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Operational flood control of a low-lying delta system using large time step Model Predictive Control
The safety of low-lying deltas is threatened not only by riverine flooding but by storm-induced coastal flooding as well. For the purpose of flood control, these deltas are mostly protected in a man-made environment, where dikes, dams and other adjustable infrastructures, such as gates, barriers and pumps are widely constructed. Instead of always reinforcing and heightening these structures, it is worth considering making the most of the existing infrastructure to reduce the damage and manage the delta in an operational and overall way. In this study, an advanced real-time control approach, Model Predictive Control, is proposed to operate these structures in the Dutch delta system (the Rhine–Meuse delta). The application covers non-linearity in the dynamic behavior of the water system and the structures. To deal with the non-linearity, a linearization scheme is applied which directly uses the gate height instead of the structure flow as the control variable. Given the fact that MPC needs to compute control actions in real-time, we address issues regarding computational time. A new large time step scheme is proposed in order to save computation time, in which different control variables can have different control time steps. Simulation experiments demonstrate that Model Predictive Control with the large time step setting is able to control a delta system better and much more efficiently than the conventional operational schemes. 相似文献
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A new approach is presented for the numerical solution of the complete 1D Saint-Venant equations. At each time step, the governing system of partial differential equations (PDEs) is split, using a fractional time step methodology, into a convective prediction system and a diffusive correction system. Convective prediction system is further split into a convective prediction and a convective correction system, according to a specified approximated potential. If a scalar exact potential of the flow field exists, correction vanishes and the solution of the convective correction system is the same solution of the prediction system. Both convective prediction and correction systems are shown to have at each x − t point a single characteristic line, and a corresponding eigenvalue equal to the local velocity. A marching in space and time (MAST) technique is used for the solution of the two systems. MAST solves a system of two ordinary differential equations (ODEs) in each computational cell, using for the time discretization a self-adjusting fraction of the original time step. The computational cells are ordered and solved according to the decreasing value of the potential in the convective prediction step and to the increasing value of the same potential in the convective correction step. The diffusive correction system is solved using an implicit scheme, that leads to the solution of a large linear system, with the same order of the cell number, but sparse, symmetric and well conditioned. The numerical model shows unconditional stability with regard of the Courant–Friedrichs–Levi (CFL) number, requires no special treatment of the source terms and a computational effort almost proportional to the cell number. Several tests have been carried out and results of the proposed scheme are in good agreement with analytical solutions, as well as with experimental data. 相似文献
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A new methodology is proposed for the development of parameter-independent reduced models for transient groundwater flow models. The model reduction technique is based on Galerkin projection of a highly discretized model onto a subspace spanned by a small number of optimally chosen basis functions. We propose two greedy algorithms that iteratively select optimal parameter sets and snapshot times between the parameter space and the time domain in order to generate snapshots. The snapshots are used to build the Galerkin projection matrix, which covers the entire parameter space in the full model. We then apply the reduced subspace model to solve two inverse problems: a deterministic inverse problem and a Bayesian inverse problem with a Markov Chain Monte Carlo (MCMC) method. The proposed methodology is validated with a conceptual one-dimensional groundwater flow model. We then apply the methodology to a basin-scale, conceptual aquifer in the Oristano plain of Sardinia, Italy. Using the methodology, the full model governed by 29,197 ordinary differential equations is reduced by two to three orders of magnitude, resulting in a drastic reduction in computational requirements. 相似文献
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Xinya Li Bill X. Hu 《Stochastic Environmental Research and Risk Assessment (SERRA)》2013,27(5):1181-1191
