Advection-dispersion modelling tools: what about numerical dispersion?

In general the transport of dissolved substances and fine suspended particles is governed by the one-dimensional advection-dispersion equation. In order to model the transport of dissolved substances and fine suspended particles, the advection-dispersion equation is incorporated into commonly used urban drainage modelling tools such as InfoWorks CS (Wallingford Software, United Kingdom) and MOUSE (DHI Software, Denmark). Two examples show the use of InfoWorks CS and MOUSE using standard model settings. Modelling results using tracer experiments show that numerical model parameters need to be altered in order to calibrate the model. Using tracer experiments as a model calibration tool, it is shown that a non-negligible amount of dispersion is generated by InfoWorks CS and MOUSE and that it is in fact the numerical dispersion that is calibrated.

Download Full-text

Uncertainty of model parameters in stream pollution using fuzzy arithmetic

Journal of Hydroinformatics ◽

10.2166/hydro.2008.037 ◽

2008 ◽

Vol 10 (3) ◽

pp. 189-200 ◽

Cited By ~ 1

Author(s):

H. Mpimpas ◽

P. Anagnostopoulos ◽

J. Ganoulis

Keyword(s):

Dispersion Equation ◽

Fuzzy Numbers ◽

Quality Parameters ◽

Quality Parameter ◽

Fuzzy Arithmetic ◽

Model Parameters ◽

Water Stream ◽

Stream Pollution ◽

Advection Dispersion ◽

The One

Fuzzy arithmetic is employed for the analysis of uncertainties in water-stream pollution, when the various model parameters involved are imprecise. The one-dimensional advection–dispersion equation, for both a conservative and a non-conservative substance, was solved analytically for point and Gaussian-hill input loads of pollution, considering the dispersion and decay coefficients involved as fuzzy numbers. The solution of the advection–dispersion equation was also conducted numerically for the same input loads with the finite-difference method, employing a Lagrangian–Eulerian scheme. The good agreement between analytical and numerical results presented in the form of fuzzy numbers confirms the reliability of the numerical scheme. The advection–dispersion equation of a non-conservative substance was then solved numerically for ten different water quality parameters, in order to study the water pollution in a water stream. The dispersion coefficient, the source terms and the input loads were expressed as fuzzy numbers, and the concentration of each quality parameter was obtained in fuzzy-number form. With fuzzy modeling, imprecise data can be represented and imprecise output produced, with minimal input data requirements and without the need of a large number of computations.

Download Full-text

Behavior of sensitivities in the one-dimensional advection-dispersion equation: Implications for parameter estimation and sampling design

Water Resources Research ◽

10.1029/wr023i002p00253 ◽

1987 ◽

Vol 23 (2) ◽

pp. 253-272 ◽

Cited By ~ 96

Author(s):

Debra S. Knopman ◽

Clifford I. Voss

Keyword(s):

Parameter Estimation ◽

Dispersion Equation ◽

Sampling Design ◽

One Dimensional ◽

Advection Dispersion ◽

The One

Download Full-text

A Discrete Method Based on the CE-SE Formulation for the Fractional Advection-Dispersion Equation

Discrete Dynamics in Nature and Society ◽

10.1155/2015/303857 ◽

2015 ◽

Vol 2015 ◽

pp. 1-9

Author(s):

Silvia Jerez ◽

Ivan Dzib

Keyword(s):

Numerical Simulation ◽

Analytical Solution ◽

Fractional Derivative ◽

Dispersion Equation ◽

Numerical Algorithm ◽

Initial Condition ◽

Discrete Method ◽

One Dimensional ◽

Advection Dispersion ◽

The One

We obtain a numerical algorithm by using the space-time conservation element and solution element (CE-SE) method for the fractional advection-dispersion equation. The fractional derivative is defined by the Riemann-Liouville formula. We prove that the CE-SE approximation is conditionally stable under mild requirements. A numerical simulation is performed for the one-dimensional case by considering a benchmark with a discontinuous initial condition in order to compare the results with the analytical solution.

Download Full-text

Initial-boundary value problems for the one-dimensional linear advection–dispersion equation with decay

Zeitschrift für Naturforschung A ◽

10.1515/zna-2020-0106 ◽

2020 ◽

Vol 75 (8) ◽

pp. 713-725 ◽

Cited By ~ 1

Author(s):

Guenbo Hwang

Keyword(s):

Boundary Conditions ◽

Dirichlet Boundary ◽

Boundary Value ◽

Initial Boundary ◽

Initial Boundary Value Problems ◽

One Dimensional ◽

Advection Dispersion ◽

Asymptotically Periodic ◽

The One ◽

Initial Boundary Value

AbstractInitial-boundary value problems for the one-dimensional linear advection–dispersion equation with decay (LAD) are studied by utilizing a unified method, known as the Fokas method. The method takes advantage of the spectral analysis of both parts of Lax pair and the global algebraic relation coupling all initial and boundary values. We present the explicit analytical solution of the LAD equation posed on the half line and a finite interval with general initial and boundary conditions. In addition, for the case of periodic boundary conditions, we show that the solution of the LAD equation is asymptotically t-periodic for large t if the Dirichlet boundary datum is periodic in t. Furthermore, it can be shown that if the Dirichlet boundary value is asymptotically periodic for large t, then so is the unknown Neumann boundary value, which is uniquely characterized in terms of the given asymptotically periodic Dirichlet boundary datum. The analytical predictions for large t are compared with numerical results showing the excellent agreement.

