Numerical Simulation of Water-Quality Model on Flooding Using Revised Lax-Diffusive and Modified Siemieniuch-Gladwell Methods

Kanawoot Subklay, Nopparat Pochai


In 2011, Thailand has been confronted a largest flooding. The mass
of water has been drenched from many main and branch rivers to cover wide
areas. The residents who lived in the flooding area have to build a manmade
sandbag dike to protect their village. The flooding has been taken for a long time
meanwhile the flooding water becomes contaminated. There are some residents
in their flooding area want to drain their contaminated water to a nearest area.
They have been destroyed their sandbag dike. Consequently, the dispute among
residents is occurred. In this research, a mathematical simulation of a waterquality on a long period flooding using a couple of two models is proposed. The
first model is the one-dimensional shallow water equations that provide the water
elevation and velocity. The second model is a one-dimensional advection-dispersion
equation that provides the water pollutant concentrations after the sandbag dike
has been destroyed. A revised Lax-diffusive is used to approximate the solution
of the first model. Consequently, the numerical solutions of the second model are
obtained by using the traditional and modified Siemieniuch-Gladwell schemes.

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The Thai Journal of Mathematics organized and supported by The Mathematical Association of Thailand and Thailand Research Council and the Center for Promotion of Mathematical Research of Thailand (CEPMART).

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