Browsing by Author "Yang, JC"

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A comprehensive unsteady depth-averaged model with orthogonal curvilinear coordinate system
(1998)
Hsieh, TY
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Yang, JC
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土木工程學系
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Department of Civil Engineering
A mathematical model is developed here to solve unsteady depth-averaged shallow water flow equations. To enhance applicability, an orthogonal curvilinear coordinate system is used. The governing equations are solved by the two-step split-operator algorithm. Based on the finite-volume concept, all of the spatial derivatives are estimated with implicit central difference of second-order accuracy, while the convection terms are solved by a hybrid scheme. The effective stresses incorporates with a constant eddy-viscosity turbulence formulation to approximate the laminar and turbulent Reynolds stresses and with the secondary flow velocity profile proposed by de Vriend [1] to approximate the bend flow pattern. Two case studies including unsteady flow and bend flow are proposed herein to verify the model. Comparison with the experimental data shows that the model is efficient and robust. Finally, the model is applied to Tan-Shui River, a natural channel in Taiwan. The agreement between the computed results and field data is satisfactory.
An accurate integral-based scheme for advection-diffusion equation
(2001-10-01)
Tsai, TL
;
Yang, JC
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Huang, LH
;
土木工程學系
;
Department of Civil Engineering
This paper proposes an accurate integral-based scheme for solving the advection-diffusion equation. In the proposed scheme the advection-diffusion equation is integrated over a computational element using the quadratic polynomial interpolation function. Then elements are connected by the continuity of first derivative at boundary points of adjacent elements. The proposed scheme is unconditionally stable and results in a tridiagonal system of equations which can be solved efficiently by the Thomas algorithm. Using the method of fractional steps, the proposed scheme can be extended straightforwardly from one-dimensional to multi-dimensional problems without much difficulty and complication. To investigate the computational performances of the proposed scheme five numerical examples are considered: (i) dispersion of Gaussian concentration distribution in one-dimensional uniform flow; (ii) one-dimensional viscous Burgers equation; (iii) pure advection of Gaussian concentration distribution in two-dimensional uniform flow; (iv) pure advection of Gaussian concentration distribution in two-dimensional rigid-body rotating flow; and (v) three-dimensional diffusion in a shear flow. In comparison not only with the QUICKEST scheme, the fully time-centred implicit QUICK scheme and the fully time-centred implicit TCSD scheme for one-dimensional problem but also with the ADI-QUICK scheme, the ADI-TCSD scheme and the MOSQUITO scheme for two-dimensional problems, the proposed scheme shows convincing computational performances. Copyright (C) 2001 John Wiley & Sons, Ltd.
An accurate integral-based scheme for dispersion equation
(2001)
Tsai, TL
;
Yang, JC
;
Huang, LH
;
土木工程學系
;
Department of Civil Engineering
This paper proposes an accurate integral-based scheme for solving dispersion equation. In the newly-proposed scheme the dispersion equation is integrated over a computational element using the quadratic polynomial interpolation function. Then elements are connected by the continuity of first derivative at boundary point of adjacent elements. The newly-proposed scheme is unconditionally stable and preserves a tridiagonal system of equations which can be solved efficiently by the Thomas algorithm. Using the method of fractional steps, the newly-proposed scheme, originally developed for one-dimensional problems, can be extended straightforward to multi-dimensional problems. To investigate the computational performances of the newly-proposed scheme five numerical examples are considered : (i) dispersion of Gaussian concentration distribution in one-dimensional uniform flow, (ii)one-dimensional viscous burger's equation, (iii) pure advection of Gaussian concentration distribution in two-dimensional uniform flow, (iv) pure advection of Gaussian concentration distribution in two-dimensional rigid-body rotating flow and (v) three-dimensional diffusion in a shear flow. In comparison not only with the QUICKEST scheme, fully time-centred implicit QUICK scheme and fully time-centred implicit TCSD scheme for one-dimensional problem but also with the ADI-QUICK scheme, ADI-TCSD scheme and MOSQUITO scheme for two-dimensional problems, the newly-proposed scheme shows convincing computational performances.
