Papers by Romuald Szymkiewicz
Uncertainty analysis of simplified 1D and 2D shallow water equations via the Karhunen–Loéve expansion and Monte Carlo simulations
Stochastic Environmental Research and Risk Assessment, Dec 11, 2023
Research Square (Research Square), Feb 2, 2023
Groundwater is a vital water resource which has a significant role in the irrigation and food ind... more Groundwater is a vital water resource which has a significant role in the irrigation and food industry. Drawdown is a change in groundwater level due to various causes, especially pumping from wells. Forecasting water level oscillations is an important necessity for planning the integrated management of any watershed basin. In the present study, the Theis equation was applied to stochastic analysis of groundwater flow in confined aquifers, through the Karhunen-Loeve expansion (KLE) method. The quantification of the uncertainty associated with the statistical moments of hydraulic head is the aim of this research. The KLE method takes two steps; first, aquifer transmissivity () as an input random field is decomposed in the form of a set of orthogonal Gaussian random expressions in which eigen 2 structures related to the covariance function of were obtained from the Fredholm equation. Then, the hydraulic head ℎ(,) was expanded with polynomial terms in which some coefficients were computed from the governing equation. The statistical moments (i.e., mean values and variances) of ℎ(,) were calculated and compared with Monte Carlo simulations (MCS) to validate the results.
Hydrological Sciences Journal-journal Des Sciences Hydrologiques, Oct 1, 1996
The Chezy formula for steady flow in a uniform symmetrical channel with constant slope-friction f... more The Chezy formula for steady flow in a uniform symmetrical channel with constant slope-friction factor is mathematically examined. The problem of the determination of the channel shape above a reference level for a given rating curve of flow area vs discharge with a constant ratio (m) of slope to mean velocity above a reference level is posed and then solved. It is shown that there is a double solution of the problem. One solution (being of main interest) is unlimited and gives a shape widening with depth, while the other has an upper bound and yields a shape narrowing with depth. It is shown that a solution to the problem exists for a negative value of m. A relationship is examined between the width-to-depth ratio of a rectangular initial shape and a shape above a reference level for m values close to zero. In particular, the solutions for negative values of m, i.e. for discharge decreasing with increasing flow area, are evidently against common sense. Analyse des paradoxes résultant de la formule de Chezy avec rugosité constante: II. Courbe surface-débit Résumé La formule de Chézy pour l'écoulement permanent dans un canal symétrique dont le facteur pente-frottement est constant a été analysé mathématiquement. Le problème de la détermination de la forme de la section transversale du canal au dessus d'un niveau initial, le rapport (m) de la pente à de la vitesse moyenne étant constant, a été posé et résolu. On a montré qu'il existe deux solutions à ce problème. L'une des solutions (celle qui nous intéresse le plus), n'est pas bornée, fournit une section croissante avec la hauteur, tandis que la seconde est bornée supérieurement et fournit une section qui decroit avec la hauteur. Il a été démontré qu'il existe une solution au problème pour des valeurs négatives de m. On a examiné la relation entre les rapports largeur/hauteur pour une section initiale rectangulaire et une section au dessus d'un niveau initial pour des valeurs de m proches de zéro. Les solutions pour les valeurs négatives de m, l'écoulement décroissant alors que la surface croit, contredisent le sens commun.
Solution of the advection-diffusion equation using the spline function and finite elements
Communications in Numerical Methods in Engineering, Mar 1, 1993
This paper deals with the solution of the one‐dimensional advection–diffusion equation. The metho... more This paper deals with the solution of the one‐dimensional advection–diffusion equation. The method of solution is based on the process‐splitting technique. The transport equation is split up into the advection part and the diffusion part at every time step. The advection transport equation is solved by a method of characteristics using a spline function for interpolation. This solution approach proves to be very effective because it reduces numerical dispersion and wiggles. The diffusion equation is solved by the standard Galerkin finite‐element method. A comparison of calculations with the results of Holly and Preissmann and with analytical solutions demonstrates the great accuracy of the proposed method.
