Anti-Dissipative Schemes for Advection and Application to Hamilton–Jacobi–Bellmann Equations

We propose two new antidiffusive schemes for advection (or linear transport), one of them being a mixture of Roe’s Super-Bee scheme and of the “Ultra-Bee” scheme. We show how to apply these schemes to treat time-dependent first order Hamilton–Jacobi–Bellman equations with discontinuous initial data, possibly infinitely-valued. Numerical tests are proposed, in one and two space dimensions, in order to validate the methods AMS subject classifications. Primary 65M12, Secondary 58J47     

Numerical Solution of Fractional Advection-Dispersion Equation

Numerical schemes and stability criteria are developed for solution of the one-dimensional fractional advection-dispersion equation (FRADE) derived by revising Fick’s first law. Employing 74 sets of dye test data measured on natural streams, it is found that the fractional order F of the partial differential operator acting on the dispersion term varies around the most frequently occurring value of F = 1.65 in the range of 1.4 to 2.0. Two series expansions are proposed for approximation of the limit definitions of fractional derivatives. On this ground, two three-term finite-difference schemes?“1.3 Backward Scheme” having the first-order accuracy and “F.3 Central Scheme” possessing the F-th order accuracy?are presented for fractional order derivatives. The F.3 scheme is found to perform better than does the 1.3 scheme in terms of error and stability analyses and is thus recommended for numerical solution of FRADE. The fractional dispersion model characterized by the FRADE and the F.3 scheme can accurately simulate the long-tailed dispersion processes in natural rivers.     

Fully transient analytical solution for degradable organic contaminant transport through GMB/GCL/AL composite liners

In this study, analytical solution for degradable organic contaminant transport through a composite liner consisting of a geomembrane (GMB) layer, a geosynthetic clay liner (GCL) and an attenuation layer (AL) is derived by the separation of variables method. The transient contaminant transport in the whole composite liner can be well described avoiding some weird phenomena in existing analytical solutions. The results of parametric study show that GCL has significant effect on improving the barrier efficiency especially for scenarios with high leachate head. The biodegradation and adsorption in GCL have significant influence on the contaminant transport through the composite liner when the half-life of contaminant in GCL is less than 5 years. Otherwise, the effect can be neglected.     

Modeling and optimization of activated sludge bioreactors for wastewater treatment taking into account spatial inhomogeneities

In this work, we study optimal and suboptimal control strategies for the treatment of a polluted water resource by using aside a continuous bioreactor. The control consists in choosing the inlet volumetric flow rate for filling the bioreactor with contaminated water from a considered resource (lake, reservoir, water-table, …). The treated outflow returns to the resource. We tackle an optimization problem which aims to minimize the time needed to reach a prescribed minimal value of contamination in the resource by choosing the input flow. Next, we study the influence of inhomogeneities of concentrations in the bioreactor, considering a system based on partial differential equations which describe its dynamics. We show that applying the optimal feedback control derived for perfectly mixed bioreactor does not allow to reach the target with small diffusion parameters as it drives the bioreactor to washout (the bioreactor equilibrium with no biomass). In this case, a suboptimal feedback (which reaches the target in finite time) is obtained with the help of a Hybrid Genetic Algorithm. Furthermore, we consider that the fluid flow velocity of the water entering into the bioreactor follows either a uniform or a nonuniform profile, showing that the optimal volumetric flow rates obtained with the uniform profile are not optimal if the profile is nonuniform, even when high diffusion coefficients are considered in the model.     

Spectral characterization of mixing properties of annular MHD micromixers

We develop a quantitative analysis of mixing regimes in an annular MHD-driven micromixer recently proposed by Gleeson et al. as a prototype for biomolecular applications. The analysis is based on the spectral properties of the advection–diffusion operator, with specific focus on the dependence of the dominant eigenvalue–eigenfunction on the Peclet number and on the system geometry. A theoretical prediction for the dominant eigenvalue encompassing all mixing regimes is developed and validated by comparison with numerical simulations. The theoretical prediction is extended to an open inflow–outflow version of the reactor, which shows the occurrence of new regimes associated with the existence of a nonuniform axial flow.     

