Yves Secretan

A two-dimensional finite element drying-wetting shallow water model for rivers and estuaries

A new finite element model has been developed to simulate two-dimensional free surface flow in rivers and estuaries. The variables of the model are the specific discharge and the water level. The algorithm takes into account the natural boundaries of the flow, defined by the contour lines of zero depth, with a new approach that accepts positive and negative values for the water depth. In this way, we consider a wet or dry area when the water depth is positive or negative respectively. A 6-node triangular element and an implicit Euler scheme are respectively used for spatial and time discretization of the mathematical model. The solution procedure is based on the inexact Newton-GMRES type solver with incomplete factorization as preconditioning. The numerical results of the proposed approach are in good agreement with an analytic solution and also with the classical approach.

Decision support system for micro-hydro power plants in the Amazon region under a sustainable development perspective

One of the main obstacles to the socio-economic development of the Brazilian Amazon is the lack of electric energy in the numerous small isolated communities of the region that hampers value-added agricultural production, revenue growth and creation of jobs. One way to solve this problem is by setting up micro-hydro power (MHP) plants under a sustainable development perspective. This paper presents a decision support system (DSS) that analyzes this solution. The system considers the hydrological, topographical, geotechnical, environmental, energy, economic and social aspects of the target site. A detailed analysis is made of the hydrological model that employs a rainfall run-off model for small catchment analysis; the energy planning favors a two-turbine method to determine the maximum energy production during demand peaks, and the economic aspects show that the costs of energy generated by MHP plants are comparable to those from rural grid systems and lower than those from from diesel generators. Thus, the use of the hydro-power resources of the small catchments of Amazonia combined with the minimization of the environmental impacts caused by MHP not only fulfills the energy demand of the small communities of region, but is also viable economically along with job creation and revenue generation, and it supports the perspective of sustainable development.

Integrated two-dimensional macrophytes-hydrodynamic modeling

Lake Saint-Francois is the first fluvial lake downstream of the Great Lakes. Aquatic macrophytes are abundant because of water level stabilization and increased nutrient loads. The influence of plants on flow modification is very important and must be considered in order to simulate hydrodynamic conditions. The spatial distribution of plant species is linked to their instream flow preferences. Several abiotic variables are of importance: light penetration, wave energy, current velocity, nutrients in substrate and physical characteristics of the substrate are controlling the species and their biomass. Field characterization of macrophytes was performed using echosounder transects in association with a submersible video camera. This technique allowed the calibration of each echofacies for species identification and their relative proportion, height and density. The main eleven assemblages appear to be strongly correlated with abiotic conditions. A basic interpretation key was set up in order to describe plant distribution over the entire lake. Species, relative proportion, density and plant height were interpolated between transects. This information is used to adjust the Mannings friction coefficient for each assemblage. Simulations of the flow fields with plants and in absence of plants show a contrasted pattern. During the summer (with plants), the flow is mainly concentrated in deep channels where velocities are clearly increased by approximately 20% compared to spring-fall simulation (without plants).

Temporal and spatial variability of tidal‐fluvial dynamics in the St. Lawrence fluvial estuary: An application of nonstationary tidal harmonic analysis

Predicting tides in upstream reaches of rivers is a challenge, because tides are highly nonlinear and nonstationary, and accurate short-time predictions of river flow are hard to obtain. In the St. Lawrence fluvial estuary, tide forecasts are produced using a one-dimensional model (ONE-D), forced downstream with harmonic constituents, and upstream with daily discharges using 30 day flow forecasts from Lake Ontario and the Ottawa River. Although this operational forecast system serves its purpose of predicting water levels, information about nonstationary tidal-fluvial processes that can be gained from it is limited, particularly the temporal changes in mean water level and tidal properties (i.e., constituent amplitudes and phases), which are function of river flow and ocean tidal range. In this paper, a harmonic model adapted to nonstationary tides, NS_TIDE, was applied to the St. Lawrence fluvial estuary, where the time-varying external forcing is directly built into the tidal basis functions. Model coefficients from 13 analysis stations were spatially interpolated to allow tide predictions at arbitrary locations as well as to provide insights into the spatiotemporal evolution of tides. Model hindcasts showed substantial improvements compared to classical harmonic analyses at upstream stations. The model was further validated by comparison with ONE-D predictions at a total of 32 stations. The slightly lower accuracy obtained with NS_TIDE is compensated by model simplicity, efficiency, and capacity to represent stage and tidal variations in a very compact way and thus represents a new means for understanding tidal rivers.

ON OPEN BOUNDARIES IN THE FINITE ELEMENT APPROXIMATION OF TWO-DIMENSIONAL ADVECTION-DIFFUSION FLOWS

SUMMARY A steady-state and transient finite element model has been developed to approximate, with simple triangular elements, the two-dimensional advection—di⁄usion equation for practical river surface flow simulations. Essentially, the space—time Crank—Nicolson—Galerkin formulation scheme was used to solve for a given conservative flow-field. Several kinds of point sources and boundary conditions, namely Cauchy and Open, were theoretically and numerically analysed. Steady-state and transient numerical tests investigated the accuracy of boundary conditions on inflow, noflow and outflow boundaries where di⁄usion is important (di⁄usive boundaries). With the proper choice of boundary conditions, the steady-state Galerkin and the transient Crank—Nicolson—Galerkin finite element schemes gave stable and precise results for advectiondominated transport problems. Comparisons indicated that the present approach can give equivalent or more precise results than other streamline upwind and high-order time-stepping schemes. Di⁄usive boundaries can be treated with Cauchy conditions when the flow enters the domain (inflow), and with Open conditions when the flow leaves the domain (outflow), or when it is parallel to the boundary (noflow). Although systems with mainly di⁄usive noflow boundaries may still be solved precisely with Open conditions, they are more susceptible to be influenced by other numerical sources of error. Moreover, the treatment of open boundaries greatly increases the possibilities of correctly modelling restricted domains of actual and numerical interest. ( 1997 by John Wiley & Sons, Ltd.

