Water pollution estimation based on the 2D transport–diffusion model and the Singular Evolutive Interpolated Kalman filter

Tran, Tri; Pham, Dinh-Tuan; Hoang, Van Lai; Nguyen, Hong Phong

doi:10.1016/j.crme.2013.10.007

Cited by 9 publications

(16 citation statements)

References 14 publications

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“…, N p and k = 1, 2, 3). On this cell the approximations of partial derivatives ∂w/∂x and ∂w/∂y are introduced in [3].…”

Section: Methodsmentioning

confidence: 99%

“…We suppose that there are some passive substances dissolved in the flow. Then the transport and diffusion processes of the pollutant are governed by the following equation (see [1][2][3][4][5][6])…”

Section: Deriving a 2d Water Pollution Modelmentioning

confidence: 99%

“…. Based on the hydraulic model IMECH 2DUSZ [2,3] a 2D water pollution model is developed then numerically solved due to a finite volume the directions of the normal vector common to two elements are different. It leads to a numerical solution closer to the exact solution than the one obtained by using the former methods.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An improved numerical method for a 2D pollution water model: Direct model

Phong¹,

Ha²,

Dimet

et al. 2017

Vietnam J. Mech.

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In this paper a 2D pollution water model with an improved numerical method is considered. In order to reduce the approximation errors of the numerical scheme, a new approximation method is introduced to calculate the concentration flux between two cells (j-cell and l-cell) in the direction of the normal vector \(\vec {n}\) orthogonal to their common side. The advantage of this approximation is that the concentration flux \({\partial C}/{\partial \vec {n}}\) from j-cell to l-cell and the other one from l-cell to j-cell are only different by their signs but not by their absolute values. Therefore, the errors of concentration simulated by this scheme are reduced and less than those obtained by a normal differential implicit discretization. This improvement of the scheme will be illustrated by two test cases. In the numerical tests we will display the difference between the exact solution, the classical scheme and the proposed scheme. Numerical results demonstrate the improvement of this approach.

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“…, N p and k = 1, 2, 3). On this cell the approximations of partial derivatives ∂w/∂x and ∂w/∂y are introduced in [3].…”

Section: Methodsmentioning

confidence: 99%

Section: Deriving a 2d Water Pollution Modelmentioning

confidence: 99%

See 1 more Smart Citation

An improved numerical method for a 2D pollution water model: Direct model

Phong¹,

Ha²,

Dimet

et al. 2017

Vietnam J. Mech.

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show abstract

“…In order to numerically solve the above model equations, a cell-centered nite volume method is used (see [23]) accompanied by an explicit scheme in time [25]. To study the response function gradient, we consider the problem of a water ow running into the channel with the length 3000m, the width 800m, and the bottom elevation z b = .…”

Section: Simulation Experiments On Computing the Response-function Gramentioning

confidence: 99%

General sensitivity analysis in data assimilation

Dimet¹,

Shutyaev²,

Tran³

2014

Russian Journal of Numerical Analysis and Mathematical Modelling

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International audienceThe problem of variational data assimilation for a nonlinear evolution model is formulated as an optimal control problem to nd the initial condition function (analysis). The operator of the model, and hence the optimal solution, depend on the parameters which may contain uncertainties. A response function is considered as a functional of the solution after assimilation. Based on the second-order adjoint techniques, the sensitivity of the response function to the parameters of the model is studied. The gradient of the response function is related to the solution of a non-standard problem involving the coupled system of direct and adjoint equations. The solvability of the non-standard problem is studied. Numerical algorithms for solving the problem are developed. The results are applied for the 2D hydraulic and pollution models. Numerical examples on computation of the gradient of the response function are presented

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“…-By the same way as [16,28] -The process finding the coefficient is shown in Figure 3. By this process the error of obtain coefficient in the end optimal process is less than 0.00001 percentage.…”

Section: Algorithm To Solve the Optimal Control Problemmentioning

confidence: 99%

Application of Data Assimimilation for Parameter Correction in Super Cavity Modelling

Son

Hai

et al. 2016

JST

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On the imperfect water entry, a high speed slender body moving in the forward direction rotates inside the cavity. The super cavity model describes the very fast motion of body in water.In the super cavity model the drag coefficient plays important role in body's motion. In some references this drag coefficient is simply chosen by different values in the interval 0.8-1.0. In some other references this drag coefficient is written by the formula k is corrected so that the simulation body velocities are closer to observation data. To find the convenient drag coefficient the data assimilation method by differential variation is applied. In this method the observing data is used in the cost function. The data assimilation is one of the effected methods to solve the optimal problems by solving the adjoin problems and then finding the gradient of cost function.

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Water pollution estimation based on the 2D transport–diffusion model and the Singular Evolutive Interpolated Kalman filter

Cited by 9 publications

References 14 publications

An improved numerical method for a 2D pollution water model: Direct model

An improved numerical method for a 2D pollution water model: Direct model

General sensitivity analysis in data assimilation

Application of Data Assimimilation for Parameter Correction in Super Cavity Modelling

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