two cases. For the subsurface an advanced time-splitting procedure is used to solve the advection-dispersion equation for transport and a standard finite element scheme is used to solve Richards equation for flow. The surface-subsurface interactions are resolved using a mass balance-based surface boundary condition switching algorithm that partitions water and solute into actual fluxes across the land surface and changes in water and mass storage. The time stepping strategy allows the different time scales that characterize surface and subsurface water and solute dynamics to be efficiently and accurately captured. The model features and performance are demonstrated in a series of numerical experiments of hillslope drainage and runoff generation.  相似文献   

2.
In this paper, we deduced the corresponding first-order velocity–stress equation for curvilinear coordinates from the first-order velocity–stress equation based on the modified Biot/squirt model for a two-dimensional two-phase medium. The equations are then numerically solved by an optimized high-order non-staggered finite difference scheme, that is, the dispersion relation preserving/optimization MacCormack scheme. To implement undulating free-surface topography, we derive an analytical relationship between the derivatives of the particle velocity components and use the compact finite-difference scheme plus a traction-image method. In the undulating free surface and the undulating subsurface interface of two-phase medium, the complex reflected wave and transmitted wave can be clearly recognized in the numerical simulation results. The simulation results show that the curvilinear-grid finite-difference method, which uses a body-conforming grid to describe the undulating surface, can accurately reduce the numerical scattering effect of seismic wave propagation caused by the use of ladder-shaped grid to fit the surfaces when undulating topography is present in a two-phase isotropic medium.  相似文献   

3.
The interaction between fluid and sediment particles is widely involved in hydraulic engineering problems. In the current study, an explicit incompressible mesh-free method in the framework of the Moving Particle Semi-implicit(MPS) method is proposed to simulate the interaction between the two phases in submerged conditions. The proposed method solves two sets of the continuity and momentum equations, respectively, for the fluid phase and the sediment phase according to the mixture theory. In th...  相似文献   

4.
Gang Liu  Fuguo Tong  Bin Tian 《水文研究》2019,33(26):3378-3390
This work introduces water–air two‐phase flow into integrated surface–subsurface flow by simulating rainfall infiltration and run‐off production on a soil slope with the finite element method. The numerical model is formulated by partial differential equations for hydrostatic shallow flow and water–air two‐phase flow in the shallow subsurface. Finite element computing formats and solution strategies are presented to obtain a numerical solution for the coupled model. An unsaturated seepage flow process is first simulated by water–air two‐phase flow under the atmospheric pressure boundary condition to obtain the rainfall infiltration rate. Then, the rainfall infiltration rate is used as an input parameter to solve the surface run‐off equations and determine the value of the surface run‐off depth. In the next iteration, the pressure boundary condition of unsaturated seepage flow is adjusted by the surface run‐off depth. The coupling process is achieved by updating the rainfall infiltration rate and surface run‐off depth sequentially until the convergence criteria are reached in a time step. A well‐conducted surface run‐off experiment and traditional surface–subsurface model are used to validate the new model. Comparisons with the traditional surface–subsurface model show that the initiation time of surface run‐off calculated by the proposed model is earlier and that the water depth is larger, thus providing values that are closer to the experimental results.  相似文献   

5.
Problems in hydrology and water management that involve both surface water and groundwater are best addressed with simulation models that can represent the interactions between these two flow regimes. In the current generation of coupled models, a variety of approaches is used to resolve surface–subsurface interactions and other key processes such as surface flow propagation. In this study we compare two physics-based numerical models that use a 3D Richards equation representation of subsurface flow. In one model, surface flow is represented by a fully 2D kinematic approximation to the Saint–Venant equations with a sheet flow conceptualization. In the second model, surface routing is performed via a quasi-2D diffusive formulation and surface runoff follows a rill flow conceptualization. The coupling between the land surface and the subsurface is handled via an explicit exchange term resolved by continuity principles in the first model (a fully-coupled approach) and by special treatment of atmospheric boundary conditions in the second (a sequential approach). Despite the significant differences in formulation between the two models, we found them to be in good agreement for the simulation experiments conducted. In these numerical tests, on a sloping plane and a tilted V-catchment, we examined saturation excess and infiltration excess runoff production under homogeneous and heterogeneous conditions, the dynamics of the return flow process, the differences in hydrologic response under rill flow and sheet flow parameterizations, and the effects of factors such as grid discretization, time step size, and slope angle. Low sensitivity to vertical discretization and time step size was found for the two models under saturation excess and homogeneous conditions. Larger sensitivity and differences in response were observed under infiltration excess and heterogeneous conditions, due to the different coupling approaches and spatial discretization schemes used in the two models. For these cases, the sensitivity to vertical and temporal resolution was greatest for processes such as reinfiltration and ponding, although the differences between the hydrographs of the two models decreased as mesh and step size were progressively refined. In return flow behavior, the models are in general agreement, with the largest discrepancies, during the recession phase, attributable to the different parameterizations of diffusion in the surface water propagation schemes. Our results also show that under equivalent parameterizations, the rill and sheet flow conceptualizations used in the two models produce very similar responses in terms of hydrograph shape and flow depth distribution.  相似文献   