Emergence of New Explanatory Variables for 2D Habitat Modelling in Large Rivers: The St. Lawrence Experience

The St. Lawrence River is one of the most important large rivers in North America. This 600-km long watercourse is characterized by a high degree of physical heterogeneity, including fast moving narrow reaches separated by fluvial lakes reaching 10 km in width. The mean annual discharge from the outflow of Lake Ontario is 7500 m3/s and has been managed for hydropower and transportation since the 1960s. With the management plan currently under review an effort is being made to include criteria that take into account the impacts of regulation on the biotic components of the river ecosystem. High resolution 2D spatial modelling of river habitats and floodplains is a powerful tool to make quantitative impact assessments of the biota. Physical variables commonly used in habitat models include depth, velocity and substrate size. In addition, other abiotic variables such as wind-generated wave stress, light penetration, water temperature, sedimentation of fine particles, specific discharge and bottom slope, that define the local ’hydroperiod’ have been suggested. Our proposed approach integrates abiotic data obtained from numerical models, field measurements and biological information to overcome problems inherent in temporally and spatially heterogeneous river systems. This approach was tested with a habitat model applied to submerged aquatic vegetation, various categories of wetlands, benthic organisms and various life stages of a number offish species. Logistic regression is the statistical model currently used to synthesize the relationships between abiotic and biotic factors. The short-term objective of this modelling exercise in the St. Lawrence River is to understand the underlying links between fluvial physics and biota. A longer-term objective is to provide a real-time analysis of key variables and to quantify the links between trophic levels.

Efficient ILU preconditioning and inexact‐Newton‐GMRES to solve the 2D steady shallow water equations

This paper presents a practical use of incomplete lower-upper factorization (ILU) preconditioning inexact-Newton-GMRES(m) for solving the steady shallow water equations. An efficient algorithm to store in a compact row format the ILU preconditioning matrix is proposed. Numerical experiments shows a linear variation of both CPU time and storage versus the matrix dimension until more than a million. Two examples are performed where the first one shows that an increment of solution norm based convergence is inaccurate. The second one reveal the importance of mesh numbering and unknowns ordering on convergence rate. An empirical criterion for choosing a good mesh numbering is also proposed. It is found that the Sloan numbering method enhances efficiency of the solver.

Pristine Lake Saint-François, St. Lawrence River: Hydrodynamic Simulation and Cumulative Impact

Abstract Lake Saint-Francois is a fluvial lake of the St. Lawrence system which is used for hydropower production and commercial navigation. For 150 years, it was dredged and dammed regularly without any impact analysis being made. The cumulative impact of dredging and damming on large rivers such as the St. Lawrence is an issue with only qualitative answers. Bidimensional hydrodynamics was used to simulate ancient flow conditions and to produce quantitative descriptors. Two Numerical Field Models (NFM) were prepared, one representing present state geometry, which contains 300,000 sounding points, and the other representing pristine state, based on 1900 and 1870 measurements and containing 70,000 soundings. These two NFMs were compared, showing important changes in the morphology of the lake. The NFMs were then used for bidimensional hydrodynamic simulations of both actual and pristine states for 3 different discharges: 5,000 m 3 /s, 7,500 m 3 /s, and 10,000 m 3 /s. Results highlight the cumulative physical transformation of the system. Hydrodynamic simulations and velocity differences show an increase of velocities over shoals for discharge under 8,800 m 3 /s, and a decrease of velocities in deeper water for the same range of discharge. Dredging and straightening around Cornwall Island resulted in changes from 64% to 71% of the total river flow passing through the south channel while the flow in the north channel decreased from 36% to 29%. These hydrodynamic transformations had a definitive impact on sedimentation and most probably on aquatic plant distribution.

A water flow pattern analysis of Guajará Bay: Amazon Estuary - Brazil

This work describes the steps required to construct a hydrodynamic model of the Guajara Bay, using Geographic Information Systems and the Finite Element Method. An overview of the problem that motivates this modelling procedure, i.e., the pollutant dispersion, is presented. The computer software used is then discussed, stressing the links between the data model entities. The calibration procedure is described. The methods used to obtain field data and the results obtained are presented, alongside the main flow patterns of the water. The simulations and applications of the model are discussed at the end of the paper.

Hydrodynamic modeling and morphological analysis of Lake Água Preta: one of the water sources of Belém-PA-Brazil

The main contribution from this paper includes the hydrodynamic modeling and morphological analysis of Lake Agua Preta in Belem city, Para State, Brazil. The lake bathymetry was taken through the data provided by COSANPA (the local sanitation and water supply company) dating back to 1975, and from a 2009 field study. Both bathymetries produced two terrain elevation models, which were used for morphological analysis and hydrodynamic simulations. The morphological analysis has revealed that, from 1975 to 2009, the annual mean rate of sedimentation varies between 23,065 and 29,081 m3/year. Through this result, the sedimentation time of Lake Agua Preta, from 2009, has been calculated, which varies between 295 and 381 years, maintaining the same rate of sedimentation, water consumption and pumping. The hydrodynamic model simulated the depths and velocities, showing a slight flow with velocities ranging from 0 to 33 cm/s. This flow is established between water input and output of the lake, which is used as reservoir of Belem city.