Bend-flow simulation using 2D depth-averaged model
(1999-10-01)
Lien, HC
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Hsieh, TY
;
Yang, JC
;
Yeh, KC
;
土木工程學系
The purpose of this paper is to present a 2D depth-averaged model for simulating and examining flow patterns in channel bends. In particular, this paper proposes a 2D depth-averaged model that takes into account the influence of the secondary flow phenomenon through the calculation of the dispersion stresses arisen from the integration of the products of the discrepancy between the mean and the true velocity distributions. The proposed model uses an orthogonal curvilinear coordinate system to efficiently and accurately simulate the flow field with irregular boundaries. As for the numerical solution procedure, the two-step split-operator approach consisting of the dispersion step and the propagation step with the staggered grid is used to numerically solve the flow governing equations. Two sets of experimental data from de Vriend and Koch and from Rozovskii were used to demonstrate the model's capabilities. The former data set was from a mildly curved channel, whereas the latter was from a sharply curved channel. The simulations considering the secondary flow effect agree well with the measured data. Furthermore, an examination of the dispersion stress terms shows that the dispersion stresses play a major role in the transverse convection of the momentum shifting from the inner bank to the outer bank for flows in both mild and sharp bends.
Characteristics method using cubic-spline interpolation for advection-diffusion equation
(2004-06-01)
Tsai, TL
;
Yang, JC
;
Huang, LH
;
土木工程學系
;
防災與水環境研究中心
The characteristics method by using the cubic-spline interpolation is comparable to the Holly-Preissmann scheme in solving the advection portion of the advection-diffusion equation. In order to conduct a cubic-spline interpolation, an additional constraint must be specified at each endpoint. In general, four types of endpoint constraints are available, i.e., the first derivative, second derivative, quadratic, and not-a-knot constraints. The goal of this paper is to examine each type of endpoint constraints. Two hypothetical cases are used to conduct the investigation. Among the four types of constraints examined herein, the not-a-knot constraint and the first derivative constraint with high-order finite difference approximation yield the best results. However, as far as accuracy and simple implementation are concerned the not-a-knot constraint should be the best choice in solving the advection-diffusion equation.
Characteristics method with cubic-spline interpolation for open channel flow computation
(2004-10-30)
Tsai, TL
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Chiang, SW
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Yang, JC
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防災與水環境研究中心
;
Disaster Prevention and Water Environment Research Center
In the framework of the specified-time-interval scheme, the accuracy of the characteristic method is Greatly related to the form of the interpolation. The linear interpolation was commonly used to couple the characteristics method (LI method) in open channel flow computation. The LI method is easy to implement, but it leads to an inevitable smoothing of the solution. The characteristics method with the Hermite cubic interpolation (HP method, originally developed by Holly and Preissmann, 1977) was then proposed to largely reduce the error induced by the LI method. In this paper, the cubic-spline interpolation on the space line or on the time line is employed to integrate with characteristics method (CS method) for unsteady flow computation in open channel. Two hypothetical examples, including gradually and rapidly varied flows, are used to examine the applicability of the CS method as compared with the LI method, the HP method, and the analytical solutions. The simulated results show that the CS method is comparable to the HP method and more accurate than the LI method. Without tackling the additional equations for spatial or temporal derivatives, the CS method is easier to implement and more efficient than the HP method. Copyright (C) 2004 John Wiley Sons, Ltd.
Closure to "Investigation on the stability of two-dimensional depth-averaged models for bend-flow simulation" by T. Y. Hsieh and J. C. Yang
(2005-07-01)
Hsieh, TY
;
Yang, JC
;
土木工程學系
;
防災與水環境研究中心
;
Department of Civil Engineering
Depth-averaged two-dimensional curvilinear explicit finite analytic model for open-channel flows
(2000-05-30)
Hsu, CT
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Yeh, KC
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Yang, JC
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土木工程學系
;
Department of Civil Engineering
A depth-averaged two-dimensional model has been developed in the curvilinear co-ordinate system for free-surface flow problems. The non-linear convective terms of the momentum equations are discretized based on the explicit-finite-analytic method with second-order accuracy in space and first-order accuracy in time. The other terms of the momentum equations, as well as the mass conservation equation, are discretized by the finite difference method. The discretized governing equations are solved in turn, and iteration in each time step is adopted to guarantee the numerical convergence. The new model has been applied to various flow situations, even for the cases with the presence of sub-critical and supercritical flows simultaneously or sequentially. Comparisons between the numerical results and the experimental data show that the proposed model is robust with satisfactory accuracy. Copyright (C) 2000 John Wiley & Sons, Ltd.
