The ‘front limitation’ algorithm A new and fast finite-difference method for groundwater pollution problems

The simulation of pollutant transport in groundwater requires the numerical solution of the advection-dispersion equation. Until now the main difficulty in solving this equation was to satisfy the discretization requirements which guaranteed a reasonably accurate solution. In the paper a new algorithm (named the front limitation algorithm) is demonstrated which avoids most diffusion-dispersion and source-sink terms and with explicit handling of the advection term. The new algorithm avoids numerical dispersion. The method fulfils the mass balance in each grid element. Neither a grid Péclet number criterion nor the Neumann criterion are required. The method has little grid orientation effect. It, however, requires a low Courant number and time step criteria with respect to source-sink terms. The new method was verified in 1D, 2D and 3D cases with analytical solutions and with random walk simulation runs. It allows to work with relatively coarse grids and is therefore well-suited for parameter identification and optimal control problems, where a model has to be solved many times in a row.