Numerical methods for diffusion-reaction-transport processes in unsaturated porous media

Abstract.

This paper introduces a new grid refinement and coarsening technique for the approximation of partial differential equations including a first order time derivative. This hierarchical movement algorithm is based on the nested iteration method. The combination of this algorithm, a quasi Newton method and the Schur-complement multi-grid method leads to an efficient method for the solution of partial differential equations describing complex real life problems. As a test case, diffusion-reaction-transport processes in heterogeneous unsaturated porous media are considered. Some simulation results are presented.