Fractional steps scheme of finite analytic method for advection-diffusion equation
(2005-01-01)
Tsai, TL
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Tseng, CM
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Yang, JC
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土木工程學系
;
防災與水環境研究中心
For simply finding local analytic solution, the time derivative in the traditional finite analytic (FA) method is generally replaced with a first-order finite difference approximation as a source term. However, this may induce excessive numerical diffusion, especially for advection-dominated transport problems. In this paper, a fractional steps scheme of the FA method without using the finite difference approximation to time derivative is proposed by applying the one-dimensional FA method whose local analytic solution is obtained from both spatial and time domains, together with the method of fractional steps. Four hypothetical examples, including two-dimensional and three-dimensional cases, are employed to investigate this newly proposed method as compared with the traditional FA method, the optimal unsteady FA method, and the alternating direction scheme of the hybrid FA method. The results show that the fractional steps scheme of the FA method can greatly diminish numerical diffusion and is superior to the other methods compared herein.
Groundwater modeling by layer based three-dimensional concept
(2000)
Tsai, TL
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Huang, LH
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Yang, JC
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土木工程學系
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Department of Civil Engineering
Due to its simplicity and efficiency, the conventional quasi three-dimensional concept has been widely applied in analyzing groundwater flow in multiaquifer system, especially for regional problem. But the conventional quasi three-dimensional concept is not able to deal with the discontinuous and interconnected strata and fully three-dimensional flow. Therefore, in order not only to overcome these shortcomings but also to maintain efficiency, we propose a new layer based three-dimensional concept to develop a groundwater simulation model. This new concept assumes that the pore pressure of every aquifer and aquitard in the vertical direction can be depicted by the quadratic polynomial interpolation function, then the vertical integration is performed on each layer to ensure the continuity of pore pressure and flux at the interfaces between any two layers. The finite analytical numerical method is adopted to develop the present groundwater simulation model. The results show that the present model is capable of simulating fully three-dimensional flow pattern.
Hybrid finite-difference scheme for solving the dispersion equation
(2002-01-01)
Tsai, TL
;
Yang, JC
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Huang, LH
;
土木工程學系
;
Department of Civil Engineering
An efficient hybrid finite-difference scheme capable of solving the dispersion equation with general Peclet conditions is proposed. In other words, the scheme can simultaneously deal with pure advection, pure diffusion, and/or dispersion. The proposed scheme linearly combines the Crank-Nicholson second-order central difference scheme and the Crank-Nicholson Galerkin finite-element method with linear basis functions. Using the method of fractional steps, the proposed scheme can be extended straightforwardly from one-dimensional to multidimensional problems without much difficulty. It is found that the proposed scheme produces the best results, in terms of numerical damping and oscillation, among several non-split-operator schemes. In addition, the accuracy of the proposed scheme is comparable with a well-known and accurate split-operator approach in which the Holly-Preissmann scheme is used to solve the pure advection process while the Crank-Nicholson second-order central difference scheme is applied to the pure diffusion process. Since the proposed scheme is a non-split-operator approach, it does not compute the two processes separately. Therefore, it is simpler and more efficient than the split-operator approach.
Identification and stochastic generation of representative rainfall temporal patterns in Hong Kong territory
(2006-04-01)
Wu, SJ
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Yang, JC
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Tung, YK
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土木工程學系
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Department of Civil Engineering
In hydrosystem engineering design and analysis, temporal pattern for rainfall events of interest is often required. In this paper, statistical cluster analysis of dimensionless rainfall pattern is applied to identify representative temporal rainfall patterns typically occurred in Hong Kong Territory. For purpose of selecting an appropriate rainfall pattern in engineering applications, factors affecting the occurrence of different rainfall patterns are examined by statistical contingency tables analysis through which the inter-dependence of the occurrence frequency of rainfall patterns with respect to geographical location, rainfall duration and depth, and seasonality is investigated. Furthermore, due to inherent variability of rainfall mass curves or hyetographs within each classified rainfall pattern, a practical procedure to probabilistically generate plausible rainfall patterns is described. The procedure preserves the inherent stochastic features of random dimensionless rainfall hyetograph ordinates, which in general are correlated non-normal multivariate compositional variables.