Numerical models with fine discretization normally demand large computational time and space, which lead to computational burden for state estimations or model parameter inversion calculation. This article presented a reduced implicit finite difference scheme that based on proper orthogonal decomposition (POD) for two-dimensional transient mass transport in heterogeneous media. The reduction of the original full model was achieved by projecting the high-dimension full model to a low-dimension space created by POD bases, and the bases are derived from the snapshots generated from the model solutions of the forward simulations. The POD bases were extracted from the ensemble of snapshots by singular value decomposition. The dimension of the Jacobian matrix was then reduced after Galerkin projection. Thus, the reduced model can accurately reproduce and predict the original model’s transport process with significantly decreased computational time. This scheme is practicable with easy implementation of the partial differential equations. The POD method is illustrated and validated through synthetic cases with various heterogeneous permeability field scenarios. The accuracy and efficiency of the reduced model are determined by the optimal selection of the snapshots and POD bases. 相似文献
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An efficient and accurate numerical model for multicomponent compressible single-phase flow in fractured media is presented. The discrete-fracture approach is used to model the fractures where the fracture entities are described explicitly in the computational domain. We use the concept of cross flow equilibrium in the fractures. This will allow large matrix elements in the neighborhood of the fractures and considerable speed up of the algorithm. We use an implicit finite volume (FV) scheme to solve the species mass balance equation in the fractures. This step avoids the use of Courant–Freidricks–Levy (CFL) condition and contributes to significant speed up of the code. The hybrid mixed finite element method (MFE) is used to solve for the velocity in both the matrix and the fractures coupled with the discontinuous Galerkin (DG) method to solve the species transport equations in the matrix. Four numerical examples are presented to demonstrate the robustness and efficiency of the proposed model. We show that the combination of the fracture cross-flow equilibrium and the implicit composition calculation in the fractures increase the computational speed 20–130 times in 2D. In 3D, one may expect even a higher computational efficiency. 相似文献
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Tom J. Coulthard Jeff C. Neal Paul D. Bates Jorge Ramirez Gustavo A. M. de Almeida Greg R. Hancock 《地球表面变化过程与地形》2013,38(15):1897-1906
Landscape evolution models (LEMs) simulate the geomorphic development of river basins over long time periods and large space scales (100s–1000s of years, 100s of km2). Due to these scales they have been developed with simple steady flow models that enable long time steps (e.g. years) to be modelled, but not shorter term hydrodynamic effects (e.g. the passage of a flood wave). Nonsteady flow models that incorporate these hydrodynamic effects typically require far shorter time steps (seconds or less) and use more expensive numerical solutions hindering their inclusion in LEMs. The recently developed LISFLOOD‐FP simplified 2D flow model addresses this issue by solving a reduced form of the shallow water equations using a very simple numerical scheme, thus generating a significant increase in computational efficiency over previous hydrodynamic methods. This leads to potential convergence of computational cost between LEMs and hydrodynamic models, and presents an opportunity to combine such schemes. This paper outlines how two such models (the LEM CAESAR and the hydrodynamic model LISFLOOD‐FP) were merged to create the new CAESAR‐Lisflood model, and through a series of preliminary tests shows that using a hydrodynamic model to route flow in an LEM affords many advantages. The new model is fast, computationally efficient and has a stronger physical basis than a previous version of the CAESAR model. For the first time it allows hydrodynamic effects (tidal flows, lake filling, alluvial fans blocking valley floor) to be represented in an LEM, as well as producing noticeably different results to steady flow models. This suggests that the simplification of using steady flow in existing LEMs may bias their findings significantly. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
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Distributed approximation of open-channel flow routing accounting for backwater effects 总被引：2，自引：0，他引：2
Simon Munier Xavier Litrico Gilles Belaud Pierre-Olivier Malaterre 《Advances in water resources》2008,31(12):1590-1602
In this article, we propose a new model, called LBLR for Linear Backwater Lag-and-Route, which approximates the Saint-Venant equations linearized around a non-uniform flow in a finite channel (with a downstream boundary condition). A classical frequency approach is used to build the distributed Saint-Venant transfer function providing the discharge at any point in the channel in the Laplace domain with respect to the upstream discharge. The moment matching method is used to match a second-order-with-delay model on the theoretical distributed Saint-Venant transfer function. Model parameters are then expressed analytically as functions of the pool characteristics. The proposed model efficiently accounts for the effects of downstream boundary condition on the channel dynamics. 相似文献
