Abstract:

Research shows that if the advection term is dominant in the solution of unsteady underground water solute transport model, the model shows characteristics of a hyperbolic equation. The efficient method of solving such problems is to adopt the non-standard Galerkin finite element method for such characteristics. This article adopts four methods, Wavelet-Galerkin finite element, upwind finite element, characteristic finite element and standard Galerkin finite element, to slove the advection dominant solute transport model and compare the results with analytic solutions. The results indicate that the standard Galerkin finite element method may result in strong numerical oscillation and the Wavelet-Galerkin finite element method boasts a good space-time orientation effect. The upwind finite element method could effectively decrease the numerical oscillation, but the upwind factor has a big impact on the solution and leads to delay in time. The characteristic finite element method could improve the precision of solution and thus it is the first choice to solve advection dominant groundwater solute transport models.

Key words: finite element method, wavelet, upwind scheme, characteristic scheme, solute transport model