Research Square (Research Square), Apr 7, 2022
The paper considers the problem of inverse flood routing in reservoir operation strategy. The aim... more The paper considers the problem of inverse flood routing in reservoir operation strategy. The aim of the work is to investigate the possibility of determining the hydrograph at the upstream end based on the hydrograph required at the downstream end using simplified open channel flow models. To accomplish this, the linear kinematic wave equation, the diffusive wave equation and the linear Muskingum equation are considered. To achieve the hydrograph at the upstream end, an inverse solution of the aforementioned equations with backward integration in the x direction is carried out. For the numerical solution of the kinematic wave equation, the finite difference box scheme is used, whereas for the Muskingum equation, the -scheme is applied. It is shown that both these equations are able to provide satisfying results because of their exceptional properties related to numerical diffusion. In the paper, an alternative approach to solving inverse routing using the diffusive wave model and the Muskingum model is also presented. To this end, both models are described by a convolution which involves the instantaneous unit hydrograph (IUH) corresponding to the linear diffusive wave equation. Consequently, instead of a solution of partial or ordinary differential equations, the integral equation with Laguerre polynomials, used for the expansion of the upstream hydrograph, is solved.
Utwór nie moĪe byü powielany i rozpowszechniany, w jakiejkolwiek formie i w jakikolwiek sposób, b... more Utwór nie moĪe byü powielany i rozpowszechniany, w jakiejkolwiek formie i w jakikolwiek sposób, bez pisemnej zgody wydawcy
Journal of Civil Engineering, Environment and Architecture, 2017
W pracy omówiono historię i aktualny stan zagospodarowania dolnej Wisły oraz najistotniejsze argu... more W pracy omówiono historię i aktualny stan zagospodarowania dolnej Wisły oraz najistotniejsze argumenty na rzecz gospodarczego wykorzystania jej potencjału. Wskazano, że najlepszym sposobem kompleksowego i integralnego rozwiązania problemów związanych z zagrożeniem niesionym przez dolną Wisłę i wykorzystaniem istniejących możliwości jest powrót do idei budowy kaskady stopni wodnych. Takie podejście umożliwi kompleksowe rozwiązanie problemów zagrożenia powodzią, produkcji energii, transportu wodnego, zaopatrzenia w wodę, retencji wód opadowych oraz sportu i rekreacji. Dla porównania przedstawiono stan rozwoju infrastruktury hydrotechnicznej w Europie i na świecie. Słowa kluczowe: potencjał dolnej Wisły, drogi wodne, energetyka wodna, ochrona przed powodzią, kaskada stopni wodnych Problem gospodarczego wykorzystania dolnej Wisły 151 PROBLEMS OF EXPLOITATION OF THE LOWER VISTULA RIVER S u m m a r y In the paper the history and current situation dealing with the possibilities of making use of the lower Vistula River potential are presented and discussed. Taking into account the hydrological characteristics and the remarkable various possibilities represented by the Vistula River, it is shown that building of a cascade of reservoirs could be probably the best solution. This investment will make possible to solve simultaneously such problems as production of hydro-energy, water transport, flood protection, supplying of water for agriculture and industry, development of sports and recreation, increasing of stored water capacity etc. Application of the modern solutions and technologies should limit negative impact of the hydraulic structures on the natural environment of the Vistula valley. For comparison similar projects carried out in many other countries in the past and currently realized are also presented.
Water Resources Management
The paper considers the problem of inverse flood routing in reservoir operation strategy. The aim... more The paper considers the problem of inverse flood routing in reservoir operation strategy. The aim of the work is to investigate the possibility of determining the hydrograph at the upstream end based on the hydrograph required at the downstream end using simplified open channel flow models. To accomplish this, the linear kinematic wave equation, the diffusive wave equation and the linear Muskingum equation are considered. To achieve the hydrograph at the upstream end, an inverse solution of the afore mentioned equations with backward integration in the x direction is carried out. The numerical solution of the kinematic wave equation and the Muskingum equation bases on the finite difference scheme. It is shown that both these equations are able to provide satisfying results because of their exceptional properties related to numerical diffusion. In the paper, an alternative approach to solve the inverse routing using the diffusive wave model is also presented. To this end, it is descr...
Application of the Simplified Models to Inverse Flood Routing in Upper Narew River (Poland)
In the paper a problem of inverse flood routing is considered. The study deals with Upper Narew R... more In the paper a problem of inverse flood routing is considered. The study deals with Upper Narew River (Poland). To solve the inverse problem two approaches are applied, based on the kinematic wave equation and the storage equation, respectively. In the first approach, the hydrograph at the upstream end is determined via the inverse solution of the governing equation with backward integration in the x direction. In the second approach, the standard initial value problem for the storage equation, completed by the steady flow equation, is solved with a negative time step, i.e., with an integration towards the diminishing time. It is shown that the proposed methods are equivalent.
The paper is concerned with solving the transport pollutant problem for a steady, gradually varie... more 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 solut...
