The aim of this research was to show the impact of the flow conditions and variations in the aeration intensity on changes in the predicted dissolved oxygen (DO) concentrations in a full-scale activated sludge reactor. The Activated Sludge Model No. 1 was used to describe the biochemical processes. The studies were performed at the Rock Creek wastewater treatment plant in Hillsboro, OR (USA). T...

We study a uniform flow in a parallel plate geometry to model contaminant transport through a saturated porous medium in a semi-infinite domain in order to simulate an experimental apparatus mainly constituted by a chamber filled with a glass beads bed. The general solution of the advection dispersion equation in a porous medium was obtained by utilizing the Jacobi θ3 Function. The analytical s...

This paper deals with an inverse problem for identifying multiparameters in 1D space fractional advection dispersion equation FADE on a finite domain with final observations. The parameters to be identified are the fractional order, the diffusion coefficient, and the average velocity in the FADE. The forward problem is solved by a finite difference scheme, and then an optimal perturbation regul...

We implement an exponential integrator for large and sparse systems of ODEs, generated by FE (Finite Element) discretization with mass-lumping of advection-diffusion equations. The relevant exponentiallike matrix function is approximated by polynomial interpolation, at a sequence of real Leja points related to the spectrum of the FE matrix (ReLPM, Real Leja Points Method). Application to 2D and...

An analysis is reported here for three-time level integration methods following the global spectral analysis (GSA) described in High Accuracy Computing Methods , T.K. Sengupta, Cambridge Univ. Press, USA. The focus is on the second order Adams–Bashforth (AB2) and the extrapolation in time (EXT2) methods. Careful distinction is made for the first time step at t = 0 by either Euler forward or fou...

Multispecies contaminant transport in the Earth's subsurface is commonly modelled using advection-dispersion equations coupled via first-order reactions. Analytical and semi-analytical solutions for such problems are highly sought after but currently limited to either one species, homogeneous media, certain reaction networks, specific boundary conditions or a combination thereof. In this paper,...

We consider the dispersion properties of tracer particles moving in nonequilibrium heterogeneous periodic media. The tracer motion is described by a Fokker-Planck equation with arbitrary spatially periodic (but constant in time) local diffusion tensors and drifts, eventually with the presence of obstacles. We derive a Kubo-like formula for the time-dependent effective diffusion tensor valid in ...

We derive a general formulation of the time domain random walk (TDRW) approach to model the hydrodynamic transport of inert solutes in complex geometries and heterogeneous media. We demonstrate its formal equivalence with the discretized advection-dispersion equation and show that the TDRW is equivalent to a continuous time random walk (CTRW) characterized by space-dependent transition times an...

Modeling the contaminant transport process in soils requires the solute transport parameters. Displacement experiments were carried out on soil columns (Sand – Silt – Clay) by injecting a solution of 0.8 M KCl in a steady state. Breakthrough curves are symmetrical, characteristics of an equilibrium solute transport. The hydrodynamic dispersion coefficients were estimated by optimizing the measu...

A one-step conservative level set method, combined with a global mass correction method, is developed in this study to simulate the incompressible two-phase flows. The present framework do not need to solve the conservative level set scheme at two separated steps, and the global mass can be exactly conserved. The present method is then more efficient than two-step conservative level set scheme....