6.
Flow and displacement of non-Newtonian fluids in porous media occurs in many subsurface systems, related to underground natural resource recovery and storage projects, as well as environmental remediation schemes. A thorough understanding of non-Newtonian fluid flow through porous media is of fundamental importance in these engineering applications. Considerable progress has been made in our understanding of single-phase porous flow behavior of non-Newtonian fluids through many quantitative and experimental studies over the past few decades. However, very little research can be found in the literature regarding multi-phase non-Newtonian fluid flow or numerical modeling approaches for such analyses.For non-Newtonian fluid flow through porous media, the governing equations become nonlinear, even under single-phase flow conditions, because effective viscosity for the non-Newtonian fluid is a highly nonlinear function of the shear rate, or the pore velocity. The solution for such problems can in general only be obtained by numerical methods.We have developed a three-dimensional, fully implicit, integral finite difference simulator for single- and multi-phase flow of non-Newtonian fluids in porous/fractured media. The methodology, architecture and numerical scheme of the model are based on a general multi-phase, multi-component fluid and heat flow simulator — TOUGH2. Several rheological models for power-law and Bingham non-Newtonian fluids have been incorporated into the model. In addition, the model predictions on single- and multi-phase flow of the power-law and Bingham fluids have been verified against the analytical solutions available for these problems, and in all the cases the numerical simulations are in good agreement with the analytical solutions. In this presentation, we will discuss the numerical scheme used in the treatment of non-Newtonian properties, and several benchmark problems for model verification.In an effort to demonstrate the three-dimensional modeling capability of the model, a three-dimensional, two-phase flow example is also presented to examine the model results using laboratory and simulation results existing for the three-dimensional problem with Newtonian fluid flow.  相似文献   

7.
A Lagrangian particle tracking scheme has been extended to simulate advective transport through coupled surface and subsurface flows. This extended scheme assumes a two-dimensional flow field for the overland domain and a three-dimensional flow field for the subsurface domain. Moreover it is assumed that the flow fields are simulated by a cell centered finite difference method. Pathlines in both the subsurface and the overland domain are simulated by classical particle tracking methods. Exchange of particles between the two domains is simulated by newly-developed algorithms presented in this study. Different algorithms are used depending on the direction of the exchange across the interface between the two domains. In the subsurface domain knowledge about a particle’s pathline is enough to detect a transfer to the surface domain and the solution is straightforward. However, in the two-dimensional overland domain pathlines are parallel to the land surface. Therefore the velocity field in the overland domain alone cannot be used to detect a transfer to the subsurface. We propose a relatively simple algorithm to estimate the probability of transfer to the subsurface domain. It is shown that this algorithm can also be used to handle the transfer from the overland domain to the atmosphere domain. The algorithm to estimate the transfer probabilities is based on the mass balance of water on a streamtube aligned with the particle’s pathline. This newly developed technique ensures that transit time distributions can be simulated accurately. These new relationships are implemented in an existing particle tracking code and are verified using analytical solutions for transit times.  相似文献   

