Te-Yung Hsieh

Use of two-step split-operator approach for 2D shallow water flow computation

The objective of this paper is to present a methodology of using a two-step split-operator approach for solving the shallow water flow equations in terms of an orthogonal curvilinear co-ordinate system. This approach is in fact one kind of the so-called fractional step method that has been popularly used for computations of dynamic flow. By following that the momentum equations are decomposed into two portions, the computation procedure involves two steps. The first step (dispersion step) is to compute the provisional velocity in the momentum equation without the pressure gradient. The second step (propagation step) is to correct the provisional velocity by considering a divergence-free velocity field, including the effect of the pressure gradient. This newly proposed method, other than the conventional split-operator methods, such as the projection method, considers the effects of pressure gradient and bed friction in the second step. The advantage of this treatment is that it increases flexibility, efficiency and applicability of numerical simulation for various hydraulic problems. Four cases, including back-water flow, reverse flow, circular basin flow and unsteady flow, have been demonstrated to show the accuracy and practical application of the method. Copyright

Numerical examination on the secondary-current effect for contaminant transport in curved channel

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 θb,. Empirical relations including the classification on effect level of secondary current and the MaxC*-SI-θ 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.

Modelling of hyperconcentrated flow in steep-sloped channels

ABSTRACT An unsteady two-dimensional depth-averaged numerical model for hyperconcentrated flows in steep-sloped alluvial channels is developed and applied to the Zhuoshui River in Central Taiwan. In this model, the suspended load and bed load are both included to reproduce actual sediment transport characteristics of steep-sloped channels in the chosen study river reaches. A rheological relationship for Bingham fluid and the formula for the sediment carrying capacity, established through laboratory experiments, are used to describe the hyperconcentrated flow behaviour in the model. At peak discharge during Typhoon Morakot, bed shear stress from the hyperconcentrated flow model can be 150% larger than that from the clear water model. According to the simulation for Tung-Pu-Rey Creek, an upstream tributary of Zhuoshui River, the temporal evolution of bed changes obtained from the model can be used to provide plausible explanations for the reasons behind levee failure during Typhoon Toraji.