Wavelet based multiscale scheme for two-dimensional advection–dispersion equation

In this paper, wavelet based adaptive solver is developed for two dimensional advection dominating solute problem which generates sharp concentration front in the solution. In order to handle simultaneously smooth and shock-like behavior, the framework uses finite element discretization followed by wavelets for multiscale decomposition. Daubechies wavelet filter is incorporated to eliminate spurious oscillations at very high Peclet number. The developed solution is compared with the analytical solution to assess the accuracy and robustness. The advantages of the present method over the commonly used methods such as FDM and FEM for solving the problems which show non-physical oscillation in the numerical solution are demonstrated.