A numerical treatment of a non-dimensional form of a water quality model in the Rama-nine reservoir

Abstract

The purposes of this research are to develop mathematical models and numerical methods for approximating water flow directions and pollution levels in a Rama-nine reservoir, Pathumthani, Thailand with non-uniform current. The Rama-nine reservoir is opened with two parallel canals. The pollution levels in a reservoir are assessing via data collection at the real field. It is quite complex and the results obtained tentatively deviate from one point of time and position to another. There are many research works applied a mathematical model called the dispersion model to estimate the water pollutant concentration. The approximation accuracy received is seemingly unsatisfied, especially, when the water flow is not uniformly distributed.The research begins with revising a mathematical model that combines two existing mathematical models: a non-dimensional form of hydrodynamic model and a dispersion model. The model is to make suitable to the Rama-nine reservoir.The LaxWendroff method is subsequently used in a non-dimensional form of a shallow water equation to approximate the water velocity and elevation. Next, we use the forward differences in time and backward difference in space in advection-diffusion equation. Combined the equation with the calculated velocity is thus used in the dispersion model to approximate the concentration levels of the pollutants. The result of this research showed that the proposed *concentration of the pollutants in a Rama-nine reservoir at any various time and position. The accuracy of approximation is within the units of centimeters and seconds. In addition, this research has shown that the proposed model can be applied to other water sources having non-uniformly distributed water flows.

Numerical Simulations of Water Quality Measurement Model in an Opened-Closed Reservoir with Contaminant Removal Mechanism

“…In [11], the Lax-Wendroff finite difference method is also proposed to approximate the water elevation and water flow velocity with a rectangular domain. In [12], the mathematical models and numerical methods for approximating water current and pollutant concentration level in Rama-nine reservoirs are presented. In [13], 2 International Journal of Differential Equations the Lax-Wendroff method for solving the dimensional form of shallow water equation in spherical model with Matlab program is proposed.…”