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Katerina Spanoudaki Anastasios I. Stamou Aikaterini Nanou-Giannarou 《Journal of Hydrology》2009,375(3-4):410-427
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
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The estimation of peak linear response via elastic design (response) spectra continues to form the basis of earthquake‐resistant design of structural systems in various codes of practice all over the world. Many response spectrum‐based formulations of peak linear response require an additional input of the spectral velocity (SV) ordinates consistent with the specified seismic hazard. SV ordinates have been conventionally approximated by pseudo spectral velocity (PSV) ordinates, which are close to the SV ordinates only over the intermediate frequency range coinciding with the velocity‐sensitive region. At long periods, PSV ordinates underestimate the SV ordinates, and this study proposes a formulation of a correction factor (>1) that needs to be multiplied by the PSV ordinates in order to close the gap between the two sets of ordinates. A simple model is proposed in the form of a power function in oscillator period to estimate this factor in terms of two governing parameters which are in turn estimated from two single‐parameter scaling equations. The parameters considered for the scaling equations are (1) the period at which the PSV spectrum is maximized and (2) the rate of decay of the pseudo spectral acceleration (PSA) amplitudes at long periods. For a given damping ratio, four regression coefficients are determined for the scaling equations with the help of 205 ground motions recorded in western USA. A numerical study undertaken with the help of several design PSA spectra and ensembles of spectrum‐compatible ground motions illustrates the effectiveness of the proposed correction factor, together with the proposed scaling models, in comparison with the PSV approximation in a variety of design situations. Both the input parameters mentioned above can be easily obtained from the specified design spectrum, and thus the proposed model is convenient to use. 相似文献
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In this paper, a computational model for the simulation of coupled hydromechanical and electrokinetic flow in fractured porous media is introduced. Particular emphasis is placed on modeling CO2 flow in a deformed, fractured geological formation and the associated electrokinetic flow. The governing field equations are derived based on the averaging theory and the double porosity model. They are solved numerically with a mixed discretization scheme, formulated on the basis of the standard Galerkin finite element method, the extended finite element method, the level-set method and the Petrov–Galerkin method. The standard Galerkin method is utilized to discretize the equilibrium and the diffusive dominant field equations, and the extended finite element method, together with the level-set method and the Petrov–Galerkin method, are utilized to discretize the advective dominant field equations. The level-set method is employed to trace the CO2 plume front, and the extended finite element method is employed to model the high gradient in the saturation field front. The proposed mixed discretization scheme leads to a convergent system, giving a stable and effectively mesh-independent model. The accuracy and computational efficiency of the proposed model is evaluated by verification and numerical examples. Effects of the fracture spacing on the CO2 flow and the streaming potential are discussed. 相似文献
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Recent advances in the simulation of free surface flows over mobile bed have shown that accurate and stable results in realistic problems can be provided if an appropriate coupling between the shallow water equations (SWE) and the Exner equation is performed. This coupling can be done if using a suitable Jacobian matrix. As a result, faithful numerical predictions are available for a wide range of flow conditions and empirical bed load discharge formulations, allowing to investigate the best option in each case study, which is mandatory in these type of environmental problems. When coupling the equations, the SWE are considered but including an extra conservation law for the sediment dynamics. In this way the computational cost may become unrealistic in situations where the application of the SWE over rigid bed can be used involving large time and space scales without giving up to the adequate level of mesh refinement. Therefore, for restoring the numerical efficiency, the coupling technique is simplified, not decreasing the number of waves involved in the Riemann problem but simplifying their definitions. The effects of the approximations made are tested against experimental data which include transient problems over erodible bed. The simplified model is formulated under a general framework able to insert any desirable discharge solid load formula. 相似文献
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《Advances in water resources》1998,21(7):567-579
