ABSTRACT
The most used numerical techniques for solving groundwater flow and solute transport are the Finite Differences, Finite Elements, and Finite Volumes methods. They are described on simple conceptual cases in order to keep mathematics relatively simple. Explicit, implicit, Crank-Nicolson, and Galerkin time integrations schemes are described. Useful recommendations are deduced for the practitioner in terms of spatial and time discretizations and possible other conceptual choices. For solute transport modeling, a particular attention is given to advection dominated problems, as it is the case mostly in aquifers. Specific methods are described as Eulerian or grid-based methods with upwind or upstream weighting, TVD methods, Eulerian-Lagrangian methods combining a method of characteristics with traditional FD or FE methods, and random walk methods. Peclet and Courant numerical dimensionless numbers helps the user to detect the actual numerical conditions, to adapt time steps, and to choose which specific method should be adopted. Reactive transport in a multispecies problem is a coupled problem that can be treated sequentially or in parallel.