8.
Aufeis (also known as icings) are large sheet-like masses of layered ice that form in river channels in arctic environments in the winter as groundwater discharges to the land surface and subsequently freezes. Aufeis are important sources of water for Arctic river ecosystems, bolstering late summer river discharge and providing habitat for caribou escaping insect harassment. The aim of this research is to use numerical simulations to evaluate a conceptual model of subsurface hydrogeothermal conditions that can lead to the formation of aufeis. We used a conceptual model based on geophysical data from the Kuparuk aufeis field on the North Slope of Alaska to develop a two-dimensional heterogeneous vertical profile model of groundwater flow, heat transport, and freeze/thaw dynamics. Modelling results showed that groundwater can flow to the land surface through subvertical high permeability pathways during winter months when the lower permeability soils near the land surface are frozen. The groundwater discharge can freeze on the surface, contributing to aufeis formation throughout the winter. We performed sensitivity analyses on subsurface properties and surface temperature and found that aufeis formation is most sensitive to the volume of unfrozen water available in the subsurface and the rate at which the subsurface water travels to the land surface. Although a trend of warming air temperatures will lead to a greater volume of unfrozen subsurface water, the aufeis volume can be reduced under warming conditions if the period of time for which air temperatures are below freezing is reduced.  相似文献   

9.
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10.
A two-dimensional (2D) numerical model has been developed to solve shallow water equations for simulation of dam-break flows. The spatial derivatives are discretized using a well-balanced explicit central upwind conservative scheme. The scheme is Riemann solver free and guarantees the positivity of the flow depth over complex topography if the Courant number is kept less than 0.25. The time integration is performed by Euler’s scheme. The model is verified against analytical results for water surface elevation and discharge for three benchmark test cases. A good agreement between analytical solutions and computed results is observed. The property of well-balancing in still water over an uneven bottom is also confirmed. The model is then validated by simulating a laboratory experiment in which a dam break flow propagates over a triangular obstacle. The model performance was found to be satisfactory. A dam break laboratory experimental test case on a frictionless horizontal bottom is also simulated for 2D validation of the model, and good agreement between simulation and the experimental data is observed. The suitability of the proposed model for real life applications is demonstrated by simulating the Malpasset dam-break event, which occurred in 1959 in France. The computed arrival time of the flood wave front and the maximum flow depths at various observation points matched well with the measurements on a 1/400 scale physical model. The overall performance indicates that this model can be applied for simulation of dam-break waves in real life cases.  相似文献   

11.
ABSTRACT

Many basins in nature diverge or possess diverging elements. This study formulates a diverging flow model utilizing kinematic wave theory. The kinematic equations are solved using a first order explicit finite difference scheme. The model is tested using data on a number of laboratory basins reported in the literature. A comparison of this model with the plane model shows that they yield different concentration times and hydrographs that differ in shape, depending upon the degree of divergence.  相似文献   

12.
In order to study the morphological evolution of river beds composed of heterogeneous material, the interaction among the different grain sizes must be taken into account. In this paper, these equations are combined with the two-dimensional shallow water equations to describe the flow field. The resulting system of equations can be solved in two ways: (i) in a coupled way, solving flow and sediment equations simultaneously at a given time-step or (ii) in an uncoupled manner by first solving the flow field and using the magnitudes obtained at each time-step to update the channel morphology (bed and surface composition). The coupled strategy is preferable when dealing with strong and quick interactions between the flow field, the bed evolution and the different particle sizes present on the bed surface. A number of numerical difficulties arise from solving the fully coupled system of equations. These problems are reduced by means of a weakly-coupled strategy to numerically estimate the wave celerities containing the information of the bed and the grain sizes present on the bed. Hence, a two-dimensional numerical scheme able to simulate in a self-stable way the unsteady morphological evolution of channels formed by cohesionless grain size mixtures is presented. The coupling technique is simplified without decreasing the number of waves involved in the numerical scheme but by simplifying their definitions. The numerical results are satisfactorily tested with synthetic cases and against experimental data.  相似文献   

