A hybrid Laplace transform finite analytic method for solving transport problems with large Peclet and Courant numbers

In this study, the authors develop a hybrid Laplace transform finite analytic method (LTFAM) to solve the advection–dispersion equations with large Peclet and Courant numbers. The finite analytic method with a hybrid Laplace transform can incorporate the temporal variable into the numerical scheme and effectively control the numerical dispersion and oscillation at solute sharp fronts. Since the conventional numerical methods use a large amount of time steps to iterate to the specified time, they may lead to an accumulation of computation errors from each iteration step. Instead of using many fine time steps to satisfy the condition of Courant numbers less than 1 for the conventional numerical methods, the LTFAM algorithm uses a one-step approach to compute the solute concentrations at any specified time with stable numerical solutions. The derived LTFAM algorithm is verified with two numerical simulation examples against the analytical solutions. The numerical results of the LTFAM match the analytical solutions very well, especially for solute transport in the advection-dominated cases. The developed algorithm in this paper can save a large amount of simulating time and improve the computational accuracy. Furthermore, because the solutions of the LTFAM for a set of specified times can be obtained separately in the Laplace space, independence of each time step implies that the LTFAM is well-suited for executing on high performance parallel computers. This algorithm facilitates the long-term predictions of contaminant transport in the kilometer-scale field sites.

► Develop a hybrid Laplace transform finite analytic method.
► Solve the transport problem with large Peclet and Courant numbers.
► Effectively control the numerical dispersion and oscillation at solute sharp fronts.
► Compute the solute concentrations with a one-step approach.
► Facilitate the long-term predictions of contaminant transport in field sites.