Solution of contaminant transport with equilibrium and non-equilibrium adsorption

Kačur, Jozef; Malengier, Benny; Remešíková, Mariana

doi:10.1016/j.cma.2004.05.017

Cited by 16 publications

(23 citation statements)

References 9 publications

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“…As is shown in other papers of the authors, cf. [2], this gives very good numerical results, but the convergence of the practical scheme has not been proved yet. This will be the main goal of the present paper.…”

Section: Introductionmentioning

confidence: 89%

Convergence of an operator splitting method on a bounded domain for a convection–diffusion–reaction system

Kačur

Malengier

Remešíková

2008

Journal of Mathematical Analysis and Applications

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We solve a convection-diffusion-sorption (reaction) system on a bounded domain with dominant convection using an operator splitting method. The model arises in contaminant transport in groundwater induced by a dual-well, or in controlled laboratory experiments. The operator splitting transforms the original problem to three subproblems: nonlinear convection, nonlinear diffusion, and a reaction problem, each with its own boundary conditions. The transport equation is solved by a Riemann solver, the diffusion one by a finite volume method, and the reaction equation by an approximation of an integral equation. This approach has proved to be very successful in solving the problem, but the convergence properties where not fully known. We show how the boundary conditions must be taken into account, and prove convergence in L 1,loc of the fully discrete splitting procedure to the very weak solution of the original system based on compactness arguments via total variation estimates. Generally, this is the best convergence obtained for this type of approximation. The derivation indicates limitations of the approach, being able to consider only some types of boundary conditions. A sample numerical experiment of a problem with an analytical solution is given, showing the stated efficiency of the method.

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Section: Introductionmentioning

confidence: 89%

Convergence of an operator splitting method on a bounded domain for a convection–diffusion–reaction system

Kačur

Malengier

Remešíková

2008

Journal of Mathematical Analysis and Applications

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“…A finite element scheme is applied to the spatial terms employing the weighted residual approach to minimize the residual error represented by Eq. (16) or (17) and integrating the equation over the spatial domain (Ω e ). Spatial discretization of governing differential equation for water flow can be written as N)] dΩ e ; f w = n e=1 Ω e [∇N T (K w ρ w ∇z)] dΩ e − n e=1 Γ e N r {ρ wvwn + ρ wvvd +ρ wvva } dΓ e in whichv wn is the approximated water velocity normal to the boundary surface,v vd the approximated diffusive vapor velocity normal to the boundary surface,v va the approximated pressure vapor velocity normal to the boundary surface and Γ e is the element boundary surface.…”

Section: Numerical Solution Of Governing Differential Equations For Wmentioning

confidence: 99%

“…Yan and Vairavmoorthy [42] developed a numerical model to simulate water flow and contaminant transport through homogeneous partially saturated media by using the finite difference technique. Kacur et al [16] presented a numerical approximation scheme for the solution of contaminant transport with diffusion and adsorption by finite volume method.…”

Section: Introductionmentioning

confidence: 99%

Finite element modeling of contaminant transport in soils including the effect of chemical reactions

Javadi

Al-Najjar

2007

Journal of Hazardous Materials

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“…One may use types of "up winding" or regularizations (see [5,6,7]), or operator splitting (see [4,8,9,10]) and interface modelling (see [11]). The "up winding" or regularizations introduce additional numerical dispersion which dampens the sensitivity of the solution on model parameters.…”

Section: Introductionmentioning

confidence: 99%

“…The "up winding" or regularizations introduce additional numerical dispersion which dampens the sensitivity of the solution on model parameters. In [4,8,9, 10] a splitting method has been used, applied to diffusion, convection and adsorption, and a semi-analytical solution has been found for nonlinear convection in the case of Langmuir and Freundlich isotherms. Dealing with sharp fronts, one should prefer methods that can accurately track the fronts.…”

Section: Introductionmentioning

confidence: 99%

Numerical modelling of convection–diffusion–adsorption problems in 1D using dynamical discretization

Kačur

Malengier²,

Trojakova

2010

Chemical Engineering Science

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Two candidates for optimal numerical methods for highly nonlinear partial differential equations are compared. The chosen methods are characterized by their speed, accuracy and simplicity of formulation. They can be easily formulated in high level scripting languages like MATLAB or python and are suited for practical implementation. The setting is that of 1D general convection-diffusion-adsorption-reaction systems, a setting of high relevance in chemical and groundwater engineering. First, the mathematical model is numerically solved by the method of lines (MOL) using a space discretization with moving grid points (r-adaptivity). The advantage is that with minimal grid points one captures the sharp fronts of the solution which can arise due to a strong adsorption. A large variety of isotherms can be included in the adsorption model for both equilibrium and non-equilibrium modes. In the second method, the mathematical model is approximated using interface modelling. However, this method is only applicable for adsorption in equilibrium mode. The numerical efficiency of the methods is discussed and the obtained numerical results are compared to determine their optimal use. Both methods are very suitable for solving inverse problems in practical implementations, as they are robust and fast.

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Solution of contaminant transport with equilibrium and non-equilibrium adsorption

Cited by 16 publications

References 9 publications

Convergence of an operator splitting method on a bounded domain for a convection–diffusion–reaction system

Convergence of an operator splitting method on a bounded domain for a convection–diffusion–reaction system

Finite element modeling of contaminant transport in soils including the effect of chemical reactions

Numerical modelling of convection–diffusion–adsorption problems in 1D using dynamical discretization

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