Lagrange-Galerkin Approximation For Advection-Dominated Contaminant Transport With Nonlinear Equilibrium Or Non-equilibrium Adsorption

An extension of the Lagrange-Galerkin approach is developed for advection-dominated problems with nonlinear adsorption, either being in equilibrium or in non-equilibrium, possibly with isotherms of the Freundlich type. The scheme should be feasable also for the hyperbolic limit case. The basic problems to deal with are the possibility of non-unique characteristics due to the nonlinear isotherms and the incorporation of the time-dependent non-equilibrium adsorption kinetics, avoiding a strong restriction on the CFL-number.