Finite Difference Methods and the Method of Characteristics for Solving Hydrodynamic Dispersion Equations
We have known the basic idea of finite difference methods (FDM) in the study of groundwater flow problems. FDM includes three major steps. First, the flow region is divided by a grid and the time interval into time steps. Second, the partial derivatives involved in the PDE are replaced by their finite difference approximations. As a result, the PDE is transformed into a system of algebraic equations. Third, the algebraic system is solved and the nodal values of the unknown function are obtained. These discrete values approximately describe the time-space distribution of the unknown variable. We will see that exactly the same steps can be used to solve advection-dispersion problems.