Download Full-text

Stable Stationary Solitons of the One-Dimensional Modified Complex Ginzburg-Landau Equation

Zeitschrift für Naturforschung A ◽

10.1515/zna-2007-7-803 ◽

2007 ◽

Vol 62 (7-8) ◽

pp. 368-372

Author(s):

Woo-Pyo Hong

Keyword(s):

Landau Equation ◽

Model Parameters ◽

Ginzburg Landau ◽

One Dimensional ◽

Paraxial Ray Approximation ◽

New Family ◽

Ginzburg Landau Equation ◽

The Stability ◽

The One ◽

Paraxial Ray

We report on the existence of a new family of stable stationary solitons of the one-dimensional modified complex Ginzburg-Landau equation. By applying the paraxial ray approximation, we obtain the relation between the width and the peak amplitude of the stationary soliton in terms of the model parameters. We verify the analytical results by direct numerical simulations and show the stability of the stationary solitons.

Download Full-text

Comparative application and optimization of different single-borehole dilution test techniques

Hydrogeology Journal ◽

10.1007/s10040-020-02271-2 ◽

2020 ◽

Author(s):

Nikolai Fahrmeier ◽

Nadine Goeppert ◽

Nico Goldscheider

Keyword(s):

Groundwater Monitoring ◽

Saturated Zone ◽

One Dimensional ◽

Monitoring Wells ◽

Advantages And Disadvantages ◽

Advection Dispersion ◽

Fractured Aquifers ◽

Tracer Distribution ◽

Deep Boreholes ◽

The One

AbstractSingle-borehole dilution tests (SBDTs) are a method for characterizing groundwater monitoring wells and boreholes, and are based on the injection of a tracer into the saturated zone and the observation of concentration over depth and time. SBDTs are applicable in all aquifer types, but especially interesting in heterogeneous karst or fractured aquifers. Uniform injections aim at a homogeneous tracer concentration throughout the entire saturated length and provide information about inflow and outflow horizons. Also, in the absence of vertical flow, horizontal filtration velocities can be calculated. The most common method for uniform injections uses a hosepipe to inject the tracer. This report introduces a simplified method that uses a permeable injection bag (PIB) to achieve a close-to-uniform tracer distribution within the saturated zone. To evaluate the new method and to identify advantages and disadvantages, several tests have been carried out, in the laboratory and in multiple groundwater monitoring wells in the field. Reproducibility of the PIB method was assessed through repeated tests, on the basis of the temporal development of salt amount and calculated apparent filtration velocities. Apparent filtration velocities were calculated using linear regression as well as by inverting the one-dimensional (1D) advection-dispersion equation using CXTFIT. The results show that uniform-injection SBDTs with the PIB method produce valuable and reproducible outcomes and contribute to the understanding of groundwater monitoring wells and the respective aquifer. Also, compared to the hosepipe method, the new injection method requires less equipment and less effort, and is especially useful for deep boreholes.

Download Full-text

Effects of different hydraulic models on predicting longitudinal profiles of reactive pollutants in activated sludge reactors

Water Science & Technology ◽

10.2166/wst.2008.676 ◽

2008 ◽

Vol 58 (3) ◽

pp. 555-561 ◽

Cited By ~ 6

Author(s):

P. Zima ◽

J. Makinia ◽

M. Swinarski ◽

K. Czerwionka

Keyword(s):

Activated Sludge ◽

Ammonia Concentration ◽

Minor Role ◽

Nitrification Rate ◽

Concentration Profiles ◽

One Dimensional ◽

Advection Dispersion ◽

In Series ◽

The One ◽

A Minor

This paper presents effects of dispersion on predicting longitudinal ammonia concentration profiles in activated sludge bioreactor located at “Wschod” WWTP in Gdansk. The aim of this study was to use the one-dimensional advection-dispersion Equation (ADE) to simulate the flow conditions (based on the inert tracer concentrations in selected points) and longitudinal profile of reactive pollutant (based on the ammonia concentration profiles in selected points). The simulation results were compared with the predictions obtained using a traditional “tanks-in-series” (TIS) approach, commonly used in designing biological reactors. The use of dispersion coefficient calculated from an empirical formula resulted in substantial differences in the tracer concentration distributions in two sampling points in the bioreactor. Simulations using the one-dimensional ADE and TIS model, with the nitrification rate incorporated as the source term, revealed that the hydraulic model plays a minor role compared to the biochemical transformations in predicting the longitudinal ammonia concentration profiles.

Download Full-text

NUMERICAL STUDIES ON THE VIBRATIONAL SPECTRUM OF FIBONACCI CHAIN: A MULTIFRACTAL ANALYSIS

International Journal of Modern Physics B ◽

10.1142/s0217979291000444 ◽

1991 ◽

Vol 05 (05) ◽

pp. 825-841 ◽

Cited By ~ 1

Author(s):

WLODZIMIERZ SALEJDA

Keyword(s):

Vibrational Spectrum ◽

Multifractal Analysis ◽

Scaling Laws ◽

Model Parameters ◽

Local Scaling ◽

One Dimensional ◽

Dynamic Matrix ◽

Numerical Studies ◽

Wide Range ◽

The One

A harmonic Hamiltonian modelling the lattice dynamics of the one-dimensional Fibonacci-type quasicrystal is studied numerically. The multifractal analysis of vibrational spectrum is performed. It is found that the integrated normalized density of states [Formula: see text], where x denotes the square of the eigenenergy of the dynamic matrix, exhibits a finite range of scaling indices α (i.e. α min ≤α≤ α max ) describing the local scaling laws of [Formula: see text]. The α-f spectra and the Renyi dimensions [Formula: see text] are calculated in a wide range of model parameters taking into account the next-nearest-neighbour (NNN) interactions of atoms. In particular, we have observed that: (1) The α-f spectra are smooth in the interval [Formula: see text]; (2) If the so-called parameter of quasi-periodicity Q increases, then αmin and the fractal dimension of vibrational spectra [Formula: see text] decrease; (3) If the strength of NNN interactions h grows then α min decreases but D increases.

Download Full-text