Vol. 11, No 4, 2007 < Volumes
(ISSN 1428-6394)

Contents:

  • Romuald Szymkiewicz From the Editor   abstract | full text
  • Michał Szydłowski and Artur Magnuszewski Free Surface Flow Modeling in Numerical Estimation of Flood Risk Zones: a Case Study   abstract | full text
  • Piotr Zima Two-dimensional Vertical Analysis of Dam-break Flow   abstract | full text
  • Dariusz Gąsiorowski Balance Errors in Numerical Solutions of Shallow Water Equations   abstract | full text
  • Katarzyna Weinerowska-Bords Determination of Selected Parameters in a 1D Open Channel Flow Model   abstract | full text
  • Romuald Szymkiewicz The Pollutant Transport Equation for a Steady, Gradually Varied Flow in an Open Channel Network: A Solution of High Accuracy   abstract | full text
  • Katarzyna Weinerowska-Bords Accuracy and Parameter Estimation of Elastic and Viscoelastic Models of the Water Hammer   abstract | full text
  • Adam Szymkiewicz and Kazimierz Burzyński Simulation of Water Flow in Double-porosity Soils on Unstructured Grids with the Finite-volume Method   abstract | full text
  • Wojciech Szpakowski Numerical Simulation of the Quaternary Aquifer Groundwater Flow of the Northern Vistula Delta Plain   abstract | full text
  • Jerzy Sawicki and Sławomira Bering Dynamic Characteristics of Coarse-Grained Trickling Filters   abstract | full text
  • Piotr Zima The CFD Modeling in Bioreactor Tracer Studies   abstract | full text
  • Wojciech Szpakowski and Jakub Szulwic A Digital Cartographic Source for Numerical Models in Hydrology   abstract | full text

Abstracts:

hRomuald Szymkiewicz From the Editor

 

hMichał Szydłowski and Artur Magnuszewski Free Surface Flow Modeling in Numerical Estimation of Flood Risk Zones: a Case Study

A case study of potential inundation of Saska Kępa in Warsaw is presented. The flood is a result of a hypothetical breach of a segment of the Vistula river embankment. The inundation's evolution is simulated numerically using a model of shallow water hydrodynamics. The finite volume method is used to solve the mathematical model of the flow. Digital models of the floodplain's relief and land cover, as well as a visualization of the simulation results, are prepared using the Geographical Information System. The computations may be useful in estimations of Warsaw's flood risk zones.

 

hPiotr Zima Two-dimensional Vertical Analysis of Dam-break Flow

The paper concerns mathematical modeling of free surface open-channel water flow. Twodimensional vertical Reynolds-averaged Navier-Stokes equations were used to simulate the flow. They were solved with the SIMPLE algorithm of the finite difference method using the Marker and Cell technique to trace free surface movement. The dam-break flow (water column collapse) problem on a horizontal and frictionless bottom was investigated as a test case. The mechanics of dam-break flow for wet and dry bed conditions was analyzed on the basis of numerical simulations. The obtained results are shown for varying head of water in the downstream channel. The possibility of using the shallow-water equations and the RANS model to simulate rapidly varied flows is discussed.

 

hDariusz Gąsiorowski Balance Errors in Numerical Solutions of Shallow Water Equations

An analysis of the conservative properties of shallow water equations is presented, focused on the consistency of their numerical solution with the conservation laws of mass and momentum. Two different conservative forms are considered, solved by an implicit box scheme. Theoretical analysis supported with numerical experiments is carried out for a rectangular channel and arbitrarily assumed flow conditions. The improper conservative form of the dynamic equation is shown not to guarantee a correct solution with respect to the conservation of momentum. Consequently, momentum balance errors occur in the numerical solution. These errors occur when artificial diffusion is simultaneously generated by a numerical algorithm.

 

hKatarzyna Weinerowska-Bords Determination of Selected Parameters in a 1D Open Channel Flow Model

Determination of the model's parameters is an important stage of mathematical models' application. In the case of a free-surface 1D unsteady flow model defined by the de Saint-Venant equations, one of the groups of parameters to be estimated is the set of parameters describing energy losses due to friction. The parameters can be estimated in different ways, but in most cases the task of their determination is an ill-posed problem. In such cases, optimization methods are the most common approach. In spite of numerous examples of such applications, these techniques are still not fully recognized, as there are several problems of different nature that require thorough analysis. Automatic optimization methods are discussed in the paper. The most important questions of choosing the objective function and the optimization algorithm are considered. Problems connected with data reliability and accessibility and their influence on the solution are discussed. The most common pitfalls of optimization applications are discussed. The analysis is supported with numerical examples.

