Analysis of floodplain inundation using 2D nonlinear diffusive wave equation solved with splitting technique

Gąsiorowski, Dariusz

doi:10.2478/s11600-012-0087-8

Cited by 14 publications

(14 citation statements)

References 22 publications

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“…It is particularly suitable for parallel implementation. According to this technique, the 2D diffusive wave equation (Equation (1)) at a given time level is split into a set of 1D equations for each of the directions [27]. This leads to two equations describing the wave propagation process in directions x and y, respectively.…”

Section: Decomposition Of the 2d Equation With The Splitting Methodsmentioning

confidence: 99%

“…The resulting system can be solved more efficiently than a system with the matrix obtained using the unsplit algorithm with triangular elements. For the 2D diffusive wave equation, such a splitting strategy has been adopted by Neal et al [25], Yu [26], and Gąsiorowski [27]. Moreover, Hsu et al presented splitting in the form of an alternative direction explicit (ADE) scheme [28].…”

Section: Introductionmentioning

confidence: 99%

“…Consequently, this can make the calculation more efficient. The implicit method, in the form of a two-level difference scheme, was applied for the solution of the diffusive wave equation in the context of a 2D flow [22] as well as a 1D flow [27]. It is interesting that, for the solution of the diffusive wave equation, the implicit methods are seldom applied despite their clear advantage over the explicit schemes.…”

Section: Introductionmentioning

confidence: 99%

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Computationally Efficient Solution of a 2D Diffusive Wave Equation Used for Flood Inundation Problems

Artichowicz¹,

Gąsiorowski²

2019

Water

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This paper presents a study dealing with increasing the computational efficiency in modeling floodplain inundation using a two-dimensional diffusive wave equation. To this end, the domain decomposition technique was used. The resulting one-dimensional diffusion equations were approximated in space with the modified finite element scheme, whereas time integration was carried out using the implicit two-level scheme. The proposed algorithm of the solution minimizes the numerical errors and is unconditionally stable. Consequently, it is possible to perform computations with a significantly greater time step than in the case of the explicit scheme. An additional efficiency improvement was achieved using the symmetry of the tridiagonal matrix of the arising system of nonlinear equations, due to the application of the parallelization strategy. The computational experiments showed that the proposed parallel implementation of the implicit scheme is very effective, at about two orders of magnitude with regard to computational time, in comparison with the explicit one.

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Section: Decomposition Of the 2d Equation With The Splitting Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Computationally Efficient Solution of a 2D Diffusive Wave Equation Used for Flood Inundation Problems

Artichowicz¹,

Gąsiorowski²

2019

Water

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“…In the preliminary stage of research only 1D surface flow model is used. Equations (8) and (9) are being solved with modified Galerkin finite elements method (FEM) [6]. For the integration of ordinary differential equation over time, two level difference scheme is applied.…”

Section: Urban Flood Inundation Modelmentioning

confidence: 99%

“…[1][2][3]. Although both sewage flow and surface flow can be done with well-known tools (numerical schemes) [4][5][6], the model as a whole is really difficult to validate. That uncertainty exists mainly due to flow exchange formulas between sewage and surface [7].…”

Section: Introductionmentioning

confidence: 99%

Interaction between storm water conduit and surface flow for urban flood inundation modelling

Hakiel¹,

Szydłowski²

2017

Int. J. SDP

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Rapid development of urban areas always comes with great side effects. One of them is the occurrence of urban floods. Growth of impervious surfaces in cities leads to increasing run-off values. This together with difficulties connected with sewage modernization in cities marks urban inundations as being one of the most important issues concerning urban water. Accurate prediction of a phenomenon is difficult as it is highly dependent on local conditions and the quality of available data about them. A most recent approach to modelling urban flooding involves a detailed description of the interaction between storm water sewage flow modelling and surface flow modelling. In this paper we will describe a numerical model of urban inundation that is being used to analyse the phenomenon, which consists of 1D storm water flow model (explicit McCormack scheme) and 1D surface flow model (diffusive wave). But before that laboratory tests describing the interaction between used models will be introduced. We will try to evaluate how different surface flow conditions affect interaction and find out if there is an easy way to implement it in coupled numerical modelling of large-scale urban areas inundations. Because tests are still being conducted and further investigation of phenomenon is being done, the conclusions are only preliminary and should be treated as a guideline for future work.

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Analysis of extreme flow uncertainty impact on size of flood hazard zones for the Wronki gauge station in the Warta river

et al. 2019

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In this paper, the impact of maximum flow uncertainty on flood hazard zone is analyzed. Two factors are taken into account: (1) the method for determination of maximum flows and (2) the limited length of the data series available for calculations. The importance of this problem is a consequence of the implementation of the EU Flood Directive in all EU member states. The factors mentioned seem to be among the most important elements responsible for potential uncertainty and inaccuracy of the developed flood hazard maps. Two methods are analyzed, namely the quantiles method and the maximum likelihood method. The maximum flows are estimated for the Wronki gauge station located in the reach of the Warta river. This simple river system is located in the central part of Poland. The length of the available data is 44 years. Hence, the series of the lengths 40, 30 and 20 years are tested and compared with reference calculations for 44 years. The hydrodynamic model HEC-RAS is used to calculate water surface profiles in steady state flow. The Python scripting language is applied for automation of HEC-RAS calculations and processing of final results in the form of inundation maps. The number of trials for each factor is not huge to keep the presented methodology useful in practice. The chosen measure of uncertainty is the range of variability for maximum flow values as well as inundation areas. The estimated values stressed the great importance of the factors analyzed for the uncertainty of the maximum flows as well as inundation areas. The impact of the data series length on the maximum flows is straightforward; a shorter data series gives a wider range of variability. However, the dependencies between other factors are more complex. Hence, the application of methodology based on the simulation and GIS data processing for assessment of this problem seems to be quite a good approach.

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Analysis of floodplain inundation using 2D nonlinear diffusive wave equation solved with splitting technique

Cited by 14 publications

References 22 publications

Computationally Efficient Solution of a 2D Diffusive Wave Equation Used for Flood Inundation Problems

Computationally Efficient Solution of a 2D Diffusive Wave Equation Used for Flood Inundation Problems

Interaction between storm water conduit and surface flow for urban flood inundation modelling

Analysis of extreme flow uncertainty impact on size of flood hazard zones for the Wronki gauge station in the Warta river

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