Investigation on the suitability of two-dimensional depth-averaged models for bend-flow simulation
(2003-08-01)
Hsieh, TY
;
Yang, JC
;
土木工程學系
;
防災與水環境研究中心
;
Department of Civil Engineering
A numerical experiment is carried out to study the suitability of two-dimensional (2D) depth-averaged modeling for bendflow simulation, in which the geometry of the studied channel is rectangular. Two commonly used 21) depth-averaged models for bend-flow simulation are considered in this study of which the bend-flow model includes the dispersion stress terms by incorporating the assumption of secondary-current velocity profile, and the conventional model neglects the dispersion stress terms. The maximum relative discrepancy of the longitudinal velocity, obtained from the comparison of these two models, is used as a criterion to judge their applicability for bend-flow simulation. The analysis of simulation results indicated that the maximum relative difference in longitudinal velocity is mainly related to the relative strength of the secondary current and the relative length of the channel. Empirical relations between the maximum relative difference in the longitudinal velocity, the relative strength of the secondary current, and the relative length of the channel for both the channel-bend region and the straight region following the bend have been established. The proposed relations provide a guideline for model users to determine the proper approach to simulate the bend-flow problem by either using the conventional model or the bend-flow model. Experimental data have been adopted herein to demonstrate the applicability and to verify the accuracy of the proposed relations.
Kinematic wave modeling of overland flow using characteristics method with cubic-spline interpolation
(2005-07-01)
Tsai, TL
;
Yang, JC
;
土木工程學系
;
防災與水環境研究中心
;
Department of Civil Engineering
Use of characteristics method integrated with cubic-spline interpolation technique (CSMOC scheme) for computation of one-dimensional and two-dimensional kinematic overland flow has been examined in this study. The characteristic trajectory is allowed to fall on space line and time line for interpolating the corresponding values at the foot of trajectory in terms of neighboring grid points. The effects of different endpoint constraints on use of cubic-spline interpolation are investigated. As far as accuracy and simplicity are concerned, the not-a-knot constraint could be a better choice. Three hypothetical examples are used to examine the capabilities of CSMOC scheme through the comparison with the analytical solution and the well-known Preissmann scheme. Some degrees of numerical diffusion and numerical oscillation, attenuating and overestimating the peak discharge, are induced by the Preissmann scheme. In contrast, the CSMOC scheme gives convincing results for the kinematic overland flow computations. (c) 2005 Elsevier Ltd. All rights reserved.
Method for performance evaluation of hydrologic and hydraulic models
(1996)
Yang, JC
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Yeh, KC
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Tung, YK
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土木工程學系
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Department of Civil Engineering
Modeling of rainfall-triggered shallow landslide
(2006-07-01)
Tsai, TL
;
Yang, JC
;
土木工程學系
;
防災與水環境研究中心
;
Department of Civil Engineering
By integrating hydrological modeling with the infinite slope stability analysis, a rainfall-triggered shallow landslide model was developed by Iverson (Water Resour Res 36:1897-1910, 2000). In Iverson's model, the infiltration capacity is assumed to be equivalent to the saturated hydraulic conductivity for finding pressure heads analytically. However, for general infiltration process, the infiltration capacity should vary with time during the period of rain, and the infiltration rate is significantly related to the variable infiltration capacity. To avoid the unrealistically high pressure heads, Iverson employed the beta-line correction by specifying that the simulated pressure heads cannot exceed those given by the beta line. In this study, the suitability of constant infiltration capacity together with the beta-line correction for hydrological modeling and landslide modeling of hillslope subjected to a rainfall is examined. By amending the boundary condition at ground surface of hillslope in Iverson's model, the modified Iverson's model with considering general infiltration process is developed to conduct this examination. The results show that the unrealistically high pressure heads from Iverson's model occur due to the overestimation of infiltration rate induced from the assumption that the infiltration capacity is identical to the saturated hydraulic conductivity. Considering with the general infiltration process, the modified Iverson's model gives acceptable results. In addition, even though the beta-line correction is applied, the Iverson's model still produces greater simulated pressure heads and overestimates soil failure potential as compared with the modified Iverson's model. Therefore, for assessing rainfall-triggered shallow landslide, the use of constant infiltration capacity together with the beta-line correction needs to be replaced by the consideration of general infiltration process.
