ABSTRACT
This chapter describes finite element and time-stepping methods for a model system for the simulation of incompressible flow and transport processes of nuclear contaminants in porous media. The model was developed for use by the Nuclear Regulatory Commission for the analysis of deep geologic nuclear waste disposal facilities. The chapter discusses a time-stepping procedure for the finite element procedure that efficiently reflects the fact that the velocity field and the pressure vary more slowly in time than the concentration and the temperature for reasonable physical data. Two efficient time-stepping procedures are introduced to treat the continuous-time method proposed by the authors which employs a mixed finite element method to approximate the pressure and the fluid velocity and a standard Galerkin method to approximate the transport of heat, brine and radionuclides for the system describing the contamination by nuclear waste in porous media.
