THE FRONT LIMITATION ALGORITHM - A NEW AND FAST FINITE-DIFFERENCE METHOD FOR GROUNDWATER POLLUTION PROBLEMS

The simulation of pollutant transport in groundwater requires the nume rical solution of the advection-dispersion equation. Until now the mai n difficulty in solving this equation was to satisfy the discretizatio n requirements which guaranteed a reasonably accurate solution. In the paper a new algorithm (named the front limitation algorithm) is demon strated which avoids most of the difficulties, The technique makes use of the control volume method with fully implicit diffusion-dispersion and source-sink terms and with explicit handling of the advection ter m. The new algorithm avoids numerical dispersion. The method fulfils t he mass balance in each grid element. Neither a grid Peclet number cri terion nor the Neumann criterion are required. The method has little g rid 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 o ptimal control problems, where a model has to be solved many times in a row. (C) 1997 Elsevier Science B.V.