Numerical examination on the secondary-current effect for contaminant transport in curved channel
(2005)
Hsieh, TY
;
Yang, JC
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土木工程學系
;
防災與水環境研究中心
;
Department of Civil Engineering
The purpose of this paper is to examine the effect of secondary current on contaminant transport in curved channel by using the 2D depth-averaged model. Two hypothetical cases are adopted. The results show that the secondary-current effect caused by flow is very limited and is reflected mainly from the circulatory transport term which is contained in the contaminant transport equation. A numerical experiment is carried out to judge the effect level of the secondary current. The results indicated that the maximum relative difference in concentration, MaxC*, obtained from the comparison of models with and without considering the secondary-current effect is mainly related to the relative strength of the secondary current SI and the relative length of the bend Theta b. Empirical relations including the classification on effect level of secondary current and the MaxC*-SI-theta(b) relation have been tentatively established. The former relation can serve as a guideline for model users to judge how important the secondary-current effect is and when the effect should be included in the model. The later relation can be regarded as an auxiliary relationship for the former to quantify the deviation between models with and without considering the secondary-current effect. The field data reported by Lau and Krishnappan [J. Hydraul. Div. ASCE 107 (1981) 209] and Holley and Abraham [J. Hydraul. Div. ASCE 99 (1973) 2313] are adopted herein to verify the applicability and the accuracy of the proposed relations.
Numerical simulation of the pit migration
(1997)
Lien, HC
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Yeh, KC
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Yang, JC
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土木工程學系
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Department of Civil Engineering
The purpose of this paper is to simulate the migration of a pit in the channel bed. When water flows over a pit, the velocity at the upstream end of the pit slows down rapidly owing to the increment of the flow depth, and that at the downstream end of the pit speeds up because of the sudden contraction of the now area. Under such a flow condition, the equilibrium sediment transport formula is inadequate to simulate the local deposition and scouring around the pit. In addition, the critical bed-shear stress without considering the bed slope effect may increase the deposition rate near the upstream end and the scouring rate near the downstream end of the pit. This paper proposes a numerical model to simulate the migration of a pit by considering the nonequilibrium sediment transport behavior and the modified critical bed-shear stress for the movement of sediment on the large bed slope. The capability of the model was verified by comparing the simulated results with one of the experiments executed by Lee et at. (1993).
Quasi-two-dimensional simulation of scour and deposition in alluvial channels
(1997-07-01)
Lee, HY
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Hsieh, HM
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Yang, JC
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Yang, CT
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土木工程學系
Most existing sediment routing models are one-dimensional models and hence they cannot be used Co simulate lateral channel bed deformations. Conversely, a two-dimensional model is computationally time consuming, and is not suitable for long-term simulation. Using the stream tube concept, a one-dimensional model is extended to a quasi-two-dimensional model in this study. It is capable of simulating lateral variations of channel cross section through the adjustments of stream tube boundaries. The model has an option to treat the suspended load and bed load separately and hence is able to simulate the deposition behavior of the suspended sediment under a nonequilibrium process. The model also provides options to solve either de Saint Venant equation or energy equation and hence can be applied in both steady and unsteady flow conditions. An assessment of this model's performance has been conducted through a comparison to an analytical solution and a set of experimental data, The application of this model to the Keelung River and the Shiemen Reservoir in Taiwan also gave convincing results.
Quasi-two-dimensional simulation of scour and deposition in alluvial channels - Closure
(1999-02-01)
Lee, HY
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Hsieh, HM
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Yang, JC
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Yang, CT
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土木工程學系