A degenerate convection-diffusion problem is approximated using the scheme that is based on the relaxation method and also the method of characteristics. A mathematical model for solute transport in unsaturated porous media is included. Moreover, multiple site adsorption is considered. Convergence of the scheme is proved and numerical experiments in 1D and 2D are presented.
We consider a scheme for nonlinear (degenerate) convection dominant diffusion problems that arise in contaminant transport in porous media with equilibrium adsorption isotherm. This scheme is based on a regularization relaxation scheme that has been introduced by Jäger and Kačur (Numer Math 60:407-427, 1991; M 2 AN Math Model Numer Anal 29(N5):605-627, 1995) with a type of numerical integration by Bermejo (SIAM J Numer Anal 32: 1995) to the modified method of characteristics with adjusted advection MMOCAA that was recently developed by Douglas et al. (Numer Math 83(3):353-369, 1999; Comput Geosci 1:155-190, 1997). We present another variant of adjusting advection method. The convergence of the scheme is proved. An error estimate of the approximated scheme is derived. Computational experiments are carried out to illustrate the capability of the scheme to conserve the mass.
Mathematics Subject Classification (2000)65M25 · 65M12 · 76M10 · 35K55 · 76S05
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