13.
In recent years there has been a growing interest in using Godunov-type methods for atmospheric flow problems. Godunov's unique approach to numerical modeling of fluid flow is characterized by introducing physical reasoning in the development of the numerical scheme (van Leer, 1999). The construction of the scheme itself is based upon the physical phenomenon described by the equation sets. These finite volume discretizations are conservative and have the ability to resolve regions of steep gradients accurately, thus avoiding dispersion errors in the solution. Positivity of scalars (an important factor when considering the transport of microphysical quantities) is also guaranteed by applying the total variation diminishing condition appropriately. This paper describes the implementation of a Godunov-type finite volume scheme based on unstructured adaptive grids for simulating flows on the meso-, micro- and urban-scales. The Harten-Lax-van Leer-Contact (HLLC) approximate Riemann solver used to calculate the Godunov fluxes is described in detail. The higher-order spatial accuracy is achieved via gradient reconstruction techniques after van Leer and the total variation diminishing condition is enforced with the aid of slope-limiters. A multi-stage explicit Runge-Kutta time marching scheme is used for maintaining higher-order accuracy in time. The scheme is conservative and exhibits minimal numerical dispersion and diffusion. The subgrid scale diffusion in the model is parameterized via the Smagorinsky-Lilly turbulence closure. The scheme uses a non-staggered mesh arrangement of variables (all quantities are cell-centered) and requires no explicit filtering for stability. A comparison with exact solutions shows that the scheme can resolve the different types of wave structures admitted by the atmospheric flow equation set. A qualitative evaluation for an idealized test case of convection in a neutral atmosphere is also presented. The scheme was able to simulate the onset of Kelvin-Helmholtz type instability and shows promise in simulating atmospheric flows characterized by sharp gradients without using explicit filtering for numerical stability.  相似文献   

14.
As the capacity of computers increases, the size and resolution of numerical models can be increased. In tidal models, however, using an explicit scheme together with high spatial resolution results in an unreasonably small time-step demanded by the CFL condition for stability. This condition is usually the most restrictive and applies to the propagation of the gravity wave.A fully nonlinear three-dimensional model has been developed, using the Galerkin method in the vertical dimension, in which the gravity wave terms are treated by an alternating-direction implicit scheme, while the friction, viscous and advective terms are treated explicitly. This permits a stable solution with a longer time-step than that required in an equivalent explicit scheme, while not needing as much computational effort as a fully implicit scheme. This semi-implicit model is compared with an explicit model in terms of efficiency, accuracy, and stability. Tidal and wind-driven flows and free oscillations in a rectangular sea model are examined, using various boundary conditions. The semi-implicit scheme takes approximately 1.1 times as long to run (per time-step) on the CRAY-1 computer as the explicit scheme.  相似文献   

15.
A multiscale adjoint (MSADJ) method is developed to compute high-resolution sensitivity coefficients for subsurface flow in large-scale heterogeneous geologic formations. In this method, the original fine-scale problem is partitioned into a set of coupled subgrid problems, such that the global adjoint problem can be efficiently solved on a coarse grid. Then, the coarse-scale sensitivities are interpolated to the local fine grid by reconstructing the local variability of the model parameters with the aid of solving embedded adjoint subproblems. The approach employs the multiscale finite-volume (MSFV) formulation to accurately and efficiently solve the highly detailed flow problem. The MSFV method couples a global coarse-scale solution with local fine-scale reconstruction operators, hence yielding model responses that are quite accurate at both scales. The MSADJ method is equally efficient in computing the gradient of the objective function with respect to model parameters. Several examples demonstrate that the approach is accurate and computationally efficient. The accuracy of our multiscale method for inverse problems is twofold: the sensitivity coefficients computed by this approach are more accurate than the traditional finite-difference-based numerical method for computing derivatives, and the calibrated models after history matching honor the available dynamic data on the fine scale. In other words, the multiscale based adjoint scheme can be used to history match fine-scale models quite effectively.  相似文献   

16.
The topography‐dependent eikonal equation formulated in a curvilinear coordinate system has recently been established and revealed as being effective in calculating first‐arrival travel times of seismic waves in an Earth model with an irregular free surface. The Lax–Friedrichs sweeping scheme, widely used in previous studies as for approximating the topography‐dependent eikonal equation viscosity solutions, is more dissipative and needs a much higher number of iterations to converge. Furthermore, the required number of iterations grows with the grid refinement and results in heavy computation in dense grids, which hampers the application of the Lax–Friedrichs sweeping scheme to seismic wave travel‐time calculation and high‐resolution imaging. In this paper, we introduce a new upwind fast sweeping solver by discretising the Legendre transform of the numerical Hamiltonian of the topography‐dependent eikonal equation using an explicit formula. The minimisation related to the Legendre transform in the sweeping scheme is solved analytically, which proved to be much more efficient than the Lax–Friedrichs algorithm in solving the topography‐dependent eikonal equation. Several numerical experiments demonstrate that the new upwind fast sweeping method converges and achieves much better accuracy after a finite number of iterations, independently of the mesh size, which makes it an efficient and robust tool for calculating travel times in the presence of a non‐flat free surface.  相似文献   