An analytical model for solute mixing in surcharged manholes

A mathematical model has been developed to describe solute mixing in surcharged manholes using the submerged jet theory. The model has been applied for straight-through flow manholes and for manholes with a difference in the level of the inlet and outlet pipes. The model is applicable to dissolved substances, i.e. the model has not been validated for high sediment concentrations (above 1 g/l) and care should be taken in such cases. Simulation results from the new model are compared with laboratory measurements and are further compared to conventional modelling techniques currently available in commercial software specially developed for modelling the water quality in sewers. The results prove that the new model produces considerably better results compared to the traditional assumption of full mixing in a manhole. The new model compares well to the laboratory measurements and hence improves the accuracy of modelling soluble pollutant transport in sewers. The applicability of the new modelling approach is discussed and further studies are recommended.     

三亚市崖城水厂净水工艺流程设计

新建三亚市崖城水厂是三亚市多水源水厂之一,供水量10万m3/d,引大隆水库水为源水(Ⅰ类源水水质,属贫营养水库,仅有时长藻),经比较采用成熟,常规水处理工艺流程——机械搅拌混合,竖向折板絮凝,平流沉淀,气水反冲V型过滤,出厂水可达到或优于国标《生活饮用水卫生标准》GB5749-2006要求。     

NUMERICAL SIMULATION OF TURBULENT FREE SURFACE FLOW OVER OBSTRUCTION

A two-dimensional hybrid numerical model, FEM-LES-VOF, for free surface flows is proposed in this study, which is a combination of three-step Taylor-Galerkin finite element method, large eddy simulation with the Smagorinsky sub-grid model and Computational Lagrangian-Eulerian Advection Remap Volume of Fluid （CLEAR-VOF） method. The present FEM-LES-VOF model allows the fluid flows involving violent free surface and turbulence subject to complex boundary configuration to be simulated in a straightforward manner with unstructured grids in the context of finite element method. Numerical simulation of a benchmark problem of dam breaking is conducted to verify the present model. Comparisons with experimental data show that the proposed model works well and is capable of producing reliable predictions for free surface flows. Using the FEM-LES-VOF model, the free surface flow over a semi-circular obstruction is investigated. The simulation results are compared with available experimental and numerical results. Good performance of the FEM-LES-VOF model is demonstrated again. Moreover, the numerical studies show that the turbulence plays an important role in the evolution of free surface when the reflected wave propagates upstream during the fluid flow passing the submerged obstacle.     

Fractional Kinetic Model for First Flush of Stormwater Pollutants

By generalizing the urban ground as a fractal surface and revising the classical Fick’s formula as a law of dispersion with a fractional-order derivative, a fractional kinetic model is developed for simulation of the first flush phenomenon of urban stormwater pollutants. The model is comprised of (1) a fractional dispersion-advection equation (FADE); (2) the kinematic-wave overland flow equation; and (3) methods for numerical solution of the equations. A split-operator method is proposed for numerical solution of the FADE by means of a newly presented F.3 finite-difference scheme for fractional partial differential equations. The kinematic-wave overland flow equation is solved using the Lax–Wendroff explicit scheme. Under a constant rainstorm the hydrograph displays an initial rising limb followed by a constant flow discharge. The pollutograph exhibits a steep receding limb (the first flush), followed by a long stretched tail (heavy tail process). The agreement between simulated and measured dispersion characteristics is found to be good, demonstrating that the fractional kinetic model is capable of accurately predicting the characteristics of the first flush phenomenon.     

Solution of population balances with growth and nucleation by high order moment-conserving method of classes

The high order method of classes, developed in our earlier work [Alopaeus, V., Laakkonen, M., Aittamaa J., 2006a. Solution of population balances with breakage and agglomeration by high order moment-conserving method of classes. Chemical Engineering Science 61, 6732-6752] for solution of population balances (PBs), is extended to problems with growth and primary nucleation. The growth problem leads to a hyperbolic partial differential equation with fundamentally different numerical characteristics than the PB with breakage and agglomeration only. However, we show that the principle of moment conservation in the numerical solution can also be applied to this advection-type problem, leading to extremely accurate numerical solutions. The method is tested for two numerical cases. The first one is mass transfer induced particle growth, and the second one is primary nucleation with constant growth (similar to the Riemann advection problem). For mass transfer induced growth, we first analyze functional form of the growth rate from mass transfer correlation viewpoint, and derive a general analytical solution for the power-law growth. The numerical results from the moment conserving method are also compared to one well established high resolution numerical method for advection problems, namely the Lax-Wendroff method with van Leer flux limiter. It was shown that the present method is far superior by predicting the distribution moments with several order of magnitudes lower numerical error. For the Riemann problem with constant growth rate, the present method predicts the shock front location exactly without any numerical diffusion.