2017年美国大学生数学建模竞赛O奖论文A-65448.pdf
版权申诉
10 浏览量
2024-03-17
21:46:49
上传
评论
收藏 1.77MB PDF 举报
For office use only
T1
T2
T3
T4
Team Control Number
65448
Problem Chosen
A
For office use only
F1
F2
F3
F4
2017 Mathematical Contest in Modeling (MCM) Summary Sheet
(Attach a copy of this page to each copy of your solution paper.)
Abstract
The Kariba Dam on the Zambezi River is confronted with foundation errosion and control limitation cur-
rently, so a strategy to maintain water management on the Zambezi River is of great value for the whole
Zambezi basin. Based on the detailed data provided by World Bank, we conduct the assessment of three op-
tions (repairing the dam, rebuilding the dam or replacing the dam with several smaller dams along the river)
and provide a reasonable and detailed model to construct a new dam system with some emergency strategies.
To begin with, a brief assessment report with potential costs and benefits is offered according to abundant
references and reliable data. The evaluation of repairing the Kariba Dam is completed refering to the Kariba
Dam Rehabilitation Project in the charge of World Bank, while the assessment of rebuilding the dam is realized
following the actual capital investment expenditure of the Stage 1 of the Kariba Project. And the assessment of
replacing the dam is carefully estimated according to the model to construct the new dam system.
Then, we concentrate on the establishment of the model for new dam system.
Firstly, a Hydrodynamic Model (HM) of the Zambezi River is established in order to estimate the flowing
and depth situation of the river. The model is constructed based on flow conservation and energy conservation,
which separately producing continuity equation and energy conservation equation, taking the normal water
cycles and on-way resistance into account. Moreover, we obtain the numerical solution of the Hydrodynamic
Model with Mathematica, and get the approximate current velocity curve and river depth curve along the
river.
Secondly, the site selection and number confirmation of the new dams is realized according to the flowing
and depth situation estimated by HM, geological data and hydrological data. The indexes for evaluation
are determined after consulting professional literatures, and Grey Relation Grade Analysis is utilized in the
selection among candidate sites so that all the indexes can be considered comprehensively and objectively.
Thirdly, a Difference Model (DM) of the Zambezi River with a dam system is established to provide suf-
ficient details for the confirmation of dam construction and modulating strategies. We separate the river into
several segments by the dams. A difference approximation of HM is applied to describe each segment of the
river. A hydraulic emprical formula is utilized to determine the discharges of the dam. In this way, the re-
currence formulas can be obtained to easily determine the runoff and river depth along the river with given
environmental and initial conditions.
Fourthly, the type of each dam is confirmed with corrected DM, with the overall water management capa-
bilities, protection and water management options for Lake Kariba evaluated and special topograph consid-
ered. Considering the loss of energy in collision, tributaries and the runoff variation with rainfall at headstram
and tributaries, DM is corrected to adapt to the reality. With the results calculated by corrected DM, the type of
each dam is confirmed balancing the safety and costs. Each type of dam has three gears of discharges, which
increases the water management options.
Finally, the strategies to handle such emergency water flow situations as flooding and drought are designed
with the new dam system established above. When solving a known catastrophe, the exhaustive method is
utilized to rule out the best strategies which realized by the gear variation of the dam. It is validated that the
new dam system can handle most extreme conditions and the method we adopted to establish the strategy is
of low sensibility considering reasonable errors.
剩余27页未读，继续阅读
资源评论
