Calibration of a 1D/1D urban flood model using 1D/2D model results in the absence of field data

2011 ◽  
Vol 64 (5) ◽  
pp. 1016-1024 ◽  
Author(s):  
J. Leandro ◽  
S. Djordjević ◽  
A. S. Chen ◽  
D. A. Savić ◽  
M. Stanić
Keyword(s):  
Field Data ◽  
Computational Time ◽  
Necessary Condition ◽  
Two Dimensional ◽  
Time Step ◽  
Urban Flood ◽  
One Dimensional ◽  
1D Model ◽  
Surface Network ◽  
2D Model

Recently increased flood events have been prompting researchers to improve existing coupled flood-models such as one-dimensional (1D)/1D and 1D/two-dimensional (2D) models. While 1D/1D models simulate sewer and surface networks using a one-dimensional approach, 1D/2D models represent the surface network by a two-dimensional surface grid. However their application raises two issues to urban flood modellers: (1) stormwater systems planning/emergency or risk analysis demands for fast models, and the 1D/2D computational time is prohibitive, (2) and the recognized lack of field data (e.g. Hunter et al. (2008)) causes difficulties for the calibration/validation of 1D/1D models. In this paper we propose to overcome these issues by calibrating a 1D/1D model with the results of a 1D/2D model. The flood-inundation results show that: (1) 1D/2D results can be used to calibrate faster 1D/1D models, (2) the 1D/1D model is able to map the 1D/2D flood maximum extent well, and the flooding limits satisfactorily in each time-step, (3) the 1D/1D model major differences are the instantaneous flow propagation and overestimation of the flood-depths within surface-ponds, (4) the agreement in the volume surcharged by both models is a necessary condition for the 1D surface-network validation and (5) the agreement of the manholes discharge shapes measures the fitness of the calibrated 1D surface-network.

scholarly journals CONSTRUCTION OF MODELS FOR BOUNDED PRICE PROCESSES: THE CASE OF THE HKD EXCHANGE RATE

2015 ◽  
Vol 10 (02) ◽  
pp. 1550011
Author(s):  
HONG BEN YEE ◽  
NIKOLAI DOKUCHAEV
Keyword(s):  
Time Series ◽  
Exchange Rate ◽  
Financial Time Series ◽  
Two Dimensional ◽  
One Dimensional ◽  
Financial Time ◽  
Ergodic Properties ◽  
1D Model ◽  
Weak Side ◽  
2D Model

This paper discusses construction of evolution models for financial time series evolving within a given interval. We calibrated a model for the case of the USD/HKD exchange rate after the separation of strong and weak side convertibility undertakings, in which the rate is confined to a specified corridor. This process represents an interesting example of a tradable bounded process. A one-dimensional (1D) model was able to replicate the bounded distribution of the process, but a two-dimensional (2D) model better captured dynamics as measured by the volatility without losing features of the 1D model. We briefly consider the ergodic properties of these models.

scholarly journals Real-time Prediction of Urban Inundation based on SWMM 1D-1D Model

2020 ◽  
Vol 20 (1) ◽  
pp. 401-411
Author(s):  
Jong Kyung Jang ◽  
Min Ki Park ◽  
Na Eun Lee ◽  
Jae Min Lee ◽  
Dong Min Yang
Keyword(s):  
Real Time ◽  
Model Simulation ◽  
Flood Damage ◽  
Two Dimensional ◽  
Flood Prediction ◽  
Urban Flood ◽  
1D Model ◽  
Simulation Results ◽  
Real Time Simulations ◽  
2D Model

The concept of a Major/Minor system was applied to use urban flood prediction techniques, based on rainfall forecasts and real-time simulations, to reduce flood damage, by notifying a possible flood risk in advance. The SWMM one dimensional (1D)-two dimensional (2D) model has become the standard approach used in urban flood modeling, as it can realistically express the interaction between drainage networks and road surfaces. However, it is limited to the flood analysis of small areas due to its two-dimensional model characteristics, such as its long simulation time. Therefore, the SWMM 1D-1D model, which is fast enough to be applied to real-time simulations, is applied to real-time flood forecasting. To improve the accuracy of the model, SWMM 1D-1D model was calibrated using the SWMM 1D-2D model simulation results, and the SWMM 1D-1D model simulation results were extracted using the SWMM5 DLL and EXCEL VBA to analyze the flood situation. Finally, the applicability of the SWMM 1D-1D model was reviewed based on a rainfall event that occurred on 25 August 2014, assuming an hour of predicted rainfall.