In this paper, details of a conjunctive surface-subsurface numerical model for the simulation of overland flow are presented. In this model, the complete one-dimensional Saint-Venant equations for the surface flow are solved by a simple, explicit, essentially non-oscillating (ENO) scheme. The two-dimensional Richards equation in the mixed form for the subsurface flow is solved using an efficient strongly implicit finite-difference scheme. The explicit scheme for the surface flow component results in a simple method for connecting the surface and subsurface components. The model is verified using the experimental data and previous numerical results available in the literature. The proposed model is used to study the two-dimensionality effects due to non-homogeneous subsurface characteristics. Applicability of the model to handle complex subsurface conditions is demonstrated. 相似文献
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Optimal allocation of water quantity and waste load in the Northwest Pearl River Delta,China 总被引：1，自引：1，他引：0
Dedi Liu Shenglian Guo Quanxi Shao Yunzhong Jiang Xiaohong Chen 《Stochastic Environmental Research and Risk Assessment (SERRA)》2014,28(6):1525-1542
The Northwest Pearl River Delta is one of the most developed areas in China and has faced serious water problems because of its fast economic growth, urbanisation and other developments. It is widely believed that an integrated management of the socio-economic factors cross individual administrative cities is an effective way to solve the water problems. To serve this purpose, this paper aims to develop an integrated model for the optimal allocation of water quantity and waste load. In order to consider the interaction between water quantity and waste load allocation, the Saint-Venant equations were used to simulate dynamic water flow for the water quantity allocation, whereas the one dimensional advection–dispersion mass transport equation was used to simulate water quality for the waste load allocation. In addition to the maximisation of the economic benefits, which is often considered as an objective of optimal water resource allocation models, the minimisation of water shortages and maximisation of waste load were also introduced as objectives of the model. To solve the multi-objective allocation model, a second generation non-dominated sorting genetic algorithm was employed because of its computational efficiency and running time. The results indicate that it is a serious task to reduce the COD in the Northwest Pearl River Delta since the maximum waste load allocations under water quality targets is less than the present amount of waste discharged into rivers in the study area. 相似文献
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The structure of a hydrodynamic model of the Lower Volga, which has been developed for solving water management problems, and some results of computer simulation of variations of water level at the reach from the Volgograd HPP to the Caspian Sea are considered. The conditions under which the one-dimensional hydrodynamic model, developed in Delft Hydraulic Laboratory of Technical University based on Saint-Venant equations, can be successfully applied in the Lower Volga are determined. 相似文献
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本文采用有理函数Krylov子空间模型降阶算法实现了同时求解多频可控源电磁法三维正演响应的快速计算.首先采用基于Yee氏交错网格的拟态有限体积法实现控制方程的空间离散,将任意频率的电场响应表示为关于频率参数的传递函数.采用有理函数Krylov子空间算法求解该传递函数.针对构建m维有理函数Krylov子空间需要求解m次（几十到上百）关于有理函数极点和离散控制方程系数矩阵的线性方程组的问题,本文提出采用单个重复极点的有理函数Krylov子空间模型降阶算法,结合直接法求解器PARDISO,采用Gram-Schmidt方法,只需要1次系数矩阵分解和m次矩阵回代即可实现有理函数Krylov子空间的构建,极大地减少了计算量.针对最优化有理函数极点选取问题,本文根据传递函数的有理函数Krylov子空间投影算法的误差分析理论,引入关于单个重复极点的收敛率函数,通过求解有理函数的最大收敛率直接给出最优化的单个重复极点公式.最终实现了不同发射频率的可控源电磁法三维正演响应的快速计算.分别计算了典型层状模型多发射频率的CSAMT和海洋CSEM的正演响应,通过与解析解的对比验证了本文算法在多发射频率正演的计算精度和计算效率;并通过一个三维海洋CSEM勘探设计最优化发射频率和接收区域选取的例子进一步说明本文算法的优点. 相似文献
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《Advances in water resources》2005,28(8):835-844
Permeability of porous media in subsurface environments is subject to potentially large uncertainties due to the heterogeneity of natural systems. In this study, a first-order reliability method (FORM) is combined with a lattice Boltzmann method (LBM) to estimate the permeability of randomly generated porous media. The proposed procedure provides an increased ease of addressing complex pore structures by employing LBM to model fluid flow, while inheriting the computational efficiency from FORM. Macroscale-equivalent permeability can thus be estimated with significantly reduced computational efforts, while maintaining a connection to the complex microscale fluid dynamics within a pore structure environment. Implemented on several randomly generated porous media domains, the proposed method provides 13–120 times the efficiency compared to Monte Carlo methods. 相似文献
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SHAO Xuejun 《国际泥沙研究》1999,(2)
1INTRODUCTIONInprocess-basedoverlandflowandsoilerosionmodels,surfacerunoffonahillslopeisoftenrepresentedaseitherbroadsheetfloworflowinrillswithassumedrectangularchannelcrosssections(e.g.,Bairdelal1992,NSERL1995).Inmostcasesthehydraulicsofoverlandflowiscalculatedbyusingthekinematicwavemodel,whichisasirnplificationofthedynamicwavemodel(theequationsystemofSaint-Venantequationandequationofcontinuity).Forabroadsheetoverlandflowonhillslopeduetorainfallexcess,theequationofcontinuityiswherehis… 相似文献