# 2D-model of contaminant water transmission processes and numerical simulation on a natural lake

## Nowadays, the water pollution problems in the lakes are urgent matters. The simulation of contaminant water transmission process plays important role in reality to improve people’s life qualities. In this paper the 2D- mathematical model simulating transmission processes of some contaminant substances in one lake of Hanoi is studied. The finite volume method is used in model. The actions between substances are considered and the simulation results are compared with the measurements. | Vietnam Journal of Mechanics, VAST, Vol. 32, No. 3 (2010), pp. 157 – 166 2D - MODEL OF CONTAMINANT WATER TRANSMISSION PROCESSES AND NUMERICAL SIMULATION ON A NATURAL LAKE Tran Thu Ha, Nguyen Hong Phong Institute of Mechanics Abstract. Nowadays, the water pollution problems in the lakes are urgent matters. The simulation of contaminant water transmission process plays important role in reality to improve people’s life qualities. In this paper the 2D- mathematical model simulating transmission processes of some contaminant substances in one lake of Hanoi is studied. The finite volume method is used in model. The actions between substances are considered and the simulation results are compared with the measurements. 1. INTRODUCTION Present-day in our country, water pollution is one of the most serious problems. Water quality is influenced directly to health of people. In this paper the 2D hydraulic and pollution models are used to simulate the transmissions of the pollution substances. The linear 2D water pollution model is studied by semi group method in [5]. The nonlinear 2D-Imech water pollution model is begun establishing in 2005 [1] by the group of Assoc. Prof. Hoang Van Lai. In this paper this model is developed to simulate transmission of the pollution substance combination acting each with others in water. 2. FORMULATION OF THE WATER POLLUTION PROBLEM 2D Pollution water model is consisted of hydraulic model and transmission - diffusion of pollution substances. The Saint - Vernant equation is written as follows: ∂z ∂ ∂ + (uh) + (vh) = 0 (in Ω) (1) ∂t ∂x ∂y ∂u ∂u ∂u ∂z gu(u2 + v 2 )1/2 +u +v +g =− ∂t ∂x ∂y ∂x Kx2 h4/3 (in Ω) (2) ∂v ∂v ∂v ∂z gv(u2 + v 2 )1/2 +u +v +g =− (in Ω) (3) ∂t ∂x ∂y ∂y Ky2 h4/3 We suppose that there are m substances dissolved in water. Then the transmission and diffusion processes of pollution substances are described by the following equation: ∂Ci ∂ ∂ ∂2 ∂2 + uCi + vCi = fi + Di ( 2 Ci + 2 Ci ) (in Ω), ∂t ∂x ∂y ∂x ∂y (i = .

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