Accurate Simulation of Contaminant Transport Using High-Order Compact Finite Difference Schemes

Numerical simulation of advective-dispersive contaminant transport is carried out by using high-order compact finite difference schemes combined with second-order MacCormack and fourth-order Runge-Kutta schemes. Both of the two schemes have accuracy of sixth-order in space. A sixth-order MacCormack scheme is proposed for the first time within this study. For the aim of demonstrating efficiency and high-order accuracy of the current methods, some numerical experiments have been done. The schemes are implemented to solve two test problems with known exact solutions. It has been exhibited that the methods are capable of succeeding high accuracy and efficiency with minimal computational effort, by comparisons of the computed results with exact solutions

Implicit finite difference techniques for the advection-diffusion equation using spreadsheets

This study proposes one-dimensional advection-diffusion equation (ADE) with finite differences method (FDM) using implicit spreadsheet simulation (ADEISS). By changing only the values of temporal and spatial weighted parameters with ADEISS implementation, solutions are implicitly obtained for the BTCS, Upwind and Crank-Nicolson schemes. The ADEISS uses iterative spreadsheet solution technique. Thus, it is not required a solution of simultaneous equations for each time step using matrix algebra. Two examples which, have the numerical and analytical solutions in literature, are solved in order to test the ADEISS performance. Both examples are solved for three schemes. It has been determined that the Crank-Nicolson scheme is in good agreement with the analytical solution; however the results of the BTCS and the Upwind schemes are lower than the analytical solution. The Upwind scheme suffers from considerably numerical diffusion whereas the BTCS scheme does not produce numerical diffusion. Thus, it provided better results than Upwind scheme which are closer to analytical results depending on the selected parameters. The ADEISS implementation is a computationally convenient procedure for the three well-known methods in the literature: The BTCS, Upwind and Crank-Nicolson. © 2006 Elsevier Ltd. All rights reserved