TASK Quarterly   Scientific Bulletin of the Centre of Informatics - Tricity Academic Supercomputer & networK   ISSN 1428-6394

## Volume 15, Number 3-4, 2011 Application of Computer Methods in Free-Surface and Pressurized Flow Modeling

Issue Editor: prof. dr hab. inz. Romuald Szymkiewicz Faculty of Civil and Environmental Engineering, Gdansk University of Technology romuald.szymkiewicz@wilis.pg.gda.pl

### Abstracts:

• D.Gasiorowski, Solution of the Dike-break Problem Using Finite Volume Method and Splitting Technique

In this paper, an approach using the finite volume method (FVM) for the solution of two-dimensional shallow water equations is described. Such equations are frequently used to simulate dam-break and dike-break induced flows. The applied numerical algorithm of the FVM is based on a wave-propagation algorithm, which ensures a stable solution and, simultaneously, minimizes numerical errors. Dimensional decomposition according to the coordinate directions was used to split two-dimensional shallow water equations into one-dimensional equations. Additionally, splitting was also applied with respect to the physical processes. The applied dimensional and physical splitting, together with the wave-propagation algorithm led to an effective algorithm and ensured proper incorporation of source terms into the scheme of the finite volume method. A detailed description of an approximation for numerical fluxes and source terms is presented. The obtained numerical results are compared with analytical solutions, laboratory experiments and other results available in the literature.

• M.Szydlowski, Numerical Simulation of Open Channel Flow between Bridge Piers

Free-surface flow in the vicinity of bridge piers on a fixed channel bed is a classical problem of open-channel hydraulics. This problem is usually analyzed using one-dimensional hydraulic models for steady-flow problems. The aim of this paper is to present a two-dimensional numerical simulation of water flow around obstacles, such as cylinders, which can act as a simplified model of real piers. The depth-averaged Navier-Stokes equations describing unsteady free-surface flow are solved using an explicit scheme of the finite-volume method. The numerical solution prepared for the simulations of unsteady free-surface flows was used here to analyze the case of steady flow. A numerical simulation of flow in the channel with the obstruction was performed for two different inflow discharges determining, respectively, the subcritical and supercritical flow in the cross-section of a channel constriction. In the second simulation, a hydraulic jump was observed downstream of the bridge section. The numerical results were compared with measurements. Water surface profiles were measured for both discharges in the hydraulic laboratory of the Faculty of Civil and Environmental Engineering at Gdansk University of Technology (GUT). Comparisons with laboratory data showed that the proposed approach constitutes a sufficiently accurate and reliable technique for predicting basic flow parameters. The method of two-dimensional modeling of flow in a river channel between bridge piers can be also integrated with the simulation of unsteady flood wave propagation, ensuring a uniform approach to the problem of flood modeling in river valleys. Moreover, a two-dimensional simulation yields detailed information about flow structure near the obstruction, which can be used to better elucidate debris transport and river bed deformation processes.

• T.Kolerski, Numerical Modeling of Ice Jam Formation in the Wloclawek Reservoir

Ice jam formation in a run-of-the-river reservoir and the effects of ice jam on water levels and water velocity were simulated using a two-dimensional model for simulating river ice dynamics (DynaRICE). The record ice jam of January 1982 in the Wloclawek Reservoir is also examined here. The simulation showed that the ice jam in question was formed by surface ice produced in the Vistula River, upstream of the reservoir. The effect of thermal production of suspended frazil in the reservoir on ice jam was negligible. The simulated water level as well as the ice jam profile were in agreement with the observed data. The ice discharge upstream of the reservoir and the volume of ice in the Wloclawek Reservoir were calculated. The results showed that there was less ice in the reservoir than claimed in previous literature. Suspended frazil and the undercover transport mechanism were not taken into account in this study.

• P.Zima, Simulation of Residence Time Distribution and Mixing in Reactors with Recirculation using 2D Approach

In this paper, we propose a 2D approach in order to create a mathematical model for the determination of the residence time distribution for a flow reactor with recirculation. Apart from characterizing the functional residence time distribution, this model can help improve the operation of the reactor at the design stage. The mathematical model was validated by comparison with experiments carried out in a hydraulic laboratory.

• W.Artichowicz, Numerical Analysis of Open Channel Steady Gradually Varied Flow using the Simplified Saint-Venant Equations

For one-dimensional open-channel flow modeling, the energy equation is usually used. There exist numerous approaches using the energy equation for open-channel flow computations, which resulted in the development of several very efficient methods for solving this problem applied to channel networks. However, the dynamic equation can be used for this purpose as well. This paper introduces a method for solving a system of non-linear equations by the discretization of the one-dimensional dynamic equation for open-channel networks. The results of the computations using the dynamic and energy equations were compared for an arbitrarily chosen problem. Also, the reasons for the differences between the solution of the dynamic and energy equation were investigated.

• W.Gorczewska-Langner, Application of Monte-Carlo Method to Modelling Influence of Selected Soil Heterogeneity on Macrodispersion of Pollutants in Unsaturated Soil Medium

The influence of soil heterogeneity on miscible solute transport in soil is analyzed. The transport process is simulated numerically using the Monte-Carlo method. This paper shows how different types of soil heterogeneity influence the process of contaminant spreading. If independent flow paths exist in the soil, the degree of the mixing of pollutants in the outflow from the soil profile is larger. If the preferential flow paths are shorter, the degree of mixing, related to the heterogeneity of the velocity field, is smaller. These effects can be captured using the Monte-Carlo method.

• K.Burzynski, A.Szymkiewicz, Unstructured Finite-volume Meshes for Two-dimensional Flow in Variably Saturated Porous Media

This paper presents a numerical algorithm for solving the equation describing variably saturated flow in porous media. The algorithm is based on a control volume finite element approach and can be applied to two-dimensional unstructured meshes consisting of triangular elements. Two methods of defining the dual control volume grid are discussed. We also demonstrate that the method of calculating the average permeability at the control volume face significantly influences numerical results.

• K.Weinerowska-Bords, Space-time Conservation Method Appplied to Numerical Solution of Water Hammer Equations

This paper is devoted to the space-time conservation (STC) method and its application to a water hammer in steel pipelines. The STC method, due to its numerical properties, in particular its high accuracy, can be an interesting alternative to traditional numerical methods, especially when dealing with problems where the numerical errors have the potential to significantly influence the solution, making interpretation very difficult. As the problem of water hammer is one of such problems, an analysis of the application of the STC method to this case can be very interesting.