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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.
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.
Numerical approximation schemes are discussed for the solution of contaminant transport with adsorption in dual-well flow. The method is based on time stepping and operator splitting for the transport with adsorption and diffusion. The nonlinear transport is solved by Godunov’s method. The nonlinear diffusion is solved by a finite volume method and by Newton’s type of linearization. The efficiency of the method is discussed.
We consider a nonstandard elliptic eigenvalue problem of second order on a two-component domain consisting of two intervals with a contact point. The interaction between the two domains is expressed through a coupling condition of nonlocal type, more specifically, in integral form. The problem under consideration is first stated in its variational form and next interpreted as a second-order differential eigenvalue problem. The aim is to set up a finite element method for this problem. The error...
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.
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.
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