17.
本文以基于改进BISQ模型的二维双相各向同性介质一阶速度-应力方程为基础,推导出了曲线坐标系下对应的方程,然后采用低频散、低耗散的同位网格MacCormack有限差分法来离散方程,并采用紧致的单边MacCormack差分格式结合牵引力镜像法来施加自由地表边界条件,实现了地震波场数值模拟.曲线网格有限差分法采用贴体网格来描述自由表面,地表的网格线紧贴地形,避免了台阶近似造成的数值散射.数值模拟结果表明,在双相介质起伏自由地表和分界面处,各类波型复杂的反射透射规律可以清晰展现,曲线网格有限差分法可以精确地解决地震波在含起伏地表的双相各向同性介质中的传播问题.  相似文献   

18.
The objective of this work is to develop a new numerical approach for the three-dimensional modelling of flow and transient solute transport in fractured porous media which would provide an accurate and efficient treatment of 3D complex geometries and inhomogeneities. For this reason, and in order to eliminate as much as possible the number of degrees of freedom, the fracture network, fractures and their intersections, are solved with a coupled 2D–1D model while the porous matrix is solved independently with a 3D model. The interaction between both models is accounted for by a coupling iterative technique. In this way it is possible to improve efficiency and reduce CPU usage by avoiding 3D mesh refinements of the fractures. The approach is based on the discrete-fracture model in which the exact geometry and location of each fracture in the network must be provided as an input. The formulation is based on a multidimensional coupling of the boundary element method-multidomain (BEM-MD) scheme for the flow and boundary element dual reciprocity method-multidomain (BE-DRM-MD) scheme for the transport. Accurate results and high efficiency have been obtained and are reported in this paper.  相似文献   

19.
Coupled modelling of surface and subsurface systems is a valuable tool for quantifying surface water–groundwater interactions. In the present paper, the 3-D non-steady state Navier–Stokes equations, after Reynolds averaging and with the assumption of a hydrostatic pressure distribution, are for the first time coupled to the 3-D saturated groundwater flow equations in an Integrated suRface watEr–grouNdwater modEl (IRENE). A finite-difference method is used for the solution of the governing equations of IRENE. A semi-implicit scheme is used for the discretisation of the surface water flow equations and a fully implicit scheme for the discretisation of the groundwater flow equations. The two sets of equations are coupled at the common interface of the surface water and groundwater bodies, where water exchange takes place, using Darcy’s law. A new approach is proposed for the solution of the coupled surface water and groundwater equations in a simultaneous manner, in such a fashion that gives computational efficiency at low computational cost. IRENE is verified against three analytical solutions of surface water–groundwater interaction, which are chosen so that different components of the model can be tested. The model closely reproduces the results of the analytical solutions and can therefore be used for analysing and predicting surface water–groundwater interactions in real-world cases.  相似文献   

20.
In this work the numerical integration of 1D shallow water equations (SWE) over movable bed is performed using a well-balanced central weighted essentially non-oscillatory (CWENO) scheme, fourth-order accurate in space and in time. Time accuracy is obtained following a Runge–Kutta (RK) procedure, coupled with its natural continuous extension (NCE). Spatial accuracy is obtained using WENO reconstructions of conservative variables and of flux and bed derivatives. An original treatment for bed slope source term, which maintains the established order of accuracy and satisfies the property of exactly preserving the quiescent flow (C-property), is introduced in the scheme. This treatment consists of two procedures. The former involves the evaluation of the point-values of the flux derivative, considered as a whole with the bed slope source term. The latter involves the spatial integration of the source term, analytically manipulated to take advantage from the expected regularity of the free surface elevation. The high accuracy of the scheme allows to obtain good results using coarse grids, with consequent gain in terms of computational effort. The well-balancing of the scheme allows to reproduce small perturbations of the free surface and of the bottom otherwise of the same order of magnitude of the numerical errors induced by the non-balancing. The accuracy, the well-balancing and the good resolution of the model in reproducing free surface flow over movable bed are tested over analytical solutions and over numerical results available in literature.  相似文献   

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