Mourad Heniche

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.

CFD analysis of several design parameters affecting the performance of the Maxblend impeller

A CFD characterization of the hydrodynamics of the Maxblend impeller with experimental validations has been carried out with viscous Newtonian and non-Newtonian inelastic fluids. The mixing cases investigated were the non-baffled configuration with Newtonian and shear-thinning fluids, and the baffled configuration with only Newtonian fluids. The study focused on the effect of the impeller bottom clearance and the Reynolds number on the power characteristics, the distribution of shear rates and the overall flow conditions in the vessel. It was found that the bottom clearance plays a significant role on the power consumption, and that the value of the Reynolds number and the power law index strongly affect the axial pumping efficiency and the shear rate profile. The best performance was obtained when the impeller Reynolds number is superior to 10.

A virtual finite element model for centered and eccentric mixer configurations

An implementation of the virtual finite element method with unstructured grids for the modeling of laminar flow in eccentric mixers is presented. The effect of the meshing strategy on the quality of the computed flow field is first carefully investigated with a centered impeller. It is shown that both the number of elements in the vicinity of the impeller and the number of kinematics constraints imposed in the virtual finite element formulation control the computational accuracy. The method is then applied to the case of an eccentric mixer provided with a Rushton turbine showing the capabilities of the proposed approach.

Analysis of the vane rheometer using 3D finite element simulation

The vane rheometer has been used for more than two decades to characterize various complex materials. The objective of this work is to investigate for the first time the flow hydrodynamics of Newtonian, shear-thinning and yield stress fluids in one such rheometer by means of three-dimensional finite element simulation. The velocity field and stress distributions are predicted using finite element meshes that are much more refined than the two-dimensional meshes of previous studies. The validity of the no-slip boundary condition on the blade surfaces, which is commonly assumed in these previous studies, is assessed by comparing the calculated torque to experimental data in the case of Newtonian, shear-thinning and yield stress fluids. The effect of the power-law index and apparent yield stress on the stress profile near the blades and away from them is investigated and discussed. It is shown, in particular, that the uniform stress assumption at the vane ends is reasonable for power-law fluids with n<0.5 an...

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.

Parallel finite element simulations of incompressible viscous fluid flow by domain decomposition with Lagrange multipliers

A parallel approach to solve three-dimensional viscous incompressible fluid flow problems using discontinuous pressure finite elements and a Lagrange multiplier technique is presented. The strategy is based on non-overlapping domain decomposition methods, and Lagrange multipliers are used to enforce continuity at the boundaries between subdomains. The novelty of the work is the coupled approach for solving the velocity-pressure-Lagrange multiplier algebraic system of the discrete Navier-Stokes equations by a distributed memory parallel ILU (0) preconditioned Krylov method. A penalty function on the interface constraints equations is introduced to avoid the failure of the ILU factorization algorithm. To ensure portability of the code, a message based memory distributed model with MPI is employed. The method has been tested over different benchmark cases such as the lid-driven cavity and pipe flow with unstructured tetrahedral grids. It is found that the partition algorithm and the order of the physical variables are central to parallelization performance. A speed-up in the range of 5-13 is obtained with 16 processors. Finally, the algorithm is tested over an industrial case using up to 128 processors. In considering the literature, the obtained speed-ups on distributed and shared memory computers are found very competitive.

Cumulative effects of fecal contamination from combined sewer overflows: Management for source water protection

The quality of a drinking water source depends largely on upstream contaminant discharges. Sewer overflows can have a large influence on downstream drinking water intakes as they discharge untreated or partially treated wastewaters that may be contaminated with pathogens. This study focuses on the quantification of Escherichia coli discharges from combined sewer overflows (CSOs) and the dispersion and diffusion in receiving waters in order to prioritize actions for source water protection. E. coli concentrations from CSOs were estimated from monitoring data at a series of overflow structures and then applied to the 42 active overflow structures between 2009 and 2012 using a simple relationship based upon the population within the drainage network. From these estimates, a transport-dispersion model was calibrated with data from a monitoring program from both overflow structures and downstream drinking water intakes. The model was validated with 15 extreme events such as a large number of overflows (n > 8) or high concentrations at drinking water intakes. Model results demonstrated the importance of the cumulative effects of CSOs on the degradation of water quality downstream. However, permits are typically issued on a discharge point basis and do not consider cumulative effects. Source water protection plans must consider the cumulative effects of discharges and their concentrations because the simultaneous discharge of multiple overflows can lead to elevated E. coli concentrations at a drinking water intake. In addition, some CSOs have a disproportionate impact on peak concentrations at drinking water intakes. As such, it is recommended that the management of CSOs move away from frequency based permitting at the discharge point to focus on the development of comprehensive strategies to reduce cumulative and peak discharges from CSOs upstream of drinking water intakes.

Dynamic tracking of flow boundaries in rivers with respect to discharge

A new Eulerian approach is proposed to track the dynamic position of flow boundaries in rivers with respect to flow discharge or tides. Associated to a two dimensional (2D) transient horizontal hydrodynamic model, it allows to define the configuration of watercourses in a broad hydrological register varying from dry conditions to severe flooding. The finite element method is used to develop the numerical prediction tool. It is employed to estimate not only the classical flow variables such as water surface level and velocity field, but also the position of the shorelines. In this paper, the strategy followed for building this «drying-wetting» model consists in letting the water surface move freely, everywhere in the domain including the dry zones, allowing it to plunge under the ground. Two practical applications on rivers of Quebec (Canada) are presented. The first one deals with steady state situations on St. Marguerite River. The second one deals with the reconstitution of flood propagation on Chicoutimi River according to the extreme flooding events of July 96 in the Saguenay region.

A Finite Element Solver for the Advection Equation Applied to Interface Tracking

A numerical strategy for the finite element simulation of the flow of two immiscible fluids has been developed based on unstructured triangular meshes. The tracking of the interface between the two fluids is accomplished by means of an advection equation for the volume fraction of one of these fluids. An accurate description of the interface is achieved by means of an automatic mesh refinement procedure developed for the simulation of fluid flow in twin‐screw extruders. The advantage of this technique comes from the use of one single reference mesh. At each time iteration, this reference mesh is adapted by splitting up the elements in the vicinity of the interface into sub‐elements. Local refinement can then be carried out with one single mesh to be generated before the simulation is started.First, the method will be presented in detail. It will then be applied to two‐dimensional classical benchmark problems: the advection skew to the mesh and the transport of a square.