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

Taylor-Galerkin method for advection-diffusion equation

WOS: 000294884200010Purpose - The purpose of this paper is to provide numerical solutions of the time-dependent advection-diffusion problem by using B-spline finite element methods in which Taylor series expansion is used for the related time discretization. Design/methodology/approach - The solution domain is partitioned into uniform mesh. The collocation and the Galerkin methods where B-spline functions are used as base functions are applied to advection-diffusion equation. Findings - Given methods are unconditionally stable and the obtained results are comparable with some earlier studies in terms of accuracy. Originality/value - Quadratic and cubic B-spline base functions are used with Taylor series expansion for the discretization of the equation