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Solution of contaminant transport with adsorption in porous media by the method of characteristics

Jozef Kacur, Roger Van Keer (2001)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

A new approximation scheme is presented for the mathematical model of convection-diffusion and adsorption. The method is based on the relaxation method and the method of characteristics. We prove the convergence of the method and present some numerical experiments in 1D. The results can be applied to the model of contaminant transport in porous media with multi-site, equilibrium and non-equilibrium type of adsorption.

Solution of contaminant transport with adsorption in porous media by the method of characteristics

Jozef Kacur, Roger Van Keer (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

A new approximation scheme is presented for the mathematical model of convection-diffusion and adsorption. The method is based on the relaxation method and the method of characteristics. We prove the convergence of the method and present some numerical experiments in 1D. The results can be applied to the model of contaminant transport in porous media with multi-site, equilibrium and non-equilibrium type of adsorption.

Solution of degenerate parabolic variational inequalities with convection

Jozef Kacur, Roger Van Keer (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Degenerate parabolic variational inequalities with convection are solved by means of a combined relaxation method and method of characteristics. The mathematical problem is motivated by Richard’s equation, modelling the unsaturated – saturated flow in porous media. By means of the relaxation method we control the degeneracy. The dominance of the convection is controlled by the method of characteristics.

Solution of degenerate parabolic variational inequalities with convection

Jozef Kacur, Roger Van Keer (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Degenerate parabolic variational inequalities with convection are solved by means of a combined relaxation method and method of characteristics. The mathematical problem is motivated by Richard's equation, modelling the unsaturated – saturated flow in porous media. By means of the relaxation method we control the degeneracy. The dominance of the convection is controlled by the method of characteristics.

Study of a low Mach nuclear core model for two-phase flows with phase transition I: stiffened gas law

Manuel Bernard, Stéphane Dellacherie, Gloria Faccanoni, Bérénice Grec, Yohan Penel (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this paper, we are interested in modelling the flow of the coolant (water) in a nuclear reactor core. To this end, we use a monodimensional low Mach number model supplemented with the stiffened gas law. We take into account potential phase transitions by a single equation of state which describes both pure and mixture phases. In some particular cases, we give analytical steady and/or unsteady solutions which provide qualitative information about the flow. In the second part of the paper, we introduce...

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