Hydrodynamiczny model dolnej Wisły z uwzględnieniem koncepcji kaskady stopni piętrzących
Praca zostala wykonana w ramach uslug doradztwa świadczonych przez Politechnike Gdanską na rzecz ... more Praca zostala wykonana w ramach uslug doradztwa świadczonych przez Politechnike Gdanską na rzecz ENERGA SA. Jej celem bylo określenie, na podstawie obliczen i symulacji numerycznych, hydraulicznych skutkow potencjalnej budowy kaskady stopni pietrzących na dolnej Wiśle, to jest na odcinku rzeki od ujścia Narwi do morza. Przedmiotem zlecenia bylo wykonanie numerycznego modelu hydraulicznego Doliny Dolnej Wisly z uwzglednieniem koncepcji kaskady stopni pietrzących; wykonanie obliczen dla przeplywow charakterystycznych - SSQ, SNQ; wykonanie obliczen dla wybranych fal wezbraniowych oraz ocena dostepnego potencjalu energetycznego Kaskady Dolnej Wisly (KDW).
Matematyczne modelowanie fal powodziowych w korytach rzecznych
Dynamika wód podziemnych w rejonach nadmorskich - wybrane przykłady analizy numerycznej
Boundary problem for equations of steady gradually varied flow in open channels
Archives of Hydro-engineering and Environmental Mechanics, 2001
Uproszczone liniowe modele transformacji fali w korycie rzecznym
Journal of Hydroinformatics
The paper concerns the numerical solution of one-dimensional (1D) and two-dimensional (2D) advect... more The paper concerns the numerical solution of one-dimensional (1D) and two-dimensional (2D) advection–diffusion equations. For the numerical solution of the 1D advection–diffusion equation, a method, originally proposed for the solution of the 1D pure advection equation, has been developed. A modified equation analysis carried out for the proposed method allowed increasing of the resulting solution accuracy and, consequently, to reduce the numerical dissipation and dispersion. This is achieved by proper choice of the involved weighting parameter being a function of the Courant number and the diffusive number. The method is adaptive because for uniform grid point and for uniform flow velocity, the weighting parameter takes a constant value, whereas for non-uniform grid and for varying flow velocity, its value varies in the region of solution. For the solution of the 2D transport equation, the dimensional decomposition in the form of Strang splitting technique is used. Consequently, th...
Water Resources Management
Two nonlinear versions of the Muskingum equation are considered. The difference between both equa... more Two nonlinear versions of the Muskingum equation are considered. The difference between both equations relates to the exponent parameter. In the first version, commonly used in hydrology, this parameter is considered as free, while in the second version, it takes a value resulting from the kinematic wave theory. Consequently, the first version of the equation is dimensionally inconsistent, whereas the proposed second one is consistent. It is shown that the difference between the results provided by both versions of the nonlinear Muskingum equation depends on the longitudinal bed slope of a channel. For an increasing slope, when a propagating wave becomes more kinematic, the value of the exponent considered as the free parameter tends to its value resulting from the kinematic wave theory. Consequently, when the character of an open channel flow tends to a kinematic one, the dimensionally inconsistent version of the nonlinear Muskingum equation becomes a consistent one. The results of the numerical analysis suggest that apart from the parameters involved in the Muskingum equation, usually considered as free, the parameters of the numerical method of the solution (the number of reservoirs and the time step) should be considered also as free parameters. This conclusion results from the fundamental property of the Muskingum equation, relating to the numerical roots of the wave attenuation process. All numerical examples and tests relate to the solutions of the system of Saint Venant equations, considered as the benchmark.
E3S Web of Conferences
The Vistula is the largest river in Poland. Lower Vistula (part of the river discussed in this pa... more The Vistula is the largest river in Poland. Lower Vistula (part of the river discussed in this paper) is almost four hundred kilometers long river section extending from the tributary Narew to the outflow to the Baltic Sea. In the 17th century the Vistula was the most navigable river in Europe. After partitioning of Poland the Vistula lost its significance. Now the Lower Vistula should provide a navigation connection to the Europe forming water routes E70 and E40. However it does not meet the criteria required for the international waterways. Moreover, the river has a quite large hydro-energy potential. There have been many plans for the development of the Lower Vistula River so far. Unfortunately none of them has been implemented. In this paper, the authors would like to present their own arguments to reactivate the Lower Vistula Cascade (LVC) project. In order to analyse the LVC idea and Lower Vistula hydraulic potential, a numerical hydraulic model of the Lower Vistula was develo...
Dimensionally Consistent Nonlinear Muskingum Equation
Journal of Hydrologic Engineering
Oscillation-Free Solution of Shallow Water Equations for Nonstaggered Grid
Journal of Hydraulic Engineering, Oct 1, 1993
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Papers by Romuald Szymkiewicz