 

hRomuald Szymkiewicz The Pollutant Transport Equation for a Steady, Gradually Varied Flow in an Open Channel Network: A Solution of High Accuracy

The paper is concerned with solving the transport pollutant problem for a steady, gradually varied flow in an open channel network. The 1D advective-diffusive transport equation is solved using the splitting technique. An analytical solution of the linear advective-diffusive equation in the form of an impulse response function is used to solve the advection-diffusion part of the governing equation. This approach, previously applied in solutions of the advection-diffusion equation for a single channel, is extended to a channel network. Numerical calculations are only required to compute the integral of convolution. The finite difference method is used to solve the second part of the governing equation, containing the source term. The applied approach has considerable advantages, especially appreciable in the case of advection-dominated transport with large gradients of concentration, since it generates no numerical dissipation or dispersion. The flow parameters are obtained via solution of the steady, gradually varied flow equation. In the final non-linear system of algebraic equations obtained through approximation of the ordinary differential equation, the depths at each cross-section of channels and the discharge at each branch of the network are considered as unknowns. The system is solved using the modified Picard iteration, which ensures convergence of the iterative process for a steady, gradually varied flow solved for both looped and tree-type open channel networks.

 

hKatarzyna Weinerowska-Bords Accuracy and Parameter Estimation of Elastic and Viscoelastic Models of the Water Hammer

The water hammer problem is considered, one of the most important questions of unsteady flows in pipelines. Although first mentioned in the scientific literature more than a hundred years ago and widely analyzed since in many research centers, the problem is not fully recognized yet. It may be considered on two levels: practical and theoretical. In both cases, several difficulties arise rendering the results less than fully satisfactory. The most important difficulties are the proper mathematical description of the phenomenon, the choice of the solution method, estimation of the model parameters and numerical aspects of solving the equations governing the phenomenon's run. They are presented in the paper and typical approaches to their solution are discussed. Numerical solutions are compared with experimental results.

 

hAdam Szymkiewicz and Kazimierz Burzyński Simulation of Water Flow in Double-porosity Soils on Unstructured Grids with the Finite-volume Method

Double-porosity soils consist of two interacting porous systems corresponding to weakly conductive aggregates and highly conductive inter-aggregate regions. The flow of water in such media can be described with a two-scale model obtained by homogenization. The model consists of a single macroscopic equation for the flow in the highly conductive porous system coupled with a number of micro-scale equations for the flow in the weakly conductive aggregates. In this paper we present a numerical algorithm to solve the resulting system of equations for the case of macroscopically two-dimensional flow. It is based on the finite volume approach for unstructured grid of triangular cells. Special attention is paid to the coupling of the micro- and macro-scale equations. An exemplary calculation is presented, concerning infiltration and redistribution of water in a hill-slope of doubleporosity structure with cubic aggregates.

 

hWojciech Szpakowski Numerical Simulation of the Quaternary Aquifer Groundwater Flow of the Northern Vistula Delta Plain

Results of Quaternary aquifer flow calculations are presented for the Vistula Delta Plain and the southern Kashubian Lakeland edge zone. The Quaternary level is one of the most important water supply resources for the city of Gdansk. The numerical simulations of groundwater flow were performed using the Modflow and Modpath codes and the Groundwater Modeling System (GMS 3.1) package. Calculations representing the state prior to the launch of the Lipce intake were performed under steady state conditions. The model was calibrated, which enabled simulation of groundwater flow under transient conditions. Calculation for the years 1969–1985 have shown the evolution of a Quaternary aquifer depression cone. The inflow from river Dead Vistula to the Quaternary aquifer is recognized through particle path solution for a selected water particle. The numerical solution has confirmed the observed increase of Cl− ions in the Grodza Kamienna intake after 1969.

 

hJerzy Sawicki and Sławomira Bering Dynamic Characteristics of Coarse-Grained Trickling Filters

A structural method of dimensioning trickling filters is proposed. Reactors applied in sanitary engineering are usually designed on the basis of formally simple technical instructions, but laboratory experiments have shown that the flow through a trickling filter can be described with the plug-flow model. With an additional function describing reaction intensity, the object's parameters can be calculated and its operation simulated for various technical conditions. If variability of the reaction rate is taken into account, numerical integration of the governing equations will be necessary.

 

hPiotr Zima The CFD Modeling in Bioreactor Tracer Studies

This paper presents the effects of dispersion on predicting longitudinal tracer concentration profiles in an activated sludge bioreactor located at the Wschód Waste-Water Treatment Plant in Gdansk. The aim of this study has been to use the one-dimensional advection-dispersion equation to simulate a non-active substance flow (based on the measured tracer concentration). The simulation results were compared with those obtained in the traditional tanks-in-series approach, commonly used in designing biological reactors. The dispersion coefficient was calculated from a statistical formula based on differences in the tracer concentration distributions at two sampling points. The study has shown that the numerical simulation using the one-dimensional tracer migration equation yields better results than the tanks-in-series model in predicting longitudinal tracer concentration profiles. This paper is an introduction to the study of reactive substances in activated sludge bioreactors.

 

hWojciech Szpakowski and Jakub Szulwic A Digital Cartographic Source for Numerical Models in Hydrology

A short review of digital data used in hydrological models is presented. There are three basic kinds of digital maps used in hydrology: raster images (scan, orthophotomap), vector maps and digital models (Digital Terrain, Landscape and Elevation Models). Hydrological models are used to analyze natural phenomena: free surface flow, the precipitation-outflow relation and groundwater flow. The choice of cartographic source depends on the problem to be solved. The article includes an analysis of two problems: (i) the solution of flood area due to extreme river flow and (ii) groundwater flow. In both cases, digital cartographic sources are presented.

 

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