scholarly journals Comparison of numerical schemes of river flood routing with an inertial approximation of the Saint Venant equations

RBRH ◽  
2018 ◽  
Vol 23 (0) ◽  
Author(s):  
Alice César Fassoni-Andrade ◽  
Fernando Mainardi Fan ◽  
Walter Collischonn ◽  
Artur César Fassoni ◽  
Rodrigo Cauduro Dias de Paiva
Keyword(s):  
Numerical Stability ◽  
Flood Routing ◽  
Computational Time ◽  
Numerical Schemes ◽  
Time Step ◽  
Simple Formulation ◽  
One Dimensional ◽  
Saint Venant Equations ◽  
Original Scheme ◽  
The One

ABSTRACT The one-dimensional flow routing inertial model, formulated as an explicit solution, has advantages over other explicit models used in hydrological models that simplify the Saint-Venant equations. The main advantage is a simple formulation with good results. However, the inertial model is restricted to a small time step to avoid numerical instability. This paper proposes six numerical schemes that modify the one-dimensional inertial model in order to increase the numerical stability of the solution. The proposed numerical schemes were compared to the original scheme in four situations of river’s slope (normal, low, high and very high) and in two situations where the river is subject to downstream effects (dam backwater and tides). The results are discussed in terms of stability, peak flow, processing time, volume conservation error and RMSE (Root Mean Square Error). In general, the schemes showed improvement relative to each type of application. In particular, the numerical scheme here called Prog Q(k+1)xQ(k+1) stood out presenting advantages with greater numerical stability in relation to the original scheme. However, this scheme was not successful in the tide simulation situation. In addition, it was observed that the inclusion of the hydraulic radius calculation without simplification in the numerical schemes improved the results without increasing the computational time.

Enhanced Explicit Scheme to Solve Transient Heat Conduction Problem

2007 ◽  
Vol 2 (1) ◽  
Author(s):  
Ganesh Hegde ◽  
Madhu Gattumane
Keyword(s):  
Heat Conduction ◽  
Correction Factor ◽  
Truncation Error ◽  
Transient Heat Conduction ◽  
Explicit Scheme ◽  
Stability And Convergence ◽  
Two Dimensional ◽  
Time Step ◽  
One Dimensional ◽  
Partial Derivatives

Improvement in accuracy without sacrificing stability and convergence of the solution to unsteady diffusion heat transfer problems by computational method of enhanced explicit scheme (EES), has been achieved and demonstrated, through transient one dimensional and two dimensional heat conduction. The truncation error induced in the explicit scheme using finite difference technique is eliminated by optimization of partial derivatives in the Taylor series expansion, by application of interface theory developed by the authors. This theory, in its simple terms gives the optimum values to the decision vectors in a redundant linear equation. The time derivatives and the spatial partial derivatives in the transient heat conduction, take the values depending on the time step chosen and grid size assumed. The time correction factor and the space correction factor defined by step sizes govern the accuracy, stability and convergence of EES. The comparison of the results of EES with analytical results, show decreased error as compared to the result of explicit scheme. The paper has an objective of reducing error in the explicit scheme by elimination of truncation error introduced by neglecting the higher order terms in the expansion of the governing function. As the pilot examples of the exercise, the implementation is aimed at solving one-dimensional and two-dimensional problems of transient heat conduction and compared with the results cited in the referred literature.

Numerical Simulation of the Austenitizing Process in Hypoeutectoid Fe-C Steels

2014 ◽  
Author(s):  
Dehao Liu ◽  
Gang Wang ◽  
Zhenguo Nie ◽  
Yiming (Kevin) Rong
Keyword(s):  
Front Tracking ◽  
Two Dimensional ◽  
Austenite Matrix ◽  
Transformation Kinetics ◽  
Special Volume ◽  
Dimensional Model ◽  
Austenitization Temperature ◽  
One Dimensional ◽  
Two Dimensional Model ◽  
2D Model

For predicting of diffusive phase transformations during the austenitizing process in hypoeutectoid Fe-C steels, a two-dimensional model has been developed. The diffusion equations are solved within each phase (α and γ) using an explicit finite volume technique formulated using a square grid. The discrete α/γ interface is represented by special volume elements α/γ. The result showing the dissolution of ferrite particles in the austenite matrix are presented at different stages of the phase transformation. Specifically, the influence of the microstructure scale and heating rate on the transformation kinetics has been investigated. Final austenitization temperature calculated with this 2D model is compared with predictions of a simpler one dimensional (1D) front-tracking calculation.

scholarly journals Two-Dimensional-One-Dimensional Alternating Direction Schemes for Coastal Systems Convection-Diffusion Problems

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3267
Author(s):  
Alexander Sukhinov ◽  
Valentina Sidoryakina
Keyword(s):  
Information Exchange ◽  
Problem Solution ◽  
Two Dimensional ◽  
Splitting Scheme ◽  
Time Step ◽  
One Dimensional ◽  
Convection Diffusion ◽  
Coastal Systems ◽  
Alternating Direction ◽  
Matter Transport

The initial boundary value problem for the 3D convection-diffusion equation corresponding to the mathematical model of suspended matter transport in coastal marine systems and extended shallow water bodies is considered. Convective and diffusive transport operators in horizontal and vertical directions for this type of problem have significantly different physical and spectral properties. In connection with the above, a two-dimensional–one-dimensional splitting scheme has been built—a three-dimensional analog of the Peaceman–Rachford alternating direction scheme, which is suitable for the operational suspension spread prediction in coastal systems. The paper has proved the theorem of stability solution with respect to the initial data and functions of the right side, in the case of time-independent operators in special energy norms determined by one of the splitting scheme operators. The accuracy has been investigated, which, as in the case of the Peaceman–Rachford scheme, with the special definition of boundary conditions on a fractional time step, is the value of the second order in dependency of time and spatial steps. The use of this approach makes it possible to obtain parallel algorithms for solving grid convection-diffusion equations which are economical in the sense of total time of problem solution on multiprocessor systems, which includes time for arithmetic operations realization and the one required to carry of information exchange between processors.

scholarly journals One-dimensional thermal equation modeled on a two-dimensional heat exchanger with variable solid-fluid interface

2021 ◽  
Vol 2090 (1) ◽  
pp. 012140
Author(s):  
Hideshi Ishida ◽  
Koichi Higuchi ◽  
Taiki Hirahata
Keyword(s):  
Heat Flux ◽  
Heat Exchanger ◽  
Model Equation ◽  
Computational Time ◽  
Two Dimensional ◽  
Fluid Interface ◽  
Thermal Equation ◽  
Fluid Equation ◽  
One Dimensional ◽  
Dimensional Equation

Abstract In this study, we are to present that a one-dimensional equation for vertically averaged temperature, modeled on a vertically thin, two-dimensional heat exchanger with variable top solid-fluid interface, recovers the two-dimensional thermal information, i.e. steady temperature and flux distribution on the top and temperature-fixed bottom faces. The relative error of these quantities is less than 5% with the maximum gradient of the height kept approximately below 0.5, while the computational time is reduced to 0.1–5%, when compared with direct two-dimensional computations, depending on the shape of the top face. The model equation, derived by the vertical averaging of the two-dimensional thermal conduction equation, is closed by an approximation that the heat exchanger is sufficiently thin in the sense that the second derivative of temperature with respect to the horizontal coordinate depends only on the coordinate. In this model equation, the fluid equation above the exchanger is decoupled by a conventional equation for the normal heat flux on the top surface. In principle, however, the coupling of the model and the fluid equation is possible through the temperature and heat flux on the top interface, recovered by the model equation. The type of mathematical modeling can be applicable to a wide variety of bodies with extremely small dimensions in some (coordinate-transformed) directions.

