Groundwater: Numerical Method Modeling

Numerical methods are tools used by people who develop codes for solving equations governing groundwater problems. All problems that we are interested in are governed by partial differential equations. The computer cannot directly solve these and one needs numerical methods to transform them into a solvable form. In essence, all numerical methods are based on, first, discretizing (i.e., substituting the continuum by a discrete medium) and, second, approximating the differential equation by a system of equations. Numerical methods differ in the way discretization and approximations are performed. To illustrate these two steps, we will first develop them in detail for a generic numerical method. We will, then, introduce the classical numerical methods (finite element, finite differences, etc.). This section ends with a discussion on specific methods for solute transport