Courtyard-level sewer data-enhanced two-dimensional hydraulic model for urban flood hazard assessment in Kunming, China

Water Policy ◽  
2014 ◽  
Vol 17 (1) ◽  
pp. 143-161
Author(s):  
Zhiqiang Xie ◽  
Qingyun Du ◽  
Zhongliang Cai ◽  
Huaixiang Liu ◽  
Sam Jamieson
Keyword(s):  
Statistical Method ◽  
Urban Areas ◽  
Flood Hazard ◽  
Ground Surface ◽  
Hydraulic Model ◽  
Two Dimensional ◽  
Urban Flood ◽  
One Dimensional ◽  
Municipal Level ◽  
Overlay Approach

This paper describes a study of urban flooding in downtown Kunming, China, simulating a major flood event that occurred in July 2008 using an improved two-dimensional (2D) hydraulic model enhanced with courtyard-level sewer data (CLSD). Although municipal authorities are not responsible for ‘private’ courtyard sewers, available records were specifically added to this model, enhancing its accuracy and usefulness. Geographic information system (GIS) flood maps, a mapping overlay approach and statistical method compared both predicted results and the recorded flood area. A statistical method also provided a measure of the correlation between the extent of the predicted flood areas and recorded flood areas (parameter ‘F’). Results of the improved 2D/CLSD model showed a correlation value for F of 51, 32.6% higher than the basic one-dimensional municipal-level sewer data (1D/MLSD) model; 26.2% higher than an interim version of the model that included a 2D ground surface (2D/MLSD). The 2D/CLSD model predicted flooding in 10 of the 12 courtyards with observed flooding. This was a major improvement over the 1D/MLSD model (three out of 12) and the 2D/MLSD model (five out of 12). Thus a CLSD-enhanced 2D hydraulic model potentially improves accuracy in predicting, mapping and understanding flood risk in urban areas.

scholarly journals Proof-of-Concept of a Quasi-2D Water-Quality Modelling Approach to Simulate Transverse Mixing in Rivers

2021 ◽  
Author(s):  
Pouya Sabokruhie ◽  
Eric Akomeah ◽  
Tammy Rosner ◽  
Karl-Erich Lindenschmidt
Keyword(s):  
Flow Direction ◽  
Computational Time ◽  
Small Scale ◽  
Change Scenario ◽  
Two Dimensional ◽  
Proof Of Concept ◽  
Transverse Mixing ◽  
Model Setup ◽  
2D Model ◽  
Modelling Approach

A quasi-two-dimensional (quasi-2D) modelling approach is introduced to mimic transverse mixing of an inflow into a river from one of its banks, either an industrial outfall or a tributary. The concentrations of determinands in the inflow vary greatly from those in the river, leading to very long mixing lengths in the river downstream of the inflow location. Ideally, a two-dimensional (2D) model would be used on a small scale to capture the mixing of the two flow streams. However, for large-scale applications of several hundreds of kilometres of river length, such an approach demands too many computational resources and too much computational time, especially if the application will at some point require ensemble input from climate-change scenario data. However, a one-dimensional (1D) model with variables varying in the longitudinal flow direction but averaged across the cross-sections is too simple of an approach to capture the lateral mixing between different flow streams within the river. Hence, a quasi-2D method is proposed in which a simplified 1D solver is still applied but the discretisation of the model setup can be carried out in such a way as to enable a 2D representation of the model domain. The quasi-2D model setup also allows secondary channels and side lakes in floodplains to be incorporated into the discretisation. To show proof-of-concept, the approach has been tested on a stretch of the lower Athabasca River in Canada flowing through the oil sands region between Fort McMurray and Fort MacKay. A dye tracer and suspended sediments are the constituents modelled in this test case.

scholarly journals Computational simulation of one-dimensional waves with the Multigrid Method / Simulação computacional de ondas unidimensionais com o Método Multigrid

2021 ◽  
Vol 7 (8) ◽  
pp. 83763-83775
Author(s):  
Maicon F. Malacarne ◽  
Marcio A. V. Pinto ◽  
Sebastião R. Franco
Keyword(s):  
Multigrid Method ◽  
Computational Simulation ◽  
Computational Time ◽  
System Of Equations ◽  
Time Step ◽  
One Dimensional ◽  
Time Stepping ◽  
Engineering Problems ◽  
Large Systems ◽  
The Finite Difference Method

Several Engineering problems are modeled computationally, these simulations involve large systems, which are commonly difficult to solve. This paper deals with the simulation of one-dimensional waves, where the system resulting from the discretization by the Finite Difference Method is solved using the Multigrid Method with the conventional Gauss-Seidel solver, in order to decrease the computational time. Temporal discretization using the Time-Stepping method, where the system of equations